Problems & Puzzles: Puzzles

 Puzzle 746. A follow up to Puzzle 742 (about golygons) Here we ask you to get the prime-golygon of n sides, with the minimal surface, as suggested by Emmanuel Vantieghem. Of course this question has sense whenever there are more than one solution of golygons for a given n value. According to the Resta contribution for the Puzzle 742 there are more than one minimal solution for n>20: "The minimal solution is unique for N=8,12,16,20. For N=24 there are 4 minimal solutions, 6 for N=28, 22 for N=32 and 348 for N=36." Q. Send the golygon with the minimal surface for n=24, 28, 32, 36 & 40. _____ Perhaps you will find useful this algorithm to compute the area of a given polygon that uses the coordinates of the vertexes of the polygon:  http://www.mathopenref.com/coordpolygonarea2.html

Contributions came from Jan van Delden, Hakan Summakoglu

***

Here are the minimal area obtained by the puzzlers-contributors.

 Name 24 28 32 36 40 44 48 52 Jan 15468 24833 44260 53549 77460 109179 143334 180025 Hakan 15468 31063 44260 53549 77460 NA NA NA

Both used as the minimal prime for each golygon the prime 3.

Here are their drawings as a pdf file.

 Records   |  Conjectures  |  Problems  |  Puzzles