In 1882 German mathematician Ferdinand Lindemann proved that the ratio of the circumference of a circle to its diameter — the number we know and love as π — is, as was long suspected, not the solution to any algebraic equation. It is, instead, transcendental. This proof provided an insight into a problem that mathematicians (professional and amateur) had struggled with for over 2,000 years: the problem of squaring the circle . Given a circle, construct a square of equal area using the standard geometric tools of a compass and straightedge. A similar problem is called the rectification of the circle , which requires constructing a straight line equal to the circumference of the circle. It turns out that constructing geometric objects with a compass and straightedge is equivalent to solving certain algebraic equations. The rectification of the circle requires constructing a line of length 2π; squaring the circle requires constructing a line of length √π. Lengths involving transcendental Read More...