If a circle is a polygon with an infinite number of sides; what has more sides, a circle or a semicircle?

Hello,

Actually a polygon can only have a countable number of sides (e.g. There are polygons with 1245 sides and 1246 sides but none with 1245.987 sides).

This means the circle seen as an infinity-sided polygon is actually a polygon with ℵ₀ sides (with ℵ₀ being the cardinality of ℕ).

A semi-polygon will have about half the number of sides of the full polygon. When the full polygon sides goes to countable infinity ℵ₀, the semi-polygon sides also goes to countable infinity ℵ₀.

►►►ANSWER

The answer is that both circle and semi-circle will have the same number of sides! And that number is the infinity number ℵ₀.

I don't really have the time to explain infinities comparatives but the following links might help you explain why the answer above is correct.

Regards,

Dragon.Jade :-)

https://www.youtube.com/watch?v=A-QoutHCu4o

https://en.wikipedia.org/wiki/Aleph_number

https://www.physicsforums.com/threads/comparing-in...

Semi says it all. "partial". Full will always have more than partial of the same diameter.