Geometry, the Glossary
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.[1]
Table of Contents
345 relations: Acceleration, Aerodynamics, Affine geometry, Affine space, Al-Mahani, Albert Einstein, Alexander Grothendieck, Alfred North Whitehead, Algebra, Algebraic curve, Algebraic equation, Algebraic geometry, Algebraic topology, Algebraic variety, Algorithm, Analytic geometry, Ancient Egypt, Ancient Egyptian mathematics, Ancient Greece, Angle, Archimedean spiral, Archimedes, Architecture, Area, Arithmetic, Artin–Tits group, Aryabhata, Aryabhatiya, Astronomy, Axiom, Axiomatic system, Babylonian mathematics, Bakhshali manuscript, Ball (mathematics), Basil Blackwell, Bernhard Riemann, Bible, Bioinformatics, Book of Optics, Brahmagupta, Brāhmasphuṭasiddhānta, Calabi–Yau manifold, Calculus, Cambridge University Press, Carl Friedrich Gauss, Cayley graph, Celestial sphere, Circle, Classical mechanics, Coherent sheaf, ... Expand index (295 more) »
Acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time.
Aerodynamics
Aerodynamics (ἀήρ aero (air) + δυναμική (dynamics)) is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing.
Affine geometry
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance and angle.
See Geometry and Affine geometry
Affine space
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.
Al-Mahani
Abu-Abdullah Muhammad ibn Īsa Māhānī (ابوعبدالله محمد بن عیسی ماهانی, flourished c. 860 and died c. 880) was a Persian mathematician and astronomer born in Mahan, (in today Kermān, Iran) and active in Baghdad, Abbasid Caliphate.
Albert Einstein
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who is widely held as one of the most influential scientists. Best known for developing the theory of relativity, Einstein also made important contributions to quantum mechanics. His mass–energy equivalence formula, which arises from relativity theory, has been called "the world's most famous equation".
See Geometry and Albert Einstein
Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born mathematician who became the leading figure in the creation of modern algebraic geometry.
See Geometry and Alexander Grothendieck
Alfred North Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.
See Geometry and Alfred North Whitehead
Algebra
Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures.
Algebraic curve
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables.
See Geometry and Algebraic curve
Algebraic equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form P.
See Geometry and Algebraic equation
Algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.
See Geometry and Algebraic geometry
Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
See Geometry and Algebraic topology
Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics.
See Geometry and Algebraic variety
Algorithm
In mathematics and computer science, an algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation.
Analytic geometry
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
See Geometry and Analytic geometry
Ancient Egypt
Ancient Egypt was a civilization of ancient Northeast Africa.
See Geometry and Ancient Egypt
Ancient Egyptian mathematics
Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c., from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt.
See Geometry and Ancient Egyptian mathematics
Ancient Greece
Ancient Greece (Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity, that comprised a loose collection of culturally and linguistically related city-states and other territories.
See Geometry and Ancient Greece
Angle
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Archimedean spiral
The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes.
See Geometry and Archimedean spiral
Archimedes
Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily.
Architecture
Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction.
Area
Area is the measure of a region's size on a surface.
Arithmetic
Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division.
Artin–Tits group
In the mathematical area of group theory, Artin groups, also known as Artin–Tits groups or generalized braid groups, are a family of infinite discrete groups defined by simple presentations.
See Geometry and Artin–Tits group
Aryabhata
Aryabhata (ISO) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.
Aryabhatiya
Aryabhatiya (IAST) or Aryabhatiyam, a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.
Astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos.
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
Axiomatic system
In mathematics and logic, an axiomatic system is any set of primitive notions and axioms to logically derive theorems.
See Geometry and Axiomatic system
Babylonian mathematics
Babylonian mathematics (also known as Assyro-Babylonian mathematics) is the mathematics developed or practiced by the people of Mesopotamia, as attested by sources mainly surviving from the Old Babylonian period (1830–1531 BC) to the Seleucid from the last three or four centuries BC.
See Geometry and Babylonian mathematics
Bakhshali manuscript
The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan, historical Gandhara).
See Geometry and Bakhshali manuscript
Ball (mathematics)
In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere.
