       Re: triangles in circles

• To: mathgroup at smc.vnet.net
• Subject: [mg26839] Re: triangles in circles
• From: "Paul Lutus" <nospam at nosite.com>
• Date: Thu, 25 Jan 2001 01:13:18 -0500 (EST)
• References: <94ma2t\$3pi@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Tom De Vries" <tdevries at shop.westworld.ca> wrote in message
news:94ma2t\$3pi 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...
>
>
>
> 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]

Here is a starting point -- it groups your five points into unique sets of
three:

<<DiscreteMath`Combinatorica`

n = 3;

qlist = {a,b,c,d,e}

l[n_,tbl_]:=KSubsets[tbl,n]

l[3,qlist]

--
Paul Lutus
www.arachnoid.com

```

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