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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?