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Krzywizna Gaussa Odwołuje się do iloczynu maksymalnej krzywizny i minimalnej krzywizny płaskiej krzywej, gdy krzywa jest wycinana w płaszczyźnie zawierającej jedną oś prostopadłą do płaszczyzny w punkcie krzywej. Jest również nazywana całkowitą krzywizną i jest niezmienna z transformacją izotropową. 가우스곡률
곡면의 한 점에서 면과 수직인 한 축을 포함하는 평면으로 곡선을 잘랐을 때 나타나는 평면곡선의 최대곡률과 최소곡률의 곱을 말한다. 전곡률이라고도 하며, 등장변환으로 불변이다.
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1
비숍 살인 사건: 열린책들 세계문학 181
드러커가 그의 책에서 구체와 하마로이드 공간 [37] 의 가우스 곡률을 정의 하기 위해 이 공식을 사용했지.... 그런데 스프리그가 이걸로 뭘 하고 있었던 걸까? 이 공식은 대학 교육 과정을 훨씬 넘어서 는 수준인데....」 그는 종이를 들고 햇빛에 비추어 ...
2
Differential Geometry and Its Applications - 123페이지
A constant negative curvature surface of revolution revolution M have constant Gauss curvature K = — 1 . We can suppose also that M is parametrized by x(u, v) = (g(u),h(u) cosu, h(u) sin v) with g'{u)2 +h'(u )2 = 1 (i.e., the profile curve is unit ...
3
Discrete Differential Geometry - 180페이지
Gauss curvature It is well known how the notion of Gauss curvature extends to such discrete surfaces M. (Banchoff [Ban67, Ban70] was probably the first to discuss this in detail, though he notes that Hilbert and Cohn-Vossen [HCV32, 29] had ...
Alexander I. Bobenko, Peter Schröder, John M. Sullivan, 2008
4
Mean Curvature Flow and Isoperimetric Inequalities - 70페이지
Until recently, the isoperimetric regions were not known in surfaces of variable curvature. In 1996, Benjamini and Cao [15] characterized the isoperimetric regions in planes of revolution with non-increasing Gauss curvature as a function of the ...
Manuel Ritoré, Vicente Miquel, Carlo Sinestrari, 2010
5
Curvature in Mathematics and Physics
Gauss's. theorema. egregium. One of the greatest, if not the greatest, achievements of the human mind was Einstein's ... in 1915, which posited that the gravitational force is due to the “curvature of space time” and that particles move along ...
6
Geometry of Manifolds with Non-negative Sectional ... - 1페이지
1. History. and. Obstructions. It is fair to say that Riemannian geometry started with Gauss's famous “Disquisitiones generales” from 1827 in which one finds a rigorous discussion of what we now call the Gauss curvature of a surface. Much has ...
Owen Dearricott, Fernando Galaz-Garcia, Lee Kennard, 2014
7
50th IMO - 50 Years of International Mathematical Olympiads - 25페이지
domains where the surface has a saddle, the Gauss map changes orientation, and thus the Gaussian curvature is negative. Note that this definition of the Gaussian curvature depends on howS is embedded in R3. One of Gauss' key results is ...
Hans-Dietrich Gronau, Hanns-Heinrich Langmann, Dierk Schleicher, 2011
8
Total Mean Curvature and Submanifolds of Finite Type - 182페이지
TOTAL MKAN CURVATURE }1. Some Results Concerning Surfaces in R For surfaces in R , the two most important geometric invariants are the Gauss curvature G and the mean curvature. According to Gauss ' Theorema Egregium, the Gauss ...
9
Curves and Surfaces - 172페이지
For example, can one characterize compact surfaces with constant Gauss or mean curvature? We first consider the Gauss curvature. The local geometry of surfaces with constant Gauss curvature was studied by F. Minding in 1838, with ...
Sebastián Montiel, Antonio Ros, Donald G. Babbitt, 2009
10
The Geometry of the Generalized Gauss Map - 236호 - 66페이지
MINIMAL SURFACES WHOSE GAUSSIAN IMAGES HAVE CONSTANT CURVATURE. Given a minimal surface S defined by a map X: M ->- N we again denote 90 *) by S the image of S under the Gauss map g . The metrics ds =X dw| 9 - o o ...
David A. Hoffman, Robert Osserman, 1980
