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#1
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How to determine the angle within hexagonal spiral?
Creating a hexagonal spiral around 0,
1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below .......16..15..14 .....17..5...4...13 ...18..6...0...3...12 19..7...1...2...11..26 ...20..8...9...10..25 .....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric |
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#3
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
I'm in agreement with you Sandy. In particular, I can't see how number like
15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric |
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#4
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How to determine the angle within hexagonal spiral?
On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)"
wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#5
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How to determine the angle within hexagonal spiral?
On Dec 30, 9:29 am, Ken Johnson wrote:
On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson Also, maybe that 80 degrees is a typo, ie 9 is the given number in cell A1 then 180 degrees will be returned in cell B1. Ken Johnson |
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#6
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
Good observation Ken. I think that you have cracked it, at least partially,
but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#7
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
I understood the spiral path being traced out, and I guess I can see that 15
is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#8
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
Thank everyone very much for any suggestions
Yes, 9 would be halfway between 60 & 120 ie 90 Deg, not 80 Deg. Along the 60 Deg, there are 1,8,21 Along the 120 Deg, there are 2,10,24 Since there is only 22 and 23 between 21 at 60 Deg and 24 at 120 Deg, then The angle for 22 and 23 can be determined by dividing the angle between 60 and 120 Deg, therefore the angle for 22 will be 80 Deg and the angle for 23 will be 100 Deg. Does anyone have any suggestions? Thank everyone for any suggestions Eric "Rick Rothstein (MVP - VB)" wrote: I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#9
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
I would think that 22 and 23 are at 80 & 100 degrees respectively. If that
is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#10
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
It seems like the OP did tell us but as it is gone midnight here, this old
man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#11
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
OK so I had to take the dog for a walk first and got to thinking about this:
In K2 enter 1 and K3 enter 3. In K4 enter the formula: =(K3-K2+1)+K3 and copy down as far as needed, In L2 enter 0 and in L3 the formula: =K2*6 and copy down as far as in Column K. These are the numbers along the 0/6 line In M2 enter the formula: =360/(L3-L2) and copy down to one row short of the the othe rtwo columns. With the required number in A1 enter in B1: =(A1-INDEX(L2:L10,MATCH(LOOKUP(A1,L2:L10),L2:L10)))*LOO KUP(A1,L2:L9,M2:M9) This should be the degrees that you are looking for. There may of course be more elegant ways of doing it. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#12
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
The formula for some angle
For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg .......16..15..14 .....17..5...4...13 ...18..6...0...3...12 19..7...1...2...11..26 ...20..8...9...10..25 .....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#13
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
Hi. Just something quick-n-dirty if I understand the question:
