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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 ...
Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis. The polynomials presently known as Eulerian polynomials in Euler's work from 1755, Institutiones calculi differentialis, part 2, p. 485/6. The coefficients of these polynomials are known as Eulerian numbers.
Homology theory can be said to start with the Euler polyhedron formula, or Euler characteristic. [16] This was followed by Riemann 's definition of genus and n -fold connectedness numerical invariants in 1857 and Betti 's proof in 1871 of the independence of "homology numbers" from the choice of basis.
Consequently , = / =, where g is the usual (topological) meaning of genus of a surface, so the definitions are compatible. When X is a compact Kähler manifold, applying h p,q = h q,p recovers the earlier definition for projective varieties.
In honor of Black Twitter's contribution, Stacker compiled a list of 20 slang words it brought to popularity, using the AAVE Glossary, Urban Dictionary, Know Your Meme, and other internet ...
File:Lagrangian vs Eulerian [further explanation needed] Eulerian perspective of fluid velocity versus Lagrangian depiction of strain. In classical field theories , the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time.
Euler (software), a numerical software package; EulerOS, a Linux operating system distribution; Euler-Werke, an aircraft manufacturer owned by August Euler. AMS Euler, a typeface; Project Euler a series of challenging mathematical/computer programming problems; Euler angles, a way to describe the orientation of a rigid body