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Paramount Polygon Poser (Posted on 2015-01-15) Difficulty: 3 of 5
Each interior angle of a regular R-gon is precisely 59/58 times that of each angle of a regular S-gon, where R ≥ S ≥ 3.

Find the largest possible value of S.

No Solution Yet Submitted by K Sengupta    
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Solution computer assisted solution | Comment 1 of 3
   10   for N1=3 to 10000
   20    A1=180*(N1-2)//N1
   30    N2=N1
   40    loop
   50      inc N2
   60      A2=180*(N2-2)//N2
   70      if A2//A1>59//58 then goto 100
   80      if A2//A1=59//58 then print N1;A1,N2;A2
   90    endloop
  100   next N1
  
 finds 

  S               R
sides angles    sides  angles
 59  10260//59   116  5130//29
 60  174         120  177
 89  15660//89   356  15930//89
 110  1944//11   1595  57348//319
 114  3360//19   3306  99120//551
 116  5130//29   6728  151335//841
 117  2300//13   13572  67850//377

Angles are in degrees. 
 
The program remains stuck on 118.

At 118 sides, the angle at each is 180*116/118 = 10440/59. Multiplying this by 59/58 gives 180, an angle impossible in a polygon: it would be an infinitely sided polygon, aka a circle.

117 is the largest possible value of S.

 
 

  Posted by Charlie on 2015-01-15 10:14:13
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