# Thread: Why not a square become a circle?

1. If four 90 degrees make up 360 then why not a square become a circle?  2.

3. Originally Posted by roybaxter If four 90 degrees make up 360 then why not a square become a circle?

In what sense do you define "become"?  4. Honest mathematics can never prove a falsehood to be true; however, there are circumstances by which a person can convince another of a falsehood through corrupt - or “illegal” - mathematics (This is how we get proofs of 1=2, and the like).  5. Deleted  6. You're adding up the angles wrong. The internal angles of a square do add up to 360 degrees, but you're comparing that to the external angles of the circle. The external angles of all 2 dimensional objects add up to 360 degrees. But the internal angles can add up to different amounts (for example a triangle adding up to 180 degrees.)

A circle can be looked at as a 2 dimensional object with infinity sides/corners. The external angle of each corner is very nearly zero. Or a theoretical anti infinity, usually represented by delta.

The internal angle of each of these infinite number of corners is very nearly 180, and if you sum the values of the internal angles they basically add up to infinity.  7. just response to the thread:
this might be possible,in fact.
(re)search "conform transforms" in complex analysis. This is not my field but it seems possible to me.  8. Originally Posted by roybaxter If four 90 degrees make up 360 then why not a square become a circle?

It does make a circle just not a well drawn circle. The best circle you can create even with the smallest elements, would be a very high number sided polygon. As atoms do not make a perfect round there would be crevices and such that would make it a polygon.

Sincerely,

William McCormick  9. A square is a shape defined by four straight lines with four right angles, while a circle is a shape defined by a curved line that is the same distance from the center at all points. While four 90-degree angles can make up a full rotation of 360 degrees, a square, and a circle are fundamentally different shapes and cannot be transformed into one another.  math quiz, mathematics, mathematics cience 