Defined set S of regular polygons on plane. Known for every polygon: at least one of it's sides is parallel to x,and this side's length is rational number. Also known- there is at least one vertex on this side that it's coordinates are rational numbers. What is the cardinality of S?
Drew Williamson
Answered question
2022-10-06
Defined set S of regular polygons on plane.
Known for every polygon: at least one of it's sides is parallel to x,and this side's length is rational number.
Also known- there is at least one vertex on this side that it's coordinates are rational numbers.
What is the cardinality of S?
Answer & Explanation
falwsay
Beginner2022-10-07Added 8 answers
Let P be a polygon in S, and let be a side of P parallel to the x-axis, let p be an endpoint of with rational coordinates, and let n be the number of sides that P has. Then P is completely determined by the following data:
- the coordinates of p;
- whether p is the left or right endpoint of ;
- the length of ;
- wherher is the top or the bottom edge of P; and
- n.
How many different combinations of values are possible?
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