Math Is Fun Forum

coolwind

Member

Registered: 2005-10-30

Posts: 30

A combinations problem

How many triangles are determined by the vertices of a regular polygon of n sides?
How many if no side of the polygon is to be a side of any triangle?

Thanks~~

ryos

Member

Registered: 2005-08-04

Posts: 394

Re: A combinations problem

a) This is a combination problem. Basically, you are choosing three vertices from a set of n, where order doesn't matter. So, the formula is:

This will give you the number of triangles you can make from the vertices of any regular polygon!

b) In order for this to work, no two vertices may be adjacent to another. Unfortunately, I don't have time right now to figure out that formula.

Last edited by ryos (2006-07-29 06:26:08)

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El que pega primero pega dos veces.

coolwind

Member

Registered: 2005-10-30

Posts: 30

Re: A combinations problem

a) This is a combination problem. Basically, you are choosing three vertices from a set of n, where order doesn't matter. So, the formula is:

This will give you the number of triangles you can make from the vertices of any regular polygon!

b) In order for this to work, no two vertices may be adjacent to another. Unfortunately, I don't have time right now to figure out that formula.

ok,thank you