See Geometry and Ball (mathematics)
Basil Blackwell
Sir Basil Henry Blackwell (29 May 18899 April 1984) was born in Oxford, England.
See Geometry and Basil Blackwell
Bernhard Riemann
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry.
See Geometry and Bernhard Riemann
Bible
The Bible (from Koine Greek τὰ βιβλία,, 'the books') is a collection of religious texts or scriptures, some, all, or a variant of which are held to be sacred in Christianity, Judaism, Samaritanism, Islam, the Baha'i Faith, and other Abrahamic religions.
Bioinformatics
Bioinformatics is an interdisciplinary field of science that develops methods and software tools for understanding biological data, especially when the data sets are large and complex.
See Geometry and Bioinformatics
Book of Optics
The Book of Optics (Kitāb al-Manāẓir; De Aspectibus or Perspectiva; Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al-Haytham, known in the West as Alhazen or Alhacen (965–c. 1040 AD).
See Geometry and Book of Optics
Brahmagupta
Brahmagupta (–) was an Indian mathematician and astronomer.
Brāhmasphuṭasiddhānta
The Brāhma-sphuṭa-siddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is a main work of Brahmagupta, written c. 628.
See Geometry and Brāhmasphuṭasiddhānta
Calabi–Yau manifold
In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics.
See Geometry and Calabi–Yau manifold
Calculus
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge.
See Geometry and Cambridge University Press
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist who contributed to many fields in mathematics and science.
See Geometry and Carl Friedrich Gauss
Cayley graph
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract structure of a group.
Celestial sphere
In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth.
See Geometry and Celestial sphere
Circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Classical mechanics
Classical mechanics is a physical theory describing the motion of objects such as projectiles, parts of machinery, spacecraft, planets, stars, and galaxies.
See Geometry and Classical mechanics
Coherent sheaf
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space.
See Geometry and Coherent sheaf
Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex.
Collineation
In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear.
Combinatorics
Combinatorics is an area of mathematics primarily concerned with the counting, selecting and arranging of objects, both as a means and as an end in itself.
See Geometry and Combinatorics
Commutative algebra
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
See Geometry and Commutative algebra
Compact space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.
See Geometry and Compact space
Compactness measure
Compactness measure is a numerical quantity representing the degree to which a shape is compact.
See Geometry and Compactness measure
A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs.
See Geometry and Compass (drawing tool)
Complex algebraic variety
In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers.
See Geometry and Complex algebraic variety
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
See Geometry and Complex analysis
Complex analytic variety
In mathematics, and in particular differential geometry and complex geometry, a complex analytic varietyComplex analytic variety (or just variety) is sometimes required to be irreducible and reduced or complex analytic space is a generalization of a complex manifold that allows the presence of singularities.
See Geometry and Complex analytic variety
Complex geometry
In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.
See Geometry and Complex geometry
Complex manifold
In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in the complex coordinate space \mathbb^n, such that the transition maps are holomorphic.
See Geometry and Complex manifold
Complex plane
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, called the imaginary axis, is formed by the imaginary numbers.
See Geometry and Complex plane
Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.
See Geometry and Computational geometry
Computer vision
Computer vision tasks include methods for acquiring, processing, analyzing and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, e.g. in the forms of decisions.
See Geometry and Computer vision
Computer-aided design
Computer-aided design (CAD) is the use of computers to aid in the creation, modification, analysis, or optimization of a design.
See Geometry and Computer-aided design
Cone
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
Configuration space (physics)
In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the space defined by these coordinates is called the configuration space of the physical system.
See Geometry and Configuration space (physics)
Congruence (geometry)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
See Geometry and Congruence (geometry)
Conic section
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.
See Geometry and Conic section
Connectedness
In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece".
See Geometry and Connectedness
Construction
Construction is a general term meaning the art and science of forming objects, systems, or organizations.
Continuous function
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.
See Geometry and Continuous function
Convex analysis
Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory.
See Geometry and Convex analysis
Convex geometry
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.
See Geometry and Convex geometry
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n.
See Geometry and Convex polytope
Convex set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them.
Coordinate system
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
See Geometry and Coordinate system
Cryptography
Cryptography, or cryptology (from κρυπτός|translit.
Crystallography
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties.
