# Geometry formula question **URL:** \ **Category:** Factual Questions\ **Created:** [February 3, 2000, 12:51am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752 "2000-02-03T00:51:00Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [February 3, 2000, 12:51am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/1 "2000-02-03T00:51:00Z")
During my idle doodling, I draw polygons and I start with a triangle and I keep adding a side until I can’t draw them anymore. Then I draw all the diagonals inside the polygon. (Hey, it’s doodling, it’s not supposed to be productive.) Is there a formula that tells you how many diagonals inside a polygon (assuming that there are no obtuse angles)? ---
**Author:** ![Patty\_O\_Furniture](https://avatars.discourse-cdn.com/v4/letter/p/96bed5/32.png) [@Patty\_O\_Furniture](https://boards.straightdope.com/u/Patty_O_Furniture)\ **Post date:** [February 3, 2000, 12:55am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/2 "2000-02-03T00:55:00Z")
Yes. ---
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [February 3, 2000, 12:58am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/3 "2000-02-03T00:58:00Z")
Finishing my question … is there a formula that tells you how many diagonals can be drawn inside of one polygon (starting with equilateral ones)? ---
**Author:** ![Patty\_O\_Furniture](https://avatars.discourse-cdn.com/v4/letter/p/96bed5/32.png) [@Patty\_O\_Furniture](https://boards.straightdope.com/u/Patty_O_Furniture)\ **Post date:** [February 3, 2000, 1:01am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/4 "2000-02-03T01:01:00Z")
Yes. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [February 3, 2000, 1:02am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/5 "2000-02-03T01:02:00Z")
Yeah, each diagonal is formed by two corners of the polygon. So, if the polygon has n sides (n corners) the number of diagonals = the number of different ways to choose two of the n corners minus the n SIDES, which is [n(n-1)/2] - n. ---
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [February 3, 2000, 1:04am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/6 "2000-02-03T01:04:00Z")
Thank you. But only one of you. ---
**Author:** ![Patty\_O\_Furniture](https://avatars.discourse-cdn.com/v4/letter/p/96bed5/32.png) [@Patty\_O\_Furniture](https://boards.straightdope.com/u/Patty_O_Furniture)\ **Post date:** [February 3, 2000, 1:06am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/7 "2000-02-03T01:06:00Z")
I figure I had a 50/50 shot at a correct (if incomplete) answer. 😃 ---
**Author:** ![Harmonious\_Discord](https://avatars.discourse-cdn.com/v4/letter/h/74df32/32.png) [@Harmonious\_Discord](https://boards.straightdope.com/u/Harmonious_Discord)\ **Post date:** [February 3, 2000, 1:18am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/8 "2000-02-03T01:18:00Z")
In otherwards it approaches a number but never really reaches it. Calculus. Is this correct? * * * I’m only your wildest fear, from the corners of your darkest thoughts. ---
**Author:** ![Harmonious\_Discord](https://avatars.discourse-cdn.com/v4/letter/h/74df32/32.png) [@Harmonious\_Discord](https://boards.straightdope.com/u/Harmonious_Discord)\ **Post date:** [February 3, 2000, 1:20am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/9 "2000-02-03T01:20:00Z")
Now let’s calculate PI using triangles to fill in a circle. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [February 3, 2000, 1:24am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/10 "2000-02-03T01:24:00Z")
No, it doesn’t have anything to do with calculus; it doesn’t approach anything, it’s just the number of diagonals. For example, a hexagon would have (6\*5/2)-6 = 9 diagonals. ---
**Author:** ![tbea925](https://avatars.discourse-cdn.com/v4/letter/t/dc4da7/32.png) [@tbea925](https://boards.straightdope.com/u/tbea925)\ **Post date:** [February 3, 2000, 1:42am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/11 "2000-02-03T01:42:00Z")
“In otherwards it approaches a number but never really reaches it.” Gee, that sounds like my social life. ---
**Author:** ![Harmonious\_Discord](https://avatars.discourse-cdn.com/v4/letter/h/74df32/32.png) [@Harmonious\_Discord](https://boards.straightdope.com/u/Harmonious_Discord)\ **Post date:** [February 3, 2000, 1:54am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/12 "2000-02-03T01:54:00Z")
Well thanks Cabbage. I didn’t want to spend anytime thinking on that one and you saved me the trouble. tbea925 Would that be 01000101. Can you believe that using that for a user name got me booted from a virtual reality world in just a few seconds? They must have put alot of extra coding into the guardian bot. * * * I’m only your wildest fear, from the corners of your darkest thoughts. ---
**Author:** ![Lord\_Jim](https://avatars.discourse-cdn.com/v4/letter/l/ecccb3/32.png) [@Lord\_Jim](https://boards.straightdope.com/u/Lord_Jim)\ **Post date:** [February 3, 2000, 3:06am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/13 "2000-02-03T03:06:00Z")
Do you get the same answer with the formula: n(n-3)/2 where “n” is the number of sides or corners. (n-3) would equal the number of diagonals posible from a given corner. ( n - itself - 2 adjacent corners) Does that work out for all polygons? ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [February 3, 2000, 3:23am UTC](https://boards.straightdope.com/t/geometry-formula-question/6752/14 "2000-02-03T03:23:00Z")
> [@](#): > > Do you get the same answer with the formula: > > ``` > n(n-3)/2 > > ``` Yeah, that would work, too.