# How Leopold Bloom tried and failed to square the circle

## That's Maths: Greek mathematicians and the central character in Ulysses grappled with the quadrature of the circle

The quadrature of the circle is one of the great problems posed by the ancient Greeks. This "squaring of the circle" was also an issue of particular interest to Leopold Bloom, the central character in James Joyce's novel Ulysses, whom we celebrate today.

The challenge is to construct a square with area equal to that of a given circle using only the methods of classical geometry. Thus, only a ruler and compass may be used in the construction, and the process must terminate in a finite number of steps.

A circle of unit radius has area pi. We must construct a line segment whose length is the square root of pi. With this as the side, the square has area pi and the job is done. But it is not possible to construct line segments of arbitrary length using the permitted method.

Squaring the circle has attracted attention from outstanding mathematicians for millenniums. In the Rhind papyrus, an ancient Egyptian mathematical script, Ahmes gives a method to construct a square of area nearly equal to that of a circle: cut one-ninth off the diameter and take the remainder as the side of the square. This corresponds to a value 3.16 for pi, close to the true value 3.14159 . . .