List of things named after Leonhard Euler

In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Many of these entities have been given simple and ambiguous names such as Euler's function, Euler's equation, and Euler's formula.

Leonhard Euler (1707–1783)

Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. In an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them after Euler.[1][2]

Conjectures

Equations

Usually, Euler's equation refers to one of (or a set of) differential equations (DEs). It is customary to classify them into ODEs and PDEs.

Otherwise, Euler's equation may refer to a non-differential equation, as in these three cases:

Ordinary differential equations

Partial differential equations

Formulas

Functions

Identities

Numbers

Theorems

  • Euler's homogeneous function theorem – A homogeneous function is a linear combination of its partial derivatives
  • Euler's infinite tetration theorem – About the limit of iterated exponentiation
  • Euler's rotation theorem – Movement with a fixed point is rotation
  • Euler's theorem (differential geometry) – Orthogonality of the directions of the principal curvatures of a surface
  • Euler's theorem in geometry – On distance between centers of a triangle
  • Euler's quadrilateral theorem – Relation between the sides of a convex quadrilateral and its diagonals
  • Euclid–Euler theorem – Characterization of even perfect numbers
  • Euler's theorem – Theorem on modular exponentiation
  • Euler's partition theorem – Relates the product and series representations of the Euler function Π(1-x^n)
  • Goldbach–Euler theorem – theorem stating that sum of 1/(k−1), where k ranges over positive integers of the form mⁿ for m≥2 and n≥2, equals 1
  • Gram–Euler theorem

Laws

Other things

  • 2002 Euler (a minor planet)
  • Euler (crater)
  • AMS Euler typeface
  • Euler (software)
  • Euler Book Prize
  • Euler Lecture, an annual lecture at the University of Potsdam
  • Euler Medal, a prize for research in combinatorics
  • Leonhard Euler Gold Medal, a prize for outstanding results in mathematics and physics
  • Euler programming language
  • Euler Society, an American group dedicated to the life and work of Leonhard Euler
  • Euler Committee of the Swiss Academy of Sciences
  • Euler–Fokker genus
  • Project Euler
  • Leonhard Euler Telescope
  • Rue Euler (a street in Paris, France)[3]
  • EulerOS, a CentOS Linux based operating system
  • French submarine Euler
  • Euler square
  • Euler top

Topics by field of study

Selected topics from above, grouped by subject, and additional topics from the fields of music and physical systems

Analysis: derivatives, integrals, and logarithms

Geometry and spatial arrangement

Graph theory

  • Euler characteristic (formerly called Euler number) in algebraic topology and topological graph theory, and the corresponding Euler's formula
  • Eulerian circuit, Euler cycle or Eulerian path – a path through a graph that takes each edge once
    • Eulerian graph has all its vertices spanned by an Eulerian path
  • Euler class
  • Euler diagram - popularly called "Venn diagrams", although some use this term only for a subclass of Euler diagrams.
  • Euler tour technique

Music

  • Euler–Fokker genus
  • Euler's tritone

Number theory

Physical systems

Polynomials

See also

Notes

  1. Richeson, David S. (2008). Euler's Gem: The polyhedron formula and the birth of topology (illustrated ed.). Princeton University Press. p. 86. ISBN 978-0-691-12677-7.
  2. Edwards, Charles Henry; Penney, David E.; Calvis, David (2008). Differential equations and boundary value problems. Pearson Prentice Hall. pp. 443 (微分方程及边值问题, 2004 edition). ISBN 9780131561076.
  3. de Rochegude, Félix (1910). Promenades dans toutes les rues de Paris [Walks along all of the streets in Paris] (VIIIe arrondissement ed.). Hachette. p. 98.
  4. Evans, Charles R.; Smarr, Larry L.; Wilson, James R. (1986). "Numerical Relativistic Gravitational Collapse with Spatial Time Slices". Astrophysical Radiation Hydrodynamics. Vol. 188. pp. 491–529. doi:10.1007/978-94-009-4754-2_15. ISBN 978-94-010-8612-7. Retrieved March 27, 2021.
  5. Schoenberg (1973). "bibliography" (PDF). University of Wisconsin. Archived from the original (PDF) on 2011-05-22. Retrieved 2007-10-28.
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