See Geometry and Crystallography
Cubic equation
In algebra, a cubic equation in one variable is an equation of the form ax^3+bx^2+cx+d.
See Geometry and Cubic equation
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.
Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
Cyclic quadrilateral
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.
See Geometry and Cyclic quadrilateral
Cylinder
A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of his time.
See Geometry and David Hilbert
Deformation (physics)
In physics and continuum mechanics, deformation is the change in the shape or size of an object.
See Geometry and Deformation (physics)
Degrees of freedom
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently.
See Geometry and Degrees of freedom
Derivative
The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input.
Descriptive geometry
Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures.
See Geometry and Descriptive geometry
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of differentiable manifolds.
See Geometry and Diffeomorphism
Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus.
See Geometry and Differentiable manifold
Differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
See Geometry and Differential geometry
Differential topology
In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds.
See Geometry and Differential topology
Digital image processing
Digital image processing is the use of a digital computer to process digital images through an algorithm.
See Geometry and Digital image processing
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
Dimension of an algebraic variety
In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways.
See Geometry and Dimension of an algebraic variety
Diophantine equation
In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, for which only integer solutions are of interest.
See Geometry and Diophantine equation
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.
See Geometry and Discrete geometry
Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
See Geometry and Discrete mathematics
Displacement (geometry)
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion.
See Geometry and Displacement (geometry)
Distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are.
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker.
See Geometry and Dover Publications
Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
Duality (projective geometry)
In projective geometry, duality or plane duality is a formalization of the striking symmetry of the roles played by points and lines in the definitions and theorems of projective planes.
See Geometry and Duality (projective geometry)
Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve.
See Geometry and Dynamical system
Econometrics
Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships.
Edwin Abbott Abbott
Edwin Abbott Abbott (20 December 1838 – 12 October 1926) was an English schoolmaster, theologian, and Anglican priest, best known as the author of the novella Flatland (1884).
See Geometry and Edwin Abbott Abbott
Element (mathematics)
In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set.
See Geometry and Element (mathematics)
Elementary arithmetic
Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division.
See Geometry and Elementary arithmetic
Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
Encyclopedia of the History of Arabic Science
The Encyclopedia of the History of Arabic Science is a three-volume encyclopedia covering the history of Arabic contributions to science, mathematics and technology which had a marked influence on the Middle Ages in Europe.
See Geometry and Encyclopedia of the History of Arabic Science
Engineering
Engineering is the practice of using natural science, mathematics, and the engineering design process to solve technical problems, increase efficiency and productivity, and improve systems.
Equation
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign.
Erlangen program
In mathematics, the Erlangen program is a method of characterizing geometries based on group theory and projective geometry.
See Geometry and Erlangen program
Euclid
Euclid (Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician.
Euclid's Elements
The Elements (Στοιχεῖα) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid 300 BC.
See Geometry and Euclid's Elements
Euclidean distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them.
See Geometry and Euclidean distance
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.
See Geometry and Euclidean geometry
Euclidean plane
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.
See Geometry and Euclidean plane
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space.
See Geometry and Euclidean space
Eudoxus of Cnidus
Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios) was an ancient Greek astronomer, mathematician, doctor, and lawmaker.
See Geometry and Eudoxus of Cnidus
Felix Klein
Felix Christian Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations between geometry and group theory.
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than.
See Geometry and Fermat's Last Theorem
Finite geometry
A finite geometry is any geometric system that has only a finite number of points.
See Geometry and Finite geometry
Finitely generated group
In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of S and of inverses of such elements.
See Geometry and Finitely generated group
Flatland
Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London.
Force
A force is an influence that can cause an object to change its velocity, i.e., to accelerate, meaning a change in speed or direction, unless counterbalanced by other forces.
Forced perspective
Forced perspective is a technique that employs optical illusion to make an object appear farther away, closer, larger or smaller than it actually is.
See Geometry and Forced perspective
Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension.
Frustum
In geometry, a morsel; (frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid.
Function of several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space \mathbb C^n, that is, -tuples of complex numbers.
See Geometry and Function of several complex variables
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures.
See Geometry and Functional analysis
Gaussian curvature
In differential geometry, the Gaussian curvature or Gauss curvature of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, and, at the given point: K.
