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

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...

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...

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...

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

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

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

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

{\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...

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

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)...

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

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...

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...

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...

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...

{\displaystyle k} -dimensional vector subspace. This idea is very similar to the Gauss map for surfaces in a 3-dimensional space.) This can with some effort be extended...

Theorema Egregium is that the Earth cannot be displayed on a map without distortion. Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major...

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

at P. The vector field of normal directions to a surface is known as Gauss map. The word "normal" is also used as an adjective: a line normal to a plane...

degree of the map to the unit circle assigning to each point of the curve, the unit tangent vector at that point (a kind of Gauss map). This relationship...

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...

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...

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....

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...

w)=-\langle d\nu (v),w\rangle \nu } where ν {\displaystyle \nu } is the Gauss map, and d ν {\displaystyle d\nu } the differential of ν {\displaystyle \nu...

cylindrical map projection first presented by Flemish geographer and mapmaker Gerardus Mercator in 1569. In the 18th century, it became the standard map projection...

The Dymaxion map projection, also called the Fuller projection, is a kind of polyhedral map projection of the Earth's surface onto the unfolded net of...

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

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