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The Exposition and Proof of Euler’s Formula.
Science and Technology of Engineering, Chemistry and Environmental ProtectionIn the 18th century, Euler’s formula (EF) was discovered by Leonhard Euler, and it has since been recognized as one of the most famous and beautiful equations in the mathematical world, occupying an extremely important place in numerous fields. The theory of complex functions has been significantly enriched by this formula, as it extends the domain of ...
Haoyue Xiang, Weichen Xiong, Yifan Zhang
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A Product Formula for Euler's Totient
Bulletin of the London Mathematical Society, 1985The author generalizes some results about the intersections (or projections) of given integral lattices with (or into) rational subspaces, and applies them to get a product formula for a numerical invariant associated to subspaces of \({\mathbb{R}}^ n\), which are orthogonal to \((1,1,...,,1)\in {\mathbb{R}}^ n\).
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A New Formula and New Constants Hidden After the Euler's Formula and the Euler's Constant
2018In this paper, the authors propose a new formula π=½eθ, in which the new constant θ is a real number. The new formula is a perfect supplement the Euler's formula eπi=−1. These two formulas together reveal the completely relationship between π and e.
Wenwei Chen, Sheng Chen
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Euler Formulas and Geometric Modeling
IEEE Computer Graphics and Applications, 1985This Physial Approach to the Euler Formula Demonstrates how Different version Can be in this article we demonstrates how different versions can be Obtained And how They Can Be Used in Boundary Geometric ...
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Panamerican mathematical journal, 2001
Modified versions of the Euler-Simpson formula, for Lipschitzian functions, functions of bounded variation and functions with derivatives in L_p-spaces, are given and applied to prove some inequalities and quadrature formulae.
Pečarić, Josip +2 more
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Modified versions of the Euler-Simpson formula, for Lipschitzian functions, functions of bounded variation and functions with derivatives in L_p-spaces, are given and applied to prove some inequalities and quadrature formulae.
Pečarić, Josip +2 more
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Euler’s Polyhedron Formula in mizar
2010Euler's polyhedron formula asserts for a polyhedron p that V - E + F = 2, where V , E, and F are, respectively, the numbers of vertices, edges, and faces of p. Motivated by I. Lakatos's philosophy of mathematics as presented in his Proofs and Refutations, in which the history of Euler's formula is used as a case study to illustrate Lakatos's views, we ...
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International Journal of Mathematical Education in Science and Technology, 2001
A formula for tilings of a rectangle, analogous to Euler's formula for polyhedra, is discussed, with particular reference to how it may be used in a classroom investigation.
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A formula for tilings of a rectangle, analogous to Euler's formula for polyhedra, is discussed, with particular reference to how it may be used in a classroom investigation.
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The American Mathematical Monthly, 1936
(1936). An Euler Summation Formula. The American Mathematical Monthly: Vol. 43, No. 1, pp. 9-21.
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(1936). An Euler Summation Formula. The American Mathematical Monthly: Vol. 43, No. 1, pp. 9-21.
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On the derivation of Euler's formula
International Journal of Mathematical Education in Science and Technology, 1975(1975). On the derivation of Euler's formula. International Journal of Mathematical Education in Science and Technology: Vol. 6, No. 3, pp. 381-382.
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