See Geometry and Gaussian curvature
General relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics.
See Geometry and General relativity
General topology
In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
See Geometry and General topology
Geodesic
In geometry, a geodesic is a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold.
Geodesy
Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D.
Geometric group theory
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).
See Geometry and Geometric group theory
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
See Geometry and Geometric topology
Geometric transformation
In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning.
See Geometry and Geometric transformation
Geometrization conjecture
In mathematics, Thurston's geometrization conjecture (now a theorem) states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it.
See Geometry and Geometrization conjecture
Geometry of numbers
Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers.
See Geometry and Geometry of numbers
Gersonides
Levi ben Gershon (1288 – 20 April 1344), better known by his Graecized name as Gersonides, or by his Latinized name Magister Leo Hebraeus, or in Hebrew by the abbreviation of first letters as RaLBaG, was a medieval French Jewish philosopher, Talmudist, mathematician, physician and astronomer/astrologer.
Giovanni Girolamo Saccheri
Giovanni Girolamo Saccheri (5 September 1667 – 25 October 1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician.
See Geometry and Giovanni Girolamo Saccheri
Girard Desargues
Girard Desargues (21 February 1591September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry.
See Geometry and Girard Desargues
Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
Greek mathematics
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the 5th century BC to the 6th century AD, around the shores of the Mediterranean.
See Geometry and Greek mathematics
Gresham College
Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England.
See Geometry and Gresham College
Grigori Perelman
Grigori Yakovlevich Perelman (a; born 13 June 1966) is a Russian mathematician who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology.
See Geometry and Grigori Perelman
Group (mathematics)
In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.
See Geometry and Group (mathematics)
Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician.
See Geometry and Harold Scott MacDonald Coxeter
Henri Poincaré
Jules Henri Poincaré (29 April 185417 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
See Geometry and Henri Poincaré
Heron's formula
In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths Letting be the semiperimeter of the triangle, s.
See Geometry and Heron's formula
In 3D computer graphics, solid objects are usually modeled by polyhedra.
See Geometry and Hidden-line removal
Hilbert space
In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional.
See Geometry and Hilbert space
Hilbert's Nullstellensatz
In mathematics, Hilbert's Nullstellensatz (German for "theorem of zeros", or more literally, "zero-locus-theorem") is a theorem that establishes a fundamental relationship between geometry and algebra.
See Geometry and Hilbert's Nullstellensatz
Hodge conjecture
In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties.
See Geometry and Hodge conjecture
Holomorphic vector bundle
In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold such that the total space is a complex manifold and the projection map is holomorphic.
See Geometry and Holomorphic vector bundle
Homeomorphism
In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
See Geometry and Homeomorphism
Howard Eves
Howard Whitley Eves (10 January 1911, New Jersey – 6 June 2004) was an American mathematician, known for his work in geometry and the history of mathematics.
Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry.
See Geometry and Hyperbolic geometry
Hyperbolic group
In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry.
See Geometry and Hyperbolic group
Hyperbolic manifold
In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension.
See Geometry and Hyperbolic manifold
Ibn al-Haytham
Ḥasan Ibn al-Haytham (Latinized as Alhazen;; full name أبو علي، الحسن بن الحسن بن الهيثم) was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.
See Geometry and Ibn al-Haytham
Ideal (ring theory)
In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements.
See Geometry and Ideal (ring theory)
Implementation
Implementation is the realization of an application, execution of a plan, idea, model, design, specification, standard, algorithm, policy, or the administration or management of a process or objective.
See Geometry and Implementation
Incidence geometry
In mathematics, incidence geometry is the study of incidence structures.
See Geometry and Incidence geometry
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century.
See Geometry and Indian mathematics
Integer triangle
An integer triangle or integral triangle is a triangle all of whose side lengths are integers.
See Geometry and Integer triangle
Integral
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations.
Irrational number
In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers.
See Geometry and Irrational number
Islamic art
Islamic art is a part of Islamic culture and encompasses the visual arts produced since the 7th century CE by people who lived within territories inhabited or ruled by Muslim populations.
Isoperimetric inequality
In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume.
