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MathGroup Archive 2001

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Re: triangles in circles

  • To: mathgroup at
  • Subject: [mg26859] Re: [mg26813] triangles in circles
  • From: "Carl K. Woll" <carlw at>
  • Date: Fri, 26 Jan 2001 01:27:12 -0500 (EST)
  • References: <>
  • Sender: owner-wri-mathgroup at


To create a list of the vertices of all the triangles, you could simply use
the function KSubsets from the package DiscreteMath`Combinatorica`. For



KSubsets[l, k] gives all
   subsets of set l containing
   exactly k elements, ordered

n = 5;
ptlist = Table[{Cos[i 2 \[Pi]/n],Sin[i 2 \[Pi]/n]}, {i, 1, n}];


I didin't include the list of the vertices of the 10 triangles produced by

Carl Woll
Physics Dept
U of Washington

----- Original Message -----
From: "Tom De Vries" <tdevries at>
To: mathgroup at
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
> 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
> create all the triangles.   I know that for more points it would get kind
> messy, but I wanted to actually draw all the triangles as I thought it
> 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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