Consider a convex polygon such that:
- Each of its sides correspond to the square root of a positive integer.
- The polygon can be inscribed in an unit circle.
Determine the total number of polygons that simultaneously satisfy the 2 properties mentioned above.
Note: Polygons that are rotations and reflections of each other are considered the same.
(In reply to
solution by Charlie)
I see from Steve Herman's comment that I prematurely rejected sqrt(4). The corrected answer:
ways of arranging
120 + 120 + 120 1 `
120 + 120 + 60 + 60 2 (alternating vs together)
120 + 90 + 90 + 60 2 (60 opposite or adjacent 120)
120 + 60 + 60 + 60 + 60 1
90 + 90 + 90 + 90 1
90 + 90 + 60 + 60 + 60 2 (90's adjacent or separated)
60 + 60 + 60 + 60 + 60 + 60 1
180 + 60 + 60 + 60 1
180 + 90 + 90 1
180 + 60 + 120 1
---
13
So there are 13 such polygons.
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Posted by Charlie
on 2023-04-29 08:25:02 |
re: my solution -- corrected
