 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Paramount Polygon Poser (Posted on 2015-01-15) 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 No Rating Comments: ( Back to comment list | You must be logged in to post comments.) 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 Please log in:

 Search: Search body:
Forums (0)