Re: triangles in circles

*To*: mathgroup at smc.vnet.net*Subject*: [mg26839] Re: triangles in circles*From*: "Paul Lutus" <nospam at nosite.com>*Date*: Thu, 25 Jan 2001 01:13:18 -0500 (EST)*References*: <94ma2t$3pi@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"Tom De Vries" <tdevries at shop.westworld.ca> wrote in message news:94ma2t$3pi at smc.vnet.net... > 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] Here is a starting point -- it groups your five points into unique sets of three: <<DiscreteMath`Combinatorica` n = 3; qlist = {a,b,c,d,e} l[n_,tbl_]:=KSubsets[tbl,n] l[3,qlist] -- Paul Lutus www.arachnoid.com