Re: triangles in circles

*To*: mathgroup at smc.vnet.net*Subject*: [mg26859] Re: [mg26813] triangles in circles*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Fri, 26 Jan 2001 01:27:12 -0500 (EST)*References*: <200101240918.EAA03630@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Tom, To create a list of the vertices of all the triangles, you could simply use the function KSubsets from the package DiscreteMath`Combinatorica`. For example, <<DiscreteMath`Combinatorica` ?KSubsets KSubsets[l, k] gives all subsets of set l containing exactly k elements, ordered lexicographically. n = 5; ptlist = Table[{Cos[i 2 \[Pi]/n],Sin[i 2 \[Pi]/n]}, {i, 1, n}]; KSubsets[ptlist,3]; I didin't include the list of the vertices of the 10 triangles produced by KSubsets. Carl Woll Physics Dept U of Washington ----- Original Message ----- From: "Tom De Vries" <tdevries at shop.westworld.ca> To: mathgroup at smc.vnet.net Subject: [mg26859] [mg26813] triangles in circles > 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 > >

**References**:**triangles in circles***From:*"Tom De Vries" <tdevries@shop.westworld.ca>