one-to-one parametrization
11Rotation representation (mathematics) — In geometry a rotation representation expresses the orientation of an object (or coordinate frame) relative to a coordinate reference frame. This concept extends to classical mechanics where rotational (or angular) kinematics is the science of… …
12Shape optimization — is part of the field of optimal control theory. The typical problem is to find the shape which is optimal in that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being solved depends on the …
13Non-critical string theory: Lorentz invariance — Usually non critical string theory is considered in frames of the approach proposed by Polyakov [1]. The other approach has been developed in [2] [3] [4]. It represents a universal method to maintain explicit Lorentz invariance in any quantum… …
14Klein bottle — In mathematics, the Klein bottle is a certain non orientable surface, i.e. , a surface (a two dimensional manifold) with no distinct inner and outer sides. Other related non orientable objects include the Möbius strip and the real projective… …
15Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …
16Second fundamental form — In differential geometry, the second fundamental form is a quadratic form on the tangent plane of a smooth surface in the three dimensional Euclidean space, usually denoted by II. Together with the first fundamental form, it serves to define… …
17Line integral — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …
18Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …
19Möbius strip — This article is about the mathematical object. For musical group, see Mobius Band (band). A Möbius strip made with a piece of paper and tape. If an ant were to crawl along the length of this strip, it would return to its starting point having… …
20Roman surface — The Roman surface (so called because Jakob Steiner was in Rome when he thought of it) is a self intersecting mapping of the real projective plane into three dimensional space, with an unusually high degree of symmetry. The mapping is not an… …