This may be wrong. http://www.research.att.com/~njas/sequences/A003215 Table[3*(n + 1)*n + 1, {n, 0, 9}] {1, 7, 19, 37, 61, 91, 127, 169, 217, 271} We note that the number of points added at each 360 rotation just increases by 6. Differences[%] {6, 12, 18, 24, 30, 36, 42, 48, 54} If given a total t (Your A1 value), then solve for n: n - (Sqrt(12*t - 3) - 3) / 6 So, when n=19, we've gone around 2 times: n=19 ?(Sqr(12*n - 3) - 3) / 6 2 For your example: n=10 ?(Sqr(12*n - 3) - 3) / 6 1.30277563773199 We've gone around once(6) and go four more steps during our second rotation (Use MOD) : Each step in degrees is: r=2 ?360/(6*r) 30 Hence 4*30 = 120 (9 is 3*30 = 90) So, if you are looking at point 100: n=100 ?(Sqr(12*n - 3) - 3) / 6 5.2662812973354 We've gone around 5.2 times: The firth rotation was point 91: n=5 ?3*(n + 1)*n + 1 91 Each degree difference during our 6th rotation is 10: ?360 / (6*6) 10 Angel is: ?10*(100-91+1) 100 Degrees Again, I hope I did this correctly..:~ -- HTH :) Dana DeLouis Windows XP & Excel 2007 "Eric" wrote in message ... The formula for some angle For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#14
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
So if I follow you correctly, changing it into one formula gives us:
=360/(6*(INT((SQRT(12*A1 - 3)-3) / 6)+1))*((A1-(3*(INT((SQRT(12*A1 - 3) - 3) / 6) + 1)*INT((SQRT(12*A1 - 3) - 3) / 6) + 1))+1) I'll leave it to Rick to cut out any extra key strokes <g -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Dana DeLouis" wrote in message ... Hi. Just something quick-n-dirty if I understand the question: This may be wrong. http://www.research.att.com/~njas/sequences/A003215 Table[3*(n + 1)*n + 1, {n, 0, 9}] {1, 7, 19, 37, 61, 91, 127, 169, 217, 271} We note that the number of points added at each 360 rotation just increases by 6. Differences[%] {6, 12, 18, 24, 30, 36, 42, 48, 54} If given a total t (Your A1 value), then solve for n: n - (Sqrt(12*t - 3) - 3) / 6 So, when n=19, we've gone around 2 times: n=19 ?(Sqr(12*n - 3) - 3) / 6 2 For your example: n=10 ?(Sqr(12*n - 3) - 3) / 6 1.30277563773199 We've gone around once(6) and go four more steps during our second rotation (Use MOD) : Each step in degrees is: r=2 ?360/(6*r) 30 Hence 4*30 = 120 (9 is 3*30 = 90) So, if you are looking at point 100: n=100 ?(Sqr(12*n - 3) - 3) / 6 5.2662812973354 We've gone around 5.2 times: The firth rotation was point 91: n=5 ?3*(n + 1)*n + 1 91 Each degree difference during our 6th rotation is 10: ?360 / (6*6) 10 Angel is: ?10*(100-91+1) 100 Degrees Again, I hope I did this correctly..:~ -- HTH :) Dana DeLouis Windows XP & Excel 2007 "Eric" wrote in message ... The formula for some angle For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#15
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
Hi Sandy. I think that looks good. Very nice.
That link had another link to the following: http://www.research.att.com/~njas/sequences/a3215.gif The op's diagram started with 0, and the zero angle begins in the -x direction. The picture above begins with 1, and the {1, 7, 19, 37, 61,...} sequence is at a different angle. The op's just wants to rotate that diagram to have the zero angle on the -x direction. If we add 1 to each point in the op's diagram, and rotate, then the two diagrams will match. -- Dana DeLouis "Sandy Mann" wrote in message ... So if I follow you correctly, changing it into one formula gives us: =360/(6*(INT((SQRT(12*A1 - 3)-3) / 6)+1))*((A1-(3*(INT((SQRT(12*A1 - 3) - 3) / 6) + 1)*INT((SQRT(12*A1 - 3) - 3) / 6) + 1))+1) I'll leave it to Rick to cut out any extra key strokes <g -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Dana DeLouis" wrote in message ... Hi. Just something quick-n-dirty if I understand the question: This may be wrong. http://www.research.att.com/~njas/sequences/A003215 Table[3*(n + 1)*n + 1, {n, 0, 9}] {1, 7, 19, 37, 61, 91, 127, 169, 217, 271} We note that the number of points added at each 360 rotation just increases by 6. Differences[%] {6, 12, 18, 24, 30, 36, 42, 48, 54} If given a total t (Your A1 value), then solve for n: n - (Sqrt(12*t - 3) - 3) / 6 So, when n=19, we've gone around 2 times: n=19 ?(Sqr(12*n - 3) - 3) / 6 2 For your example: n=10 ?(Sqr(12*n - 3) - 3) / 6 1.30277563773199 We've gone around once(6) and go four more steps during our second rotation (Use MOD) : Each step in degrees is: r=2 ?360/(6*r) 30 Hence 4*30 = 120 (9 is 3*30 = 90) So, if you are looking at point 100: n=100 ?(Sqr(12*n - 3) - 3) / 6 5.2662812973354 We've gone around 5.2 times: The firth rotation was point 91: n=5 ?3*(n + 1)*n + 1 91 Each degree difference during our 6th rotation is 10: ?360 / (6*6) 10 Angel is: ?10*(100-91+1) 100 Degrees Again, I hope I did this correctly..:~ -- HTH :) Dana DeLouis Windows XP & Excel 2007 "Eric" wrote in message ... The formula for some angle For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#16
