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The non-orientable genus, demigenus, or Euler genus of a connected, non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − k , where k is the non-orientable genus.
The genus (sometimes called the demigenus or Euler genus) of a connected non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − g, where g is the non-orientable ...
In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the degree.
It has Euler characteristic 1, hence a demigenus (non-orientable genus, Euler genus) of 1. The topological real projective plane can be constructed by taking the (single) edge of a Möbius strip and gluing it to itself in the correct direction, or by gluing the edge to a disk. Alternately, the real projective plane can be constructed by ...
Euler's partition theorem relating the product and series representations of the Euler function Π(1 − x n) Goldbach–Euler theorem, stating that sum of 1/(k − 1), where k ranges over positive integers of the form m n for m ≥ 2 and n ≥ 2, equals 1; Gram–Euler theorem
Euler invented the calculus of variations including its most well-known result, the Euler–Lagrange equation. Euler also pioneered the use of analytic methods to solve number theory problems. In doing so, he united two disparate branches of mathematics and introduced a new field of study, analytic number theory.
The title page of Elements of Algebra. Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler around 1765 in German. It was first published in Russian as "Universal Arithmetic" (Универсальная арифметика), two volumes appearing in 1768-9 [1] and in 1770 was printed from the original text.
While Euler's identity is a direct result of Euler's formula, published in his monumental work of mathematical analysis in 1748, Introductio in analysin infinitorum, [16] it is questionable whether the particular concept of linking five fundamental constants in a compact form can be attributed to Euler himself, as he may never have expressed it.
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