Transcendence of e and pi
Trascendencia de e y de pi: imposibilidad de la cuadratura del círculo
- Date
- 1882 · confidence high
- Place
- Freiburg im Breisgau, Germany
- Credited to
- Ferdinand von Lindemann (pi, 1882); Charles Hermite (e, 1873); Joseph Liouville (first transcendental numbers, 1844)
- People
- 👤 Carl Ferdinand von Lindemann1852–1939👤 Charles Hermite1822–1901👤 Joseph Liouville1809–1882
- Field
- Knowledge & symbols
What was discovered
Pi is not the root of any polynomial with rational coefficients, so it cannot be constructed with straightedge and compass, and squaring the circle is impossible. It closes the oldest of the three classical Greek problems.
Wantzel had proved in 1837 the impossibility of angle trisection and cube duplication using algebraic methods.
What it led to
- the theory of transcendental numbers
- Hilbert's seventh problem (Gelfond-Schneider)
- Baker's theory
Built on
- Euler formula and Euler identity1748
- irrationality of pi (Lambert, 1761)
- Galois theory (trisection and doubling, Wantzel 1837)