       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...
>
>
>
> 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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