RE: triangles in circles
- To: mathgroup at smc.vnet.net
- Subject: [mg26826] RE: [mg26813] triangles in circles
- From: "David Park" <djmp at earthlink.net>
- Date: Thu, 25 Jan 2001 01:13:09 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hi Tom,
The easiest method is to use the standard Combinatorica package. KSubsets
picks out all the different subsets of k elements from a larger set.
Needs["DiscreteMath`Combinatorica`"]
With[
{n = 5},
ptlist = Table[{Cos[i 2 \[Pi]/n], Sin[i 2 \[Pi]/n]}, {i, 1, n}]];
trianglepoints = KSubsets[ptlist, 3];
trianglelines = Line[Join[#, {First[#]}]] & /@ trianglepoints;
Show[Graphics[{
Circle[{0, 0}, 1],
{PointSize[0.02], Point /@ ptlist},
trianglelines
}], AspectRatio -> Automatic];
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
> From: Tom De Vries [mailto:tdevries at shop.westworld.ca]
To: mathgroup 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]
>
> Sincerely, Tom De Vries
>
>
>