Re: triangles in circles

*To*: mathgroup at smc.vnet.net*Subject*: [mg26829] Re: [mg26813] triangles in circles*From*: BobHanlon at aol.com*Date*: Thu, 25 Jan 2001 01:13:11 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Needs["DiscreteMath`Combinatorica`"]; n = 5; ptlist = Table[{Cos[i 2 \[Pi]/n], Sin[i 2 \[Pi]/n]}, {i, 1, n}]; triList = Append[#, First[#]]& /@ KSubsets[ptlist, 3]; Length[triList] 10 Show[Graphics[{ Circle[{0, 0}, 1], {PointSize[0.02], Line /@ triList} }], AspectRatio -> Automatic]; Graphically, you will get the same result by just drawing a line with each pair of points Show[Graphics[{ Circle[{0, 0}, 1], {PointSize[0.02], Line /@ KSubsets[ptlist, 2]} }], AspectRatio -> Automatic]; Bob Hanlon In a message dated 2001/1/24 5:22:16 AM, tdevries at shop.westworld.ca writes: >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] >