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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 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field. His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology.
Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər; [b] German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] ⓘ, Swiss Standard German: [ˈleɔnhard ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of ...
The God of High School [b] is a South Korean manhwa released as a webtoon written and illustrated by Yongje Park. It has been serialized in Naver Corporation's webtoon platform Naver Webtoon from April 2011 to December 2022, with the individual chapters collected and published by Imageframe under their Root label into four volumes as of January 2023.
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 ...
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.
Notably, Euler identified functions rather than curves to be the central focus in his book. [36] Logarithmic, exponential, trigonometric, and transcendental functions were covered, as were expansions into partial fractions, evaluations of ζ(2k) for k a positive integer between 1 and 13, infinite series and infinite product formulas, [ 32 ...
6 : impossible as the order of a projective plane, proved by Tarry who showed that Euler's thirty-six officers problem has no solution. However, the connection between these problems was not known until Bose proved it in 1938. [14] 7 : all isomorphic to PG(2, 7) 8 : all isomorphic to PG(2, 8)