perplexus.info :: Shapes : Inscribed Polygon Crossed Root Side Resolution

Inscribed Polygon Crossed Root Side Resolution (Posted on 2023-04-29)

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.

Submitted by K Sengupta

Rating: 5.0000 (2 votes)

Solution: (Hide)

1-1-1-1-1-1 Hexagon sqrt(2)-sqrt(2)-sqrt(2)-sqrt(2) Square Sqrt(3)-sqrt(3)-sqrt(3) Triangle 2-1-1-1 2-sqrt(2)-sqrt(2) 2-1-sqrt(3) sqrt(3)-sqrt(3)-1-1 sqrt(3)-1-sqrt(3)-1 sqrt(3)-sqrt(2)-sqrt(2)-1 sqrt(3)-sqrt(2)-1-sqrt(2) sqrt(2)-sqrt(2)-1-1-1 sqrt(2)-1-sqrt(2)-1-1 sqrt(3)-1-1-1 sqrt(3)-1-1

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
QualitнEssay	Jason Taylor	2023-05-06 13:01:58
re: There's one more	Steve Herman	2023-05-03 11:56:38
There's one more	Jer	2023-04-29 18:15:22
re: my solution -- corrected	Charlie	2023-04-29 08:25:02
solution	Charlie	2023-04-29 08:14:14
Solution (spoiler)	Steve Herman	2023-04-29 07:17:30

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