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

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'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

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

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

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

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

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

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

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