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Re: triangles in circles
*To*: mathgroup at smc.vnet.net
*Subject*: [mg26831] Re: triangles in circles
*From*: Brian Higgins <bghiggins at ucdavis.edu>
*Date*: Thu, 25 Jan 2001 01:13:12 -0500 (EST)
*References*: <94ma2t$3pi@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Tom, Here is a way (if I understand correctly what you want to do):
Load this package so we can use the KSubsets function:
Needs["DiscreteMath`Combinatorica`"];
n = 5;
ptlist = Table[{Cos[i 2 \[Pi]/n], Sin[i 2 \[Pi]/n]}, {i, 1, n}];
Define a simple color function to make the graphic look pretty
clr := RGBColor[Random[], Random[], Random[]]
Construct a list of line primitives that define our triangles
TrianglePrimitives =
Map[{clr, Line[{#[[1]], #[[2]], #[[3]], #[[1]]}]} &, KSubsets[ptlist, 3]];
Show[Graphics[{Circle[{0, 0}, 1],
{PointSize[0.02], Point /@ ptlist}, TrianglePrimitives}],
AspectRatio -> Automatic]
Enjoy,
Brian
In article <94ma2t$3pi at smc.vnet.net>,
"Tom De Vries" <tdevries at shop.westworld.ca> wrote:
> 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
>
>
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