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#1 2014-02-12 07:00:24
- JT_OO400
- Member
- Registered: 2014-02-12
- Posts: 3
Calculate the total number of `internal fields` in a regular polygon
Question: How do I calculate the total number of `internal fields` in a regular polygon?
(Visually, triangle = 1, rectangle = 4, pentagon = 11, heptagon - 45.)
1) What is the `progression` of the numbers of internal fields (Is that the correct term/), and 2) what is the formula for calculation the number, based on the number of sides?
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#2 2014-02-12 07:20:43
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Calculate the total number of `internal fields` in a regular polygon
Hi;
I am getting 50 for a heptagon.
I am getting 0,0,1,4,11,24,50,80... for n=1,2,3,4..., do you agree?
If you do then there is no known simple formula for n being even but there are complex ones.
For n being odd there is a simple formula.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2014-02-12 09:05:40
- JT_OO400
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- Registered: 2014-02-12
- Posts: 3
Re: Calculate the total number of `internal fields` in a regular polygon
Hi, bobbym,
I started out calculating the number of lines possible between 1-2-3-4-5 . . . points. I arrived at 0-1-3-6-10-15 when including the sides and diagonals of what turn out to be drawn regular polygons. The progression became apparent. So far, I cannot see the progression represented by the progression of "internal fields." (Is that what to call them?) Nor have I yet been able to devise a formula for solving it. (Still stuck with counting - or as you observed, miscounting them.)
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#4 2014-02-12 10:43:10
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Calculate the total number of `internal fields` in a regular polygon
Hi;
Call n the number of sides. When n is odd then
For instance when the number of sides of the regular polygon is 17 the number of internal fields as you call them is 2500.
When n is even it is a little more involved but doable. Do you want to see it?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2014-02-13 06:27:44
- JT_OO400
- Member
- Registered: 2014-02-12
- Posts: 3
Re: Calculate the total number of `internal fields` in a regular polygon
This is what happens when a smart aleck ex-musician tries to do algebra. If n-17, then if I interpret the formula correctly,
24-714+152881-1061208+83521 = 825496 /24 = -34,394.667,
Similarly, if n=7, {24-294+25921-74088+2401 = -46036}/24 = -1.918.1667.
What happened to 50?
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#6 2014-02-13 06:33:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Calculate the total number of `internal fields` in a regular polygon
The n = 17 is incorrect for starters.
Use this form, it will not have negative numbers.
Or I can Hornerize it for you, but try that first.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2014-02-13 14:34:48
Re: Calculate the total number of `internal fields` in a regular polygon
What are internal fields?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#8 2014-02-13 14:36:34
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Calculate the total number of `internal fields` in a regular polygon
He means internal polygons.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2014-02-13 14:42:16
Re: Calculate the total number of `internal fields` in a regular polygon
What is an internal polygon?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#10 2014-02-13 14:46:21
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Calculate the total number of `internal fields` in a regular polygon
Do this and count:
CompleteGraph[7]In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#11 2014-02-13 14:58:32
Re: Calculate the total number of `internal fields` in a regular polygon
It outputs K[sub]7[/sub]
I'll count what? The edges? There is a formula for that
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#12 2014-02-13 15:02:11
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Calculate the total number of `internal fields` in a regular polygon
The interior polygons.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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