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


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"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


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"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


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"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


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"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


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"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