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A new Euler's formula for DNA polyhedra. [PDF]
PLoS ONE, 2011 DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures.
Guang Hu, Wen-Yuan Qiu, Arnout Ceulemans
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Euler's Polyhedron Formula [PDF]
Formalized Mathematics, 2008 where V , E, and F are, respectively, the number of vertices, edges, and faces of p. The formula was first stated in print by Euler in 1758 [11]. The proof given here is based on Poincare’s linear algebraic proof, stated in [17] (with a corrected proof in [18]), as adapted by Imre Lakatos in the latter’s Proofs and Refutations [15].
Jesse Alama
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An Automatic Proof of Euler's Formula [PDF]
Computer Science Journal of Moldova, 2005 In this information age, everything is digitalized. The encoding of functions and the automatic proof of functions are important. This paper will discuss the automatic calculation for Taylor expansion coefficients, as an example, it can be applied to
Jun Zhang
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Euler's Formula and De Moivre's Formula for Quaternions
Missouri Journal of Mathematical Sciences, 1999 Natural generalizations of Euler's formula and De Moivre's formula for quaternions are derived.
Eungchun Cho
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Mathematics, 2021 In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.
Nicuşor Minculete, Diana Savin
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Applications of neutrosophic complex numbers in triangles [PDF]
Neutrosophic Sets and Systems, 2023 It may be difficult for researchers to memorize or remember the trigonometric ratios of any neutrosophic angle, and this is what prompted us to activate the role of the neutrosophic complex numbers for that.
Yaser Ahmad Alhasan +2 more
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Euler's totient function applied to complete hypergroups
AIMS Mathematics, 2023 We study the Euler's totient function (called also the Euler's phi function) in the framework of finite complete hypergroups. These are algebraic hypercompositional structures constructed with the help of groups, and endowed with a multivalued operation,
Andromeda Sonea, Irina Cristea
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The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation
Journal of Nigerian Society of Physical Sciences, 2022 The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch +2 more
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Euler-Maclaurin formulae [PDF]
Mathematical Inequalities & Applications, 2003 A number of inequalities, for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or functions in L_p-spaces, is proved by applying the Euler-Maclaurin formulae. The results are applied to obtain some error estimates for the Maclaurin quadrature rules.
Marko Matić +2 more
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Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems
Axioms, 2023 This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, E I π+U=O.
Florin F. Nichita
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