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.
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]