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
Yet another solution with defined names:
Array ={1;2;3;4;5;6;7;8;9;10} Square =3*Array*(Array-1) Luka =MAX(Square*(Square<=$A$1)) Lukb =60/MAX(Array*(Square<=$A$1)) B1 =($A$1-Luka)*Lukb |
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#17
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
Good job Sandy! The only simplification I can make (besides removing all
those spaces) is to divide out the 6 from the denominator. In addition, I have a personal preference for ordering chained multiplications and divisions to put the multiplication first; so, for the layout of A/B*C that you have, I prefer to rearrange that to A*C/B for clarity. Hence, I would present your formula (with the aforementioned division carried out) like this... =60*((A1-(3*(INT((SQRT(12*A1-3)-3)/6)+1)*INT((SQRT(12*A1-3)-3)/6)+1))+1)/(INT((SQRT(12*A1-3)-3)/6)+1) Rick "Sandy Mann" wrote in message ... So if I follow you correctly, changing it into one formula gives us: =360/(6*(INT((SQRT(12*A1 - 3)-3) / 6)+1))*((A1-(3*(INT((SQRT(12*A1 - 3) - 3) / 6) + 1)*INT((SQRT(12*A1 - 3) - 3) / 6) + 1))+1) I'll leave it to Rick to cut out any extra key strokes <g -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Dana DeLouis" wrote in message ... Hi. Just something quick-n-dirty if I understand the question: This may be wrong. http://www.research.att.com/~njas/sequences/A003215 Table[3*(n + 1)*n + 1, {n, 0, 9}] {1, 7, 19, 37, 61, 91, 127, 169, 217, 271} We note that the number of points added at each 360 rotation just increases by 6. Differences[%] {6, 12, 18, 24, 30, 36, 42, 48, 54} If given a total t (Your A1 value), then solve for n: n - (Sqrt(12*t - 3) - 3) / 6 So, when n=19, we've gone around 2 times: n=19 ?(Sqr(12*n - 3) - 3) / 6 2 For your example: n=10 ?(Sqr(12*n - 3) - 3) / 6 1.30277563773199 We've gone around once(6) and go four more steps during our second rotation (Use MOD) : Each step in degrees is: r=2 ?360/(6*r) 30 Hence 4*30 = 120 (9 is 3*30 = 90) So, if you are looking at point 100: n=100 ?(Sqr(12*n - 3) - 3) / 6 5.2662812973354 We've gone around 5.2 times: The firth rotation was point 91: n=5 ?3*(n + 1)*n + 1 91 Each degree difference during our 6th rotation is 10: ?360 / (6*6) 10 Angel is: ?10*(100-91+1) 100 Degrees Again, I hope I did this correctly..:~ -- HTH :) Dana DeLouis Windows XP & Excel 2007 "Eric" wrote in message ... The formula for some angle For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#18
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
Here's a vba function if you want to go that route:
Function Angle(x) As Double Dim n As Double n = Int((Sqr(12 * x - 3) - 3) / 6) Angle = 60 * (x / (n + 1) - 3 * n) End Function -- Dana DeLouis "Rick Rothstein (MVP - VB)" wrote in message ... Good job Sandy! The only simplification I can make (besides removing all those spaces) is to divide out the 6 from the denominator. In addition, I have a personal preference for ordering chained multiplications and divisions to put the multiplication first; so, for the layout of A/B*C that you have, I prefer to rearrange that to A*C/B for clarity. Hence, I would present your formula (with the aforementioned division carried out) like this... =60*((A1-(3*(INT((SQRT(12*A1-3)-3)/6)+1)*INT((SQRT(12*A1-3)-3)/6)+1))+1)/(INT((SQRT(12*A1-3)-3)/6)+1) Rick "Sandy Mann" wrote in message ... So if I follow you correctly, changing it into one formula gives us: =360/(6*(INT((SQRT(12*A1 - 3)-3) / 6)+1))*((A1-(3*(INT((SQRT(12*A1 - 3) - 3) / 6) + 1)*INT((SQRT(12*A1 - 3) - 3) / 6) + 1))+1) I'll leave it to Rick to cut out any extra key strokes <g -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Dana DeLouis" wrote in message ... Hi. Just something quick-n-dirty if I understand the question: This may be wrong. http://www.research.att.com/~njas/sequences/A003215 Table[3*(n + 1)*n + 1, {n, 0, 9}] {1, 7, 19, 37, 61, 91, 127, 169, 217, 271} We note that the number of points added at each 360 rotation just increases by 6. Differences[%] {6, 12, 18, 24, 30, 36, 42, 48, 54} If given a total t (Your A1 value), then solve for n: n - (Sqrt(12*t - 3) - 3) / 6 So, when n=19, we've gone around 2 times: n=19 ?