Comment Comment by BetaCygni As a non-mathematician, for a 2d circle on a flat plane:- The edge of a circle is curved (convex)- It does not matter how small a piece you cut of the edge, there will always remain a convex curve.- The edge of a square has straight edges, so you cannot put this piece at the edge. This means the old outside edge will have to be on the inside.- You cannot fit the convex edges to each other or to a straight edge.- Cutting a concave edge from the inside of the circle to fit the convex edge from the outside to will not help as it will produce a new convex edge.Ergo: there is no place to put the convex outside edge of the circle, so you cannot turn it into a square. parent BetaCygni 7 years ago
- The edge of a circle is curved (convex)
- It does not matter how small a piece you cut of the edge, there will always remain a convex curve.
- The edge of a square has straight edges, so you cannot put this piece at the edge. This means the old outside edge will have to be on the inside.
- You cannot fit the convex edges to each other or to a straight edge.
- Cutting a concave edge from the inside of the circle to fit the convex edge from the outside to will not help as it will produce a new convex edge.
Ergo: there is no place to put the convex outside edge of the circle, so you cannot turn it into a square.