## Math | Geometry

# Riemann Surface

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#### Trigonometric Tables

In mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering. The calculation of mathematical tables was an important area of study, which led to the... More »

#### Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are... More »

#### Trigonometric Functions

In mathematics, the trigonometric functions are a set of functions which relate angles to the sides of a right triangle. There are many trigonometric functions, the 3 most common being sine, cosine, tangent, followed by cotangent, secant and cosecant. The last three are called reciprocal... More »

#### Inverse Trigonometric Functions

In mathematics, the inverse trigonometric functions (occasionally called cyclometric functions) are the inverse functions of the trigonometric functions with suitably restricted domains. They are the inverse sine, cosine, tangent, cosecant, secant and cotangent functions. They are used for computing... More »

#### Trigonometry

Trigonometry (from the Greek trigonon = three angles and metro = measure) is a part of elementary mathematics dealing with angles, triangles and trigonometric functions such as sine (abbreviated sin), cosine (abbreviated cos) and tangent (abbreviated tan).
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#### Solid Geometry

In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. It was developed following the development of plane geometry.
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#### Quantum Geometry

In theoretical physics, quantum geometry is the set of new mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at very short distance scales (comparable to Planck length).
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#### Projective Geometry

In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts.
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#### Hyperbolic Geometry

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced.
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#### Finite Geometry

A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the... More »

#### Non-Euclidean Geometry

Non-Euclidean geometry is a type of geometry. Non-Euclidean geometry only uses some of the "postulates" (assumptions) that Euclidean geometry is based on. In normal geometry, parallel lines can never meet. In non-Euclidean geometry they can meet, either once (elliptic geometry), or... More »

#### Discrete Geometry

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles,... More »

#### Convex Geometry

Convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming,... More »

#### Euclidean Geometry

Euclidean geometry is a system in mathematics. People think Euclid was the first person who described it; therefore, it bears his name. He first described it in his textbook Elements. The book was the first systematic discussion of geometry as it was known at the time. In the book, Euclid first... More »

#### Tensor

Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples of such relations include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors.
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#### Riemannian Geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives, in particular, local notions of angle, length... More »

#### Riemannian Manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real smooth manifold...
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#### Lie Group

In mathematics, a Lie group /?li?/ is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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#### Differential Geometry of Surfaces

In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric.
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#### Differential Geometry of Curves

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.
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#### Differential Geometry

Differential geometry is a field of mathematics. It uses differential and integral calculus as well as linear algebra to study problems of geometry. The theory of the plane, as well as curves and surfaces in Euclidean space are the basis of this study.
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#### Computational Geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational... More »

#### Analytic Geometry

In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.
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#### Algebraic Geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry.
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#### Affine Geometry

In mathematics, affine geometry is the study of parallel lines.
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