triangles in circles

*To*: mathgroup at smc.vnet.net*Subject*: [mg26813] triangles in circles*From*: "Tom De Vries" <tdevries at shop.westworld.ca>*Date*: Wed, 24 Jan 2001 04:18:50 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello all, I'm teaching a high school math class and we are doing permutations and combinations. One of the "standard" questions is ..."given a certain number of points located around a circle, how many triangles can be formed...." The simple line below creates a circle with 5 points arranged around it. Could someone help me with a way to generate the lists of points that would create all the triangles. I know that for more points it would get kind of messy, but I wanted to actually draw all the triangles as I thought it might be an interesting graphic... Thanks for any help you might have.... n = 5; ptlist = Table[{Cos[i 2 \[Pi]/n], Sin[i 2 \[Pi]/n]}, {i, 1, n}]; Show[Graphics[{ Circle[{0, 0}, 1], {PointSize[0.02], Point /@ ptlist} }], AspectRatio -> Automatic] Sincerely, Tom De Vries

**Follow-Ups**:**Re: triangles in circles***From:*"Carl K. Woll" <carlw@u.washington.edu>