(Sqr(12*n - 3) - 3) / 6 2 For your example: n=10 ?(Sqr(12*n - 3) - 3) / 6 1.30277563773199 We've gone around once(6) and go four more steps during our second rotation (Use MOD) : Each step in degrees is: r=2 ?360/(6*r) 30 Hence 4*30 = 120 (9 is 3*30 = 90) So, if you are looking at point 100: n=100 ?(Sqr(12*n - 3) - 3) / 6 5.2662812973354 We've gone around 5.2 times: The firth rotation was point 91: n=5 ?3*(n + 1)*n + 1 91 Each degree difference during our 6th rotation is 10: ?360 / (6*6) 10 Angel is: ?10*(100-91+1) 100 Degrees Again, I hope I did this correctly..:~ -- HTH :) Dana DeLouis Windows XP & Excel 2007 "Eric" wrote in message ... The formula for some angle For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#19
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
"Rick Rothstein (MVP - VB)" wrote in
message ... Good job Sandy! All I did was to blindly transpose Dana's method into a formula. I did not understand it all sufficiently well to start messing about with it - so I passed it on to you <g Actually Herbert's Defined Name formula, which is better and which I equally well do not understand, (I would be grateful for an explanation from Herbert or anyone else), but seems to return wrong results for points above point 330. I say this because all results after point 330 are 6 Deg increases. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... Good job Sandy! The only simplification I can make (besides removing all those spaces) is to divide out the 6 from the denominator. In addition, I have a personal preference for ordering chained multiplications and divisions to put the multiplication first; so, for the layout of A/B*C that you have, I prefer to rearrange that to A*C/B for clarity. Hence, I would present your formula (with the aforementioned division carried out) like this... =60*((A1-(3*(INT((SQRT(12*A1-3)-3)/6)+1)*INT((SQRT(12*A1-3)-3)/6)+1))+1)/(INT((SQRT(12*A1-3)-3)/6)+1) Rick "Sandy Mann" wrote in message ... So if I follow you correctly, changing it into one formula gives us: =360/(6*(INT((SQRT(12*A1 - 3)-3) / 6)+1))*((A1-(3*(INT((SQRT(12*A1 - 3) - 3) / 6) + 1)*INT((SQRT(12*A1 - 3) - 3) / 6) + 1))+1) I'll leave it to Rick to cut out any extra key strokes <g -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Dana DeLouis" wrote in message ... Hi. Just something quick-n-dirty if I understand the question: This may be wrong. http://www.research.att.com/~njas/sequences/A003215 Table[3*(n + 1)*n + 1, {n, 0, 9}] {1, 7, 19, 37, 61, 91, 127, 169, 217, 271} We note that the number of points added at each 360 rotation just increases by 6. Differences[%] {6, 12, 18, 24, 30, 36, 42, 48, 54} If given a total t (Your A1 value), then solve for n: n - (Sqrt(12*t - 3) - 3) / 6 So, when n=19, we've gone around 2 times: n=19 ?(Sqr(12*n - 3) - 3) / 6 2 For your example: n=10 ?(Sqr(12*n - 3) - 3) / 6 1.30277563773199 We've gone around once(6) and go four more steps during our second rotation (Use MOD) : Each step in degrees is: r=2 ?360/(6*r) 30 Hence 4*30 = 120 (9 is 3*30 = 90) So, if you are looking at point 100: n=100 ?(Sqr(12*n - 3) - 3) / 6 5.2662812973354 We've gone around 5.2 times: The firth rotation was point 91: n=5 ?3*(n + 1)*n + 1 91 Each degree difference during our 6th rotation is 10: ?360 / (6*6) 10 Angel is: ?10*(100-91+1) 100 Degrees Again, I hope I did this correctly..:~ -- HTH :) Dana DeLouis Windows XP & Excel 2007 "Eric" wrote in message ... The formula for some angle For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#20
Posted to microsoft.public.excel.misc
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How to determine the angle within hexagonal spiral?
I like it! I don't understand it but I like it!
-- Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Dana DeLouis" wrote in message ... Here's a vba function if you want to go that route: Function Angle(x) As Double Dim n As Double n = Int((Sqr(12 * x - 3) - 3) / 6) Angle = 60 * (x / (n + 1) - 3 * n) End Function -- Dana DeLouis "Rick Rothstein (MVP - VB)" wrote in message ... Good job Sandy! The only simplification I can make (besides removing all those spaces) is to divide out the 6 from the denominator. In addition, I have a personal preference for ordering chained multiplications and divisions to put the multiplication first; so, for the layout of A/B*C that you have, I prefer to rearrange that to A*C/B for clarity. Hence, I would present your formula (with the aforementioned division carried out) like this... =60*((A1-(3*(INT((SQRT(12*A1-3)-3)/6)+1)*INT((SQRT(12*A1-3)-3)/6)+1))+1)/(INT((SQRT(12*A1-3)-3)/6)+1) Rick "Sandy Mann" wrote in message ... So if I follow you correctly, changing it into one formula gives us: =360/(6*(INT((SQRT(12*A1 - 3)-3) / 6)+1))*((A1-(3*(INT((SQRT(12*A1 - 3) - 3) / 6) + 1)*INT((SQRT(12*A1 - 3) - 3) / 6) + 1))+1) I'll leave it to Rick to cut out any extra key strokes <g -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Dana DeLouis" wrote in message ... Hi. Just something quick-n-dirty if I understand the question: This may be wrong. http://www.research.att.com/~njas/sequences/A003215 Table[3*(n + 1)*n + 1, {n, 0, 9}] {1, 7, 19, 37, 61, 91, 127, 169, 217, 271} We note that the number of points added at each 360 rotation just increases by 6. Differences[%] {6, 12, 18, 24, 30, 36, 42, 48, 54} If given a total t (Your A1 value), then solve for n: n - (Sqrt(12*t - 3) - 3) / 6 So, when n=19, we've gone around 2 times: n=19 ?(Sqr(12*n - 3) - 3) / 6 2 For your example: n=10 ?(Sqr(12*n - 3) - 3) / 6 1.30277563773199 We've gone around once(6) and go four more steps during our second rotation (Use MOD) : Each step in degrees is: r=2 ?360/(6*r) 30 Hence 4*30 = 120 (9 is 3*30 = 90) So, if you are looking at point 100: n=100 ?(Sqr(12*n - 3) - 3) / 6 5.2662812973354 We've gone around 5.2 times: The firth rotation was point 91: n=5 ?3*(n + 1)*n + 1 91 Each degree difference during our 6th rotation is 10: ?360 / (6*6) 10 Angel is: ?10*(100-91+1) 100 Degrees Again, I hope I did this correctly..:~ -- HTH :) Dana DeLouis Windows XP & Excel 2007 "Eric" wrote in message ... The formula for some angle For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#21
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How to determine the angle within hexagonal spiral?
Sandy:
Actually I just cleaned up the idea you had after you came back from walking your dog. I plotted the numbers you generated in column N and found the trendline: 3x^2 - 3x Your numbers in column M can be reduced to 60/{1,2,3....10} Like you, I limited the array to 10, so that is why my formulas work only up to 330. Instead of LOOKUP, I used the maximum of the numbers in column L that are less or equal to A1. So Lukb , Luka gives the same result as your 2 LOOKUPs. Standing on the shoulders of Giants... |
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#22
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Thank everyone very much for any suggestions
Thank everyone very much for any suggestions
Eric "Dana DeLouis" wrote: Hi. Just something quick-n-dirty if I understand the question: This may be wrong. http://www.research.att.com/~njas/sequences/A003215 Table[3*(n + 1)*n + 1, {n, 0, 9}] {1, 7, 19, 37, 61, 91, 127, 169, 217, 271} We note that the number of points added at each 360 rotation just increases by 6. Differences[%] {6, 12, 18, 24, 30, 36, 42, 48, 54} If given a total t (Your A1 value), then solve for n: n - (Sqrt(12*t - 3) - 3) / 6 So, when n=19, we've gone around 2 times: n=19 ?(Sqr(12*n - 3) - 3) / 6 2 For your example: n=10 ?(Sqr(12*n - 3) - 3) / 6 1.30277563773199 We've gone around once(6) and go four more steps during our second rotation (Use MOD) : Each step in degrees is: r=2 ?360/(6*r) 30 Hence 4*30 = 120 (9 is 3*30 = 90) So, if you are looking at point 100: n=100 ?