Results 261 to 270 of about 983 (285)

Euler’s method for weighted integral formulae

Applied Mathematics and Computation, 2008
We consider the weighted quadrature formulae using some Euler type identities. The results are applied to obtain some error estimates for the Chebyshev- Gauss formulae of the first and the second kind.
Josip Pecaric, Mihaela Ribicic Penava, Ana Vukelic   +2 more
openaire   +4 more sources

A Product Formula for Euler's Totient

Bulletin of the London Mathematical Society, 1985
The 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 \((1,1,...,,1)\in {\mathbb{R}}^ n\).
openaire   +1 more source

A New Formula and New Constants Hidden After the Euler's Formula and the Euler's Constant

2018
In 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
openaire   +1 more source

The Exposition and Proof of Euler’s Formula.

Science and Technology of Engineering, Chemistry and Environmental Protection
In 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
openaire   +1 more source

On Euler-Simpson formulae

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, Dedić, Ljuban, Matić, Marko   +2 more
openaire   +3 more sources

Euler’s Polyhedron Formula in mizar

2010
Euler'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 ...
openaire   +1 more source

An Euler Summation Formula

The American Mathematical Monthly, 1936
(1936). An Euler Summation Formula. The American Mathematical Monthly: Vol. 43, No. 1, pp. 9-21.
openaire   +1 more source

The Euler tiling formula

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.
openaire   +1 more source

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.
openaire   +1 more source

Applications of Euler’s formula

2002
Abstract You may have met Euler’s formula for regular polyhedra: if <V is the number of vertices, E the number of edges, and <F the number of faces, then <V −E +<F = 2. There are five such regular polyhedra, and you can check this equation in the five cases (see Table 3.1).
openaire   +1 more source