Leonhard Euler's body of work saluted by Google doodle

Leonhard Euler's staggering body of work has inspired Monday's Google doodle on the ocassion of his 306th birthday. Euler is best known for making important discoveries in the field of calculus and graph theory.

Leonhard Euler introduced much of the mathematical terminology and notation that is used today, such as the notion of a mathematical function, and is widely considered to be one of the greatest mathematicians of all times.

We've already looked at Euler's personal life and briefly touched upon his mathematical accomplishments. Leonhard Euler was no ordinary mathematician. As a proof, here's a list of all the things that are named after the great Swiss mathematician, courtesy Wikipedia. Some of these, like Euler's formula, are even featured in the Google doodle.

• Euler's conjectures

  • Euler's conjecture (Waring's problem)
  • Euler's sum of powers conjecture

• Euler's equations

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  • Euler's equation - usually refers to Euler's equations (rigid body dynamics), Euler's formula, Euler's homogeneous function theorem, or Euler's identity
  • Euler equations (fluid dynamics) in fluid dynamics.
  • Euler's equations (rigid body dynamics), concerning the rotations of a rigid body.
  • Euler-Bernoulli beam equation, concerning the elasticity of structural beams.
  • Euler-Cauchy equation (or Euler equation), a second-order linear differential equation
  • Euler-Lagrange equation (in regard to minimization problems in calculus of variations)
  • Euler-Lotka equation (mathematical demography)
  • Euler-Poisson-Darboux equation
  • Euler's pump and turbine equation
  • Euler-Tricomi equation - concerns transonic flow
  • Euler transform used to accelerate the convergence of an alternating series and is also frequently applied to the hypergeometric series

• Euler's formulas

  • Euler's formula e ix = cos x + i sin x in complex analysis.
  • Euler's formula for planar graphs or polyhedra: v − e + f = 2
  • Euler's formula for the critical load of a column.
  • Euler's continued fraction formula
  • Euler product formula for the Riemann zeta function.
  • Euler-Maclaurin formula (Euler's summation formula) - relation between integrals and sums
  • Euler-Rodrigues formulas concern Euler-Rodrigues parameters and 3D rotation matrices

• Euler's functions

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  • The Euler function, a modular form that is a prototypical q-series.
  • Euler's homogeneous function theorem
  • Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer.
  • Euler hypergeometric integral

• Euler's identities

  • Euler's identity e iπ + 1 = 0.
  • Euler's four-square identity, which shows that the product of two sums of four squares can itself be expressed as the sum of four squares.
  • Euler's identity may also refer to the pentagonal number theorem.

• Euler's numbers

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  • Euler's number, e ≈ 2.71828, the base of the natural logarithm, also known as Napier's constant.
  • Euler's idoneal numbers
  • Euler numbers are an integer sequence.
  • Eulerian numbers are another integer sequence.
  • Euler number (physics), the cavitation number in fluid dynamics.
  • Euler number (topology) - now, Euler characteristic
  • Lucky numbers of Euler
  • Euler-Mascheroni constant
  • Eulerian integers are the numbers of form a + bω where ω is a complex cube root of 1.

• Euler's theorems

  • Euler's homogeneous function theorem, a theorem about homogeneous polynomials.
  • Euler's infinite tetration theorem
  • Euler's rotation theorem
  • Euler's theorem (differential geometry) on the existence of the principal curvatures of a surface and orthogonality of the associated principal directions.
  • Euler's theorem in geometry, relating the circumcircle and incircle of a triangle.
  • Euclid-Euler theorem
  • Euler-Fermat theorem, that aφ(m) ≡ 1 (mod m) whenever a is coprime to m, and φ is Euler's totient function
  • Euler's theorem equating the number of partitions with odd parts and the number of partitions with distinct parts. See Glaisher's theorem.
  • Euler's adding-up theorem in economics

• Euler's laws

  • Euler's first law, the linear momentum of a body is equal to the product of the mass of the body and the velocity of its center of mass.
  • Euler's second law, the sum of the external moments about a point is equal to the rate of change of angular momentum about that point.

• Other things named after Euler

  • 2002 Euler (a minor planet)
  • AMS Euler typeface
  • Euler (software)
  • Euler acceleration or force
  • Euler Book Prize
  • Euler Medal, a prize for research in combinatorics
  • Euler programming language
  • Euler-Fokker genus
  • Project Euler

Euler's influence best on mathematics is perhaps best summarised by Pierre-Simon Laplace, who is believed to have said, "Read Euler, read Euler, he is the master of us all."

For more Google doodles, visit this page.

Best Google doodles of 2012