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Epitome of Eponyms: I Rest My Case!

Differing from the usual format for this section, one mathematician's name is associated with a great many topics. The common story is that mathematicians sometimes, trying to avoid naming everything after ***, name discoveries and theorems after the "first person after *** to discover it." Who is the mathematician ***?

  • ***'s conjecture (or Waring's problem)
  • ***'s sum of powers conjecture
  • ***–Bernoulli beam equation, concerning the elasticity of structural beams
  • ***–Cauchy equation, a second-order linear differential equation
  • ***–Lagrange equation, in regard to minimization problems in calculus of variations
  • ***–Lotka equation (mathematical demography)
  • ***–Poisson–Darboux equation
  • *** transform used to accelerate the convergence of an alternating series and is also frequently applied to the hypergeometric series
  • ***'s formula e ix = cos x + i sin x in complex analysis
  • ***'s formula for planar graphs or polyhedra: v − e + f = 2
  • ***'s formula for the critical load of a column
  • ***'s continued fraction formula
  • ***'s product formula for the Riemann zeta function
  • ***–Maclaurin formula – relation between integrals and sums
  • ***–Rodrigues formulas concern ***–Rodrigues parameters and 3D rotation matrices
  • The *** function, a modular form that is a prototypical q-series
  • ***'s homogeneous function theorem
  • ***'s totient function (or *** phi (φ) function) in number theory, counting the number of coprime integers less than an integer
  • *** hypergeometric integral
  • ***'s identity e iπ + 1 = 0
  • ***'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
  • ***'s number, e ≈ 2.71828, the base of the natural logarithm, also known as Napier's constant
  • ***'s idoneal numbers
  • *** numbers are an integer sequence
  • *** characteristic
  • ***'s Lucky numbers
  • *** integers are the numbers of form a + bω where ω is a complex cube root of 1
  • ***'s homogeneous function theorem, a theorem about homogeneous polynomials
  • ***'s infinite tetration theorem
  • ***'s rotation theorem
  • ***'s theorem (differential geometry) on the existence of the principal curvatures of a surface and orthogonality of the associated principal directions
  • ***'s theorem in geometry, relating the circumcircle and incircle of a triangle
  • ***–Fermat theorem, that aφ(m) ≡ 1 (mod m) whenever a is coprime to m, and φ is ***'s totient function
  • *** angles defining a rotation in space
  • *** brick
  • ***'s line – relation between triangle centers
  • *** operator – set of functions to create polygon meshes
  • ***'s rotation theorem
  • *** squares, usually called Graeco-Latin squares
  • *** cycle – a path through a graph that takes each edge once
  • *** class
  • *** diagram – likely better (but wrongly) known as Venn diagrams, its subclass
  • *** pseudoprime
  • ***'s Disk – a toy consisting of a circular disk that spins, without slipping, on a surface
Now, who is the mathematician *** and what do each of these eponymic ideas/formulas mean?

Answer: Leonhard Euler!