Facebook Blurb # 15 – Squaring a Circle

While this contemporary phrase is a metaphor for “trying to do the impossible,” (like finding world peace), it was in fact a conundrum that stoked the curiosity of geometers in ancient times.

Greek philosopher and astronomer Anaxagoras (510-428 BC) was the first of many mathematicians who sought to solve the problem of constructing a square whose area is equal to that of a given circle, using a finite number of steps with only a compass and a straightedge. On balance, it seemed simple enough – if the area of a circle is pi x radius (raised to the 2nd power), and assuming for simplicity that r=1, then the length of an equivalent square should be square root of pi. Except that pi is the non-terminating, transcendental and irrational number 3.14159265…

In literature, Dante Alighieri addressed the problem in his “The Divine Comedy.” And well up to the 19th century, mathematicians continued to propose solutions to a task deemed beyond human comprehension. (Let’s just say they kept going around in circles.) Today, the term “circle squarers” is applied to those who insist on performing a hopeless and vain undertaking. “Morbus cyclometricus” is the disease from which they suffer. And “squircles” are a shape that is intermediate between a square and a circle.

Have you ever wondered why pizza boxes are square while the pie is round? Why boxing rings are actually quadrangular? Why squircular plates can hold more food than circular ones? Or why the icons on your iPhone are rounded squares?

In 2004, Waterman introduced the Exception Ideal fountain pen, a lacquered instrument with gold trim and nib, and a squircular profile that, even today, stands out as a rare and distinctive design, and certainly a bold attempt to square the circle.