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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 ...
Euler's great interest in number theory can be traced to the influence of his friend in the St. Peterburg Academy, Christian Goldbach. A lot of his early work on number theory was based on the works of Pierre de Fermat, and developed some of Fermat's ideas. One focus of Euler's work was to link the nature of prime distribution with ideas in ...
Euler's identity is also a special case of the more general identity that the n th roots of unity, for n > 1, add up to 0: = = Euler's identity is the case where n = 2. A similar identity also applies to quaternion exponential: let {i, j, k} be the basis quaternions; then,
In mathematics and computational science, Heun's method may refer to the improved [1] or modified Euler's method (that is, the explicit trapezoidal rule [2]), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
2 dogs doing agility training. Outdoor agility training is a brilliant way to exercise your dog both mentally and physically. The same goes for cats, who are naturally fantastic jumpers, agile and ...
Euler: The Master of Us All (1st ed.). Mathematical Association of America. ISBN 0-88385-328-0. Dunham, William (2007). "Euler and the Fundamental Theorem of Algebra" in The Genius of Euler: Reflections on his Life and Work. Mathematical Association of America. ISBN 978-0-88385-558-4. Dunham, William (2008). The Calculus Gallery (1st ed ...
Here's how "Gladiator 2" massages history in the name of cinematic drama: A break in the blood and gore: Pedro Pascal (left) jokes with "Gladiator II" director Ridley Scott and co-star Paul Mescal ...