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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 ...
A tabulation of the numbers in a triangular array is called the Euler triangle or Euler's triangle. It shares some common characteristics with Pascal's triangle . Values of A ( n , k ) {\textstyle A(n,k)} (sequence A008292 in the OEIS ) for 0 ≤ n ≤ 9 {\textstyle 0\leq n\leq 9} are:
For example, the teardrop orbifold has Euler characteristic 1 + 1 / p , where p is a prime number corresponding to the cone angle 2 π / p . The concept of Euler characteristic of the reduced homology of a bounded finite poset is another generalization, important in combinatorics .
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.
Euler Mathematical Toolbox (or EuMathT; formerly Euler) is a free and open-source numerical software package. It contains a matrix language, a graphical notebook style interface, and a plot window. Euler is designed for higher level math such as calculus, optimization, and statistics.
An online dictionary is a dictionary that is accessible via the Internet through a web browser.They can be made available in a number of ways: free, free with a paid subscription for extended or more professional content, or a paid-only service.
However, the semi-implicit Euler method is a symplectic integrator, unlike the standard method. As a consequence, the semi-implicit Euler method almost conserves the energy (when the Hamiltonian is time-independent). Often, the energy increases steadily when the standard Euler method is applied, making it far less accurate.