Which regular polygons can be dissected into isosceles triangles by nonintersecting diagonals?
(In reply to
Equilateral triangle are certainly isosceles. by Jer)
In that case, I will postulate that any regular ngon where n can be expressed as 2^k+2^p (where k and p are integers >=0, but not both 0) can be dissected as required in the problem.
Here's a short list up to 100:
n k p
3 1 0 (assuming a regular triangle is okay with 0 "dissections")
4 1 1
5 2 0
6 2 1
8 2 2
9 3 0
10 3 1
12 3 2
16 3 3
17 4 0
18 4 1
20 4 2
24 4 3
32 4 4
33 5 0
34 5 1
36 5 2
40 5 3
48 5 4
64 5 5
65 6 0
66 6 1
68 6 2
72 6 3
80 6 4
96 6 5
In other words, it looks like A173786
Still don't know if this would be the complete list, or if it misses some ns.
Edited on January 21, 2012, 5:02 pm
Edited on January 21, 2012, 5:02 pm

Posted by Dustin
on 20120121 16:55:03 