In 1882 Ferdinand von Lindemann published the first complete proof that is transcendental. He first proved that is transcendental if is a non-zero algebraic number. Then, since is algebraic (see Euler's identity), must be transcendental. But since is algebraic, must therefore be transcendental. This approach was generalized by Karl Weierstrass to what is now known as the Lindemann–Weierstrass theorem. The transcendence of implies that geometric constructions involving compass and straightedge only cannot produce certain results, for example squaring the circle.
In 1882 Ferdinand von Lindemann published the first complete proof that is transcendental. He first proved that is transcendental if is. a non-zero algebraic number. Then, since is algebraic (see Euler's identity), must be transcendental. But since is algebraic, must therefore be transcendental This approach was generalized by Karl Weierstrass to what is now known as the Lindemann–Weierstrass theorem. The transcendence of implies that geometric constructions involving compass and straightedge only cannot produce certain results, for example squaring the circle.