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 2019-06-30, 13:37 #1 Xyzzy     "Mike" Aug 2002 769910 Posts July 2019
2019-06-30, 22:59   #2
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

17·113 Posts

Quote:
 Exactly two edges meet at each vertex
https://en.wikipedia.org/wiki/Simple_polygon

Unless there is no distinction between a "Weakly simple polygon" and a "Simple Polygon".

Quote:
 This formalizes the notion that such a polygon allows segments to touch but not to cross.

Last fiddled with by a1call on 2019-06-30 at 23:38

2019-07-01, 05:25   #3
SmartMersenne

Sep 2017

22·3·7 Posts

Quote:
 Originally Posted by a1call https://en.wikipedia.org/wiki/Simple_polygon Unless there is no distinction between a "Weakly simple polygon" and a "Simple Polygon".
Based on past experience of clarifications coming in later, you may safely assume simple means just simple, so "Exactly two edges meet at each vertex"

 2019-07-01, 06:29 #4 axn     Jun 2003 22×11×107 Posts Can 3 (consecutive) points lie in a straight line?
 2019-07-01, 06:35 #5 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 17·113 Posts With "Weakly simple polygon" your interpretation is as good as mine if not better. But I don't read any restrictions other than crossing lines.
2019-07-01, 06:37   #6
SmartMersenne

Sep 2017

22·3·7 Posts

Quote:
 Originally Posted by axn Can 3 (consecutive) points lie in a straight line?
Why not

 2019-07-01, 10:44 #7 axn     Jun 2003 22×11×107 Posts LOL. The best answer I got was exactly a difference of 7 (several polygons with area 8 and several with area 15).
 2019-07-01, 19:21 #8 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 36018 Posts Well, being a chess player, mathematician and not to mention smart, does give you an unfair advantage. But at least you didn't have to use your programming skills this time.
2019-07-01, 20:52   #9
SmartMersenne

Sep 2017

22·3·7 Posts

Quote:
 Originally Posted by axn LOL. The best answer I got was exactly a difference of 7 (several polygons with area 8 and several with area 15).
On a related note to the previous question asked: Do you have a solution with no straight line?

2019-07-01, 23:17   #10
ramgeis

Apr 2013

22×29 Posts

Quote:
 Originally Posted by SmartMersenne On a related note to the previous question asked: Do you have a solution with no straight line?
there is one without 3 consecutive points in a row.

 2019-07-02, 00:03 #11 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 192110 Posts I have confirmation. The polygons should not be weakly-simple.

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