In differential geometry, the Gauss map of a surface is a function that maps each point in the surface to a unit vector that is orthogonal to the surface...

In mathematics, the Gauss map (also known as Gaussian map or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian...

dictionary. Gauss map may refer to: The Gauss map, a mapping of the Euclidean space onto a sphere The Gauss iterated map, an iterated nonlinear map The function...

Riemannian geometry Gauss map in differential geometry Gaussian curvature, defined in his Theorema egregium Gauss circle problem Gauss–Kuzmin–Wirsing constant...

In mathematics, the Gauss–Kuzmin–Wirsing operator is the transfer operator of the Gauss map that takes a positive number to the fractional part of its...

Johann Carl Friedrich Gauss (German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] ; Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German mathematician...

than just a synonym for the ellipsoidal transverse Mercator map projection, the term Gauss–Krüger may be used in other slightly different ways: Sometimes...

{\displaystyle \gamma _{2}} . Also, a neighborhood of (s, t) is mapped under the Gauss map to a neighborhood of v preserving or reversing orientation depending...

mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that the...

pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi formulas) are...

the Gauss map must be preserved in such "turning"—in particular it follows that there is no such turning of S1 in R2. But the degrees of the Gauss map for...

differential dn of the Gauss map n can be used to define a type of extrinsic curvature, known as the shape operator or Weingarten map. This operator first...

parabolic line give rise to folds on the Gauss map: where a ridge crosses a parabolic line there is a cusp of the Gauss map. Ian R. Porteous (2001) Geometric...

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the...

Gauss map definition: A surface M ⊂ R 3 {\displaystyle M\subset \mathbb {R} ^{3}} is minimal if and only if its stereographically projected Gauss map...

Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813). Studies in the nineteenth century included those of Ernst Kummer (1836)...

differential geometry, the Osserman–Xavier–Fujimoto theorem concerns the Gauss maps of minimal surfaces in the three-dimensional Euclidean space. It says...

rhombic dodecahedron. The Gauss map of any convex polyhedron maps each face of the polygon to a point on the unit sphere, and maps each edge of the polygon...

of curves Gauss–Bonnet theorem for an elementary application of curvature Gauss map for more geometric properties of Gauss curvature Gauss's principle...

of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point. This map is similar to the Gauss map for surfaces...

vanish and to be linearly independent, and the resulting analog of the Gauss map is a map to the Stiefel manifold, or more generally between frame bundles....

Hsiang–Lawson's conjecture Theorema Egregium Gauss–Bonnet theorem Chern–Gauss–Bonnet theorem Chern–Weil homomorphism Gauss map Second fundamental form Curvature...

periodic orbits of the dyadic transformation (for the binary digits) and the Gauss map h ( x ) = 1 / x − ⌊ 1 / x ⌋ {\displaystyle h(x)=1/x-\lfloor 1/x\rfloor...

the complex plane is the Gauss–Kuzmin–Wirsing operator; it is the transfer operator of the Gauss map. That is, one considers maps ω ω → C {\displaystyle...

of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point. This map is similar to the Gauss map for surfaces...

zeroes of the old (and new) vector field is equal to the degree of the Gauss map from the boundary of Nε to the (n–1)-dimensional sphere. Thus, the sum...

sphere Celestial spheres Curvature Directional statistics Dyson sphere Gauss map Hand with Reflecting Sphere, M.C. Escher self-portrait drawing illustrating...

differential geometry. In his fundamental paper Gauss introduced the Gauss map, Gaussian curvature, first and second fundamental forms, proved the Theorema...

The Gall–Peters projection is a rectangular, equal-area map projection. Like all equal-area projections, it distorts most shapes. It is a cylindrical...

and so forth, because an equal-area map does not change apparent density of the phenomenon being mapped. By Gauss's Theorema Egregium, an equal-area projection...