(Sqr(12*n - 3) - 3) / 6 5.2662812973354 We've gone around 5.2 times: The firth rotation was point 91: n=5 ?3*(n + 1)*n + 1 91 Each degree difference during our 6th rotation is 10: ?360 / (6*6) 10 Angel is: ?10*(100-91+1) 100 Degrees Again, I hope I did this correctly..:~ -- HTH :) Dana DeLouis Windows XP & Excel 2007 "Eric" wrote in message ... The formula for some angle For the number 1 series [1,8,21,40,65 ...], the formula is N*(3N-2) on 60 Deg For the number 2 series [2,10,24,44,70 ...], the formula is N*(3N-1) on 120 Deg For the number 3 series [3,12,27,48,75 ...], the formula is N*(3N) on 180 Deg For the number 4 series [4,14,30,52,80 ...], the formula is N*(3N+1) on 240 Deg For the number 5 series [5,16,33,56,85 ...], the formula is N*(3N+2) on 300 Deg For the number 6 series [6,18,36,60,90 ...], the formula is N*(3N+3) on 360 Deg ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 90 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I need to "Sandy Mann" wrote: It seems like the OP did tell us but as it is gone midnight here, this old man is off to bed. I'll leave it to you clever folk to work it out. -- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Sandy Mann" wrote in message ... I would think that 22 and 23 are at 80 & 100 degrees respectively. If that is right then the numbers on the 0, 6 18 line (reading from right to left), would be: 0, 6, 18, 36, 90 126, 168, 216 ie 6 * { 0, 1, 3, 6, 10, 15, 21, 28, 36} with the interval between the numbers in braces increasing by 1 each time. The angle for numbers between 18 and 36 then would be 360/(36-18) = 20 Degrees. Of course only the OP will be able to tell us. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Rick Rothstein (MVP - VB)" wrote in message ... I understood the spiral path being traced out, and I guess I can see that 15 is at 90 degrees like 9 is... but there is (at least to my mind) still a problem with 22 and 23... they do not lie on a diagonal from 0 unless, in the first 4 tiers of the spiral, they are the only number on that diagonal. Anyway, I would like to see the OP give us a little bit more information on how the numbers are laid down on the spiral path. Rick "Sandy Mann" wrote in message ... Good observation Ken. I think that you have cracked it, at least partially, but it does not quite equate to what the OP said: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1 So presumably 0, 2, 10, 24 are all on the 120 deg line If so then surely 0,1, 8, 21 are on the 60 deg line But if the above is true then 9 would be halfway between 60& 120 ie 90 Deg but the OP says it is equal to 80 Deg. A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Ken Johnson" wrote in message ... On Dec 30, 5:45 am, "Rick Rothstein \(MVP - VB\)" wrote: I'm in agreement with you Sandy. In particular, I can't see how number like 15, 22 and 23 fit into the hexagonal scheme of things (they seem to be on some angle other than one of the 60 degree lines); hence, I can't figure out how to extend the sequence of numbers in order to develop a formula for it. Rick "Sandy Mann" wrote in message ... You may get an answer if you restate you request. Speaking personally I do not understand exactly what it is that you are asking. -- HTH Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Eric" wrote in message ... Creating a hexagonal spiral around 0, 1 will be inserted in 60 deg, 2 will be inserted in 120 deg, 3 will be inserted in 180 deg, 4 will be inserted in 240 deg, 5 will be inserted in 300 deg, 6 will be inserted in 360 deg, and continue on the second levels as show below ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 If a number is given in cell A1, I would like to determine the angle based on this structure of hexagonal spiral, such as 10 is the given number in cell A1, then 120 degree will be returned in cell B1, 9 is the given number in cell A1, then 80 degree will be returned in cell B1. Does anyone have any suggestions on how to determine the angle? Thanks in advance for any suggestions Eric I notice that tracing through that array of numbers from 0 to 26 results in a spiral path. But that's all I can see. Ken Johnson |
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#23
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How to determine the angle within hexagonal spiral?
Thank you Herbert, I think that what you did was very clever.
-- Regards, Sandy In Perth, the ancient capital of Scotland and the crowning place of kings Replace @mailinator.com with @tiscali.co.uk "Herbert Seidenberg" wrote in message ... Sandy: Actually I just cleaned up the idea you had after you came back from walking your dog. I plotted the numbers you generated in column N and found the trendline: 3x^2 - 3x Your numbers in column M can be reduced to 60/{1,2,3....10} Like you, I limited the array to 10, so that is why my formulas work only up to 330. Instead of LOOKUP, I used the maximum of the numbers in column L that are less or equal to A1. So Lukb , Luka gives the same result as your 2 LOOKUPs. Standing on the shoulders of Giants... |
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