One result important to this problem involved showing that if a complex number z is the root of an integral polynomial(*), then e to the z plus one cannot equal zero.
One paper that attempted to solve this problem first introduced the creation of a sequence of numbers beginning 15, 4697, and 5548, which the paper's author called genitores, and eventually led to Kochanski's approximation. Martin Gardner's construction was accurate to six decimal places; Srinivasa Ramanujan's to eight. One result important to this problem involved showing that if a complex number z is the root of an integral polynomial(*), then e to the z plus one cannot equal zero. That result is known as the Lindemann-Weierstrass theorem. Earlier attempts to solve it included the Lune of Hippocrates and Antiphon's side-doubling arguments. For 10 points, name this problem, which along with doubling the cube and trisecting the angle perplexed ancient Greek mathematicians, whose goal was to create a geometrically regular four-sided polygon of the same area as a given circle within a finite number of steps.
One paper that attempted to solve this problem first introduced the creation of a sequence of numbers beginning 15, 4697, and 5548, which the paper's author called genitores, and eventually led to Kochanski's approximation.
Squaring the Circle [accept Quadrature of the Circle]