Consider the lowly square, a four-sided shape with sides of equal length meeting at right angles. The embodiment of what we’re referring to when we refer to square miles, square kilometers, square inches, or square whatevers. The two-dimensional version of any one-dimensional length.
A trivially easy shape to draw, all you need is a straight edge and a compass — the latter for ensuring your corners are right angles (see Plato’s Divided Line for more on using a straight edge and compass). The only simpler shape is the circle.
Yet the simple square threw early mathematicians into a serious tizzy!


You may remember learning way back in grade school that you can’t divide by zero. You may remember being told that
The first
This post contains the post statistics charts I didn’t have room for in
The other face of 











