Results 21 to 30 of about 983 (285)
, 2016 Let the number of vertices, edges, and faces of a polyhedron be V, E, and F. The Euler characteristic, V-F+E, is always 2 for convex polyhedra. This Demonstration shows Euler's polyhedral formula V+F-E=2 for the Platonic solidsEducação Superior::Ciências
Zenil, Hector
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An Examination of Counterexamples in Proofs and Refutations
Philosophia Scientiæ, 2009 : Lakatos’s seminal work Proofs and Refutations introduced the methods of proofs and refutations by discussing the history and methodological development of Euler’s formula V — E+F = 2 for three dimensional polyhedra.
Samet Bağçe, Can Başkent
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A generalization of Euler's formula in Clifford algebras
, 2022 In this paper, the equation.ex.y. = 1, such that x, y. Rn, is proved using defined group homomorphism and Euler's formula, where x. y is the outer product between x and y. Firstly, this equation is verified for n = 2, 3, 4,5 using Clifford product. Then,
Mutlu Akar, Akar, Mutlu
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Multiple zeta values and Euler's reflection formula for the gamma function
, 2023 In this paper, we give a purely algebraic proof of an identity coming directly from Euler's reflection formula for the gamma function.
Sakata, Mika, Ikeda, Karin
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Computation, 2023 This study introduces an approach for modeling an arm of a Stewart platform to analyze the location of sections with a high deflection among the arms. Given the dynamic nature of the Stewart platform, its arms experience static and dynamic loads.
Reza Hassanian, Morris Riedel
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On a Conjecture of Alzer, Berg, and Koumandos
Mathematics, 2020 In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) ∈ R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ∞ ) , where ψ (
Ladislav Matejíčka
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Journal of Computational and Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Application of Padé approximation to Euler's constant and Stirling's formula
, 2021 International audienceThe Digamma function Γ' /Γ admits a well-known (divergent) asymptotic expansion involving Bernoulli's numbers. Using Touchard type orthogonal polynomials, we determine an eective bound for the error made when this asymptotic series ...
Rivoal, Tanguy, Prévost, Marc
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UNUSUAL FORMULAE FOR THE EULER CHARACTERISTIC [PDF]
Journal of Knot Theory and Its Ramifications, 2002 Everyone knows that the Euler characteristic of a combinatorial manifold is given by the alternating sum of its numbers of simplices. It is shown that there are other linear combinations of the numbers of simplices which are combinatorial invariants, but that all such invariants are multiples of the Euler characteristic.
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