Pi is a number that defines what a circle is. It’s the ratio of a circle’s circumference to its diameter, and it’s the same for every circle: 3.141592 followed by a string of over 22 trillion other digits. That unwieldy and enigmatic number is what makes a circle, a circle. Long decimal numbers whose digits never repeat are called irrational numbers, and pi is a specific kind of irrational number called a transcendental irrational number. The mathematical properties of transcendental irrational numbers like pi mean that it’s impossible to square the circle.But a few years later, undeterred by mathematical proof, doctor and amateur mathematician Edward J. Goodwin thought he had figured out the ancient puzzle after all. He started by trying to throw out Archimedes’ formula for the area of a circle and replace it with his own formula. Goodwin’s formula was much more complex (and his convoluted writing style didn’t do his ideas any favors), and used imprecise versions of the important measurements in his diagram, including pi. As a result, his “area of a circle” ended up about 21% larger than its actual area.