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- Euler's_theorem_(differential_geometry) abstract "In the mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which give the directions in which the surface curves the most and the least. The theorem is named for Leonhard Euler who proved the theorem in (Euler 1760).More precisely, let M be a surface in three-dimensional Euclidean space, and p a point on M. A normal plane through p is a plane passing through the point p containing the normal vector to M. Through each (unit) tangent vector to M at p, there passes a normal plane PX which cuts out a curve in M. That curve has a certain curvature κX when regarded as a curve inside PX. Provided not all κX are equal, there is some unit vector X1 for which k1 = κX1 is as large as possible, and another unit vector X2 for which k2 = κX2 is as small as possible. Euler's theorem asserts that X1 and X2 are perpendicular and that, moreover, if X is any vector making an angle θ with X1, then</dl>The quantities k1 and k2 are called the principal curvatures, and X1 and X2 are the corresponding principal directions. Equation (1) is sometimes called Euler's equation (Eisenhart 2004, p. 124).".
- Euler's_theorem_(differential_geometry) wikiPageExternalLink E333.html.
- Euler's_theorem_(differential_geometry) wikiPageExternalLink treatonthediffer00eiserich.
- Euler's_theorem_(differential_geometry) wikiPageID "18753256".
- Euler's_theorem_(differential_geometry) wikiPageRevisionID "583839260".
- Euler's_theorem_(differential_geometry) hasPhotoCollection Euler's_theorem_(differential_geometry).
- Euler's_theorem_(differential_geometry) subject Category:Differential_geometry_of_surfaces.
- Euler's_theorem_(differential_geometry) subject Category:Theorems_in_differential_geometry.
- Euler's_theorem_(differential_geometry) type Abstraction100002137.
- Euler's_theorem_(differential_geometry) type Communication100033020.
- Euler's_theorem_(differential_geometry) type Message106598915.
- Euler's_theorem_(differential_geometry) type Proposition106750804.
- Euler's_theorem_(differential_geometry) type Statement106722453.
- Euler's_theorem_(differential_geometry) type Theorem106752293.
- Euler's_theorem_(differential_geometry) type TheoremsInDifferentialGeometry.
- Euler's_theorem_(differential_geometry) comment "In the mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which give the directions in which the surface curves the most and the least. The theorem is named for Leonhard Euler who proved the theorem in (Euler 1760).More precisely, let M be a surface in three-dimensional Euclidean space, and p a point on M.".
- Euler's_theorem_(differential_geometry) label "Euler's theorem (differential geometry)".
- Euler's_theorem_(differential_geometry) label "Théorème d'Euler (courbure des surfaces)".
- Euler's_theorem_(differential_geometry) label "オイラーの定理 (微分幾何学)".
- Euler's_theorem_(differential_geometry) sameAs Théorème_d'Euler_(courbure_des_surfaces).
- Euler's_theorem_(differential_geometry) sameAs オイラーの定理_(微分幾何学).
- Euler's_theorem_(differential_geometry) sameAs m.04grzfm.
- Euler's_theorem_(differential_geometry) sameAs Q3526990.
- Euler's_theorem_(differential_geometry) sameAs Q3526990.
- Euler's_theorem_(differential_geometry) sameAs Euler's_theorem_(differential_geometry).
- Euler's_theorem_(differential_geometry) wasDerivedFrom Euler's_theorem_(differential_geometry)?oldid=583839260.
- Euler's_theorem_(differential_geometry) isPrimaryTopicOf Euler's_theorem_(differential_geometry).