triangles in circles

• To: mathgroup at smc.vnet.net
• Subject: [mg26813] triangles in circles
• From: "Tom De Vries" <tdevries at shop.westworld.ca>
• Date: Wed, 24 Jan 2001 04:18:50 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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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