The Square

The one shape it will not become.

For more than two thousand years, people tried to draw a square with exactly the area of a circle, using only a compass and a straightedge. No measuring. No guessing.

In 1882, Ferdinand von Lindemann proved it cannot be done. The reason is π itself: it is not only endless, it is a kind of number those two tools can never build.

The circle keeps its area. It only declines to be squared.

A 9-inch round pan holds 63.6 square inches. The square that holds exactly as much is 7.98 inches on a side.

Figure A round pan and the square that holds exactly as much. The kitchen can measure it; the compass cannot draw it.

“The Square.” Wondering About Pi, no. 3.14159265 (24 September 2026). wap.mom/square/