       Re: drawing polygon diagonals

• To: mathgroup at smc.vnet.net
• Subject: [mg112376] Re: drawing polygon diagonals
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 11 Sep 2010 05:45:27 -0400 (EDT)

```Manipulate[Module[
{pts, allPts = {Cos[#], Sin[#]} & /@
(2 Pi*
Range[0, max - 1]/max)},
pts = func[allPts, Min[n, max]];
Graphics[{Blue,
Line /@ Subsets[pts, {2}],
AbsolutePointSize,
Red, Point[pts]},
PlotRange -> 1.05 {{-1, 1}, {-1, 1}}]],
{{max, 12}, Range[8, 20]},
{func, {Take, RandomSample}},
{n, 1, max, 1, Appearance -> "Labeled"}]

Manipulate[Module[
{pts, allPts = {Cos[#], Sin[#]} & /@
(2 Pi*
Range[0, max - 1]/max)},
pts = Take[allPts, Min[n, max]];
Graphics[{Magenta,
Line /@ Subsets[pts, {2}],
Black, AbsoluteThickness[1.25],
Line /@ Subsets[Most[pts], {2}],
AbsolutePointSize,
Red, Point[pts]},
PlotRange -> 1.05 {{-1, 1}, {-1, 1}}]],
{{max, 12}, Range[8, 20]},
{n, 1, max, 1, Appearance -> "Labeled"}]

Bob Hanlon

---- MH <matthewhoek 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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