See Geometry and Isoperimetric inequality
Italian school of algebraic geometry
In relation to the history of mathematics, the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry, particularly on algebraic surfaces, centered around Rome roughly from 1885 to 1935.
See Geometry and Italian school of algebraic geometry
James Stewart (mathematician)
James Drewry Stewart, (March 29, 1941December 3, 2014) was a Canadian mathematician, violinist, and professor emeritus of mathematics at McMaster University.
See Geometry and James Stewart (mathematician)
Jay Kappraff
Jay Kappraff was an American professor of mathematics at the New Jersey Institute of Technology and author.
János Bolyai
János Bolyai (15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry.
Jean-Pierre Serre
Jean-Pierre Serre (born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory.
See Geometry and Jean-Pierre Serre
Johannes Kepler
Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music.
See Geometry and Johannes Kepler
John Wallis
John Wallis (Wallisius) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus.
Johns Hopkins University Press
Johns Hopkins University Press (also referred to as JHU Press or JHUP) is the publishing division of Johns Hopkins University.
See Geometry and Johns Hopkins University Press
Khan Academy
Khan Academy is an American non-profit educational organization created in 2006 by Sal Khan.
Lambert quadrilateral
In geometry, a Lambert quadrilateral (also known as Ibn al-Haytham–Lambert quadrilateral), is a quadrilateral in which three of its angles are right angles.
See Geometry and Lambert quadrilateral
Latin
Latin (lingua Latina,, or Latinum) is a classical language belonging to the Italic branch of the Indo-European languages.
Lattice (group)
In geometry and group theory, a lattice in the real coordinate space \mathbb^n is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
See Geometry and Lattice (group)
Lebesgue integral
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the axis.
See Geometry and Lebesgue integral
Length
Length is a measure of distance.
Leonard Mlodinow
Leonard Mlodinow (born November 26 1954) is an American theoretical physicist and mathematician, screenwriter and author.
See Geometry and Leonard Mlodinow
Leonardo da Vinci
Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
See Geometry and Leonardo da Vinci
Lexico
Lexico was a dictionary website that provided a collection of English and Spanish dictionaries produced by Oxford University Press (OUP), the publishing house of the University of Oxford.
Lie theory
In mathematics, the mathematician Sophus Lie initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory.
Line (geometry)
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light.
See Geometry and Line (geometry)
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices.
See Geometry and Linear algebra
Linear equation
In mathematics, a linear equation is an equation that may be put in the form a_1x_1+\ldots+a_nx_n+b.
See Geometry and Linear equation
Linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships.
See Geometry and Linear programming
In mathematics, the terms continuity, continuous, and continuum are used in a variety of related ways.
See Geometry and List of continuity-related mathematical topics
List of formulas in elementary geometry
This is a short list of some common mathematical shapes and figures and the formulas that describe them.
See Geometry and List of formulas in elementary geometry
List of geometers
A geometer is a mathematician whose area of study is geometry.
See Geometry and List of geometers
List of interactive geometry software
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry.
See Geometry and List of interactive geometry software
Lists of mathematics topics
Lists of mathematics topics cover a variety of topics related to mathematics.
See Geometry and Lists of mathematics topics
Low-dimensional topology
In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions.
See Geometry and Low-dimensional topology
M. C. Escher
Maurits Cornelis Escher (17 June 1898 – 27 March 1972) was a Dutch graphic artist who made woodcuts, lithographs, and mezzotints, many of which were inspired by mathematics.
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
Mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
See Geometry and Mathematical analysis
Mathematical optimization
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives.
See Geometry and Mathematical optimization
Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
See Geometry and Mathematical physics
Mathematical structure
In mathematics, a structure is a set provided with some additional features on the set (e.g. an operation, relation, metric, or topology).
See Geometry and Mathematical structure
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Mathematics in the medieval Islamic world
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built upon syntheses of Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).
See Geometry and Mathematics in the medieval Islamic world
Mean speed theorem
The mean speed theorem, also known as the Merton rule of uniform acceleration, was discovered in the 14th century by the Oxford Calculators of Merton College, and was proved by Nicole Oresme.
See Geometry and Mean speed theorem
Measure (mathematics)
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.
See Geometry and Measure