       Re: drawing polygon diagonals

• To: mathgroup at smc.vnet.net
• Subject: [mg112371] Re: drawing polygon diagonals
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Sat, 11 Sep 2010 05:44:32 -0400 (EDT)
• References: <i6755n\$873\$1@smc.vnet.net> <i6a5f5\$kjv\$1@smc.vnet.net> <i6creo\$s8p\$1@smc.vnet.net>

```Something like this?

DynamicModule[{maxpts = 12},
Manipulate[
pts = Table[{Cos[2 Pi*k/maxpts], Sin[2 Pi*k/maxpts]}, {k, 1, n}];
Graphics[
{
Black, Thickness[0.0005],
GraphicsComplex[pts, Line[Subsets[Range[n - 1], {2}]]],
Blue,
GraphicsComplex[pts, Line[{n, #} & /@ Range[n - 1]]],
Red, PointSize[0.035],
GraphicsComplex[pts, Point[Range[n]]]
},
PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}}
], {n, 2, maxpts, 1}
]
]

Cheers -- Sjoerd

On Sep 10, 10:49 am, MH <matthewh... at gmail.com> wrote:
> Thanks for your help, Dan & Sjoerd!  I have one more question because
> as I was working with this, I thought of a small improvement.  For
> now, I'll assume my biggest n-value is 12, so the current Manipulate
> statement finishes with a dodecagon.  The current code generates a
> triangle, then a square with its diagonals, then a pentagon with its
> diagonals, then a hexagon, and so on, up to a dodecagon with all its
> diagonals.  Each step shows a regular polygon with all its
> diagonals.
>
> It'd be nice, though, if as n increased (with the slider) the vertices
> of the dodecagon appeared one at a time in the correct place, and the
> lines between them also appeared.  For example, when n is 5 (and not
> yet all the way to 12), there'd be five red circles but they would NOT
> form a regular pentagon.  Instead, they'd be in the correct position
> to be vertices of a regular dodecagon.  This would be cool because a
> large collection of lines would not change from one n-value to the
> next.  Your eye would be drawn only to the new lines when you add each
> circle.  And if the new lines could appear in a separate color -- oh
> wow, that'd be great.  (For my purposes, those are the new handshakes
> when you add each person.)
>
> I hope this makes sense.  I'll do some more looking in the DocCenter.
> Thanks!  I appreciate your help and guidance.
>
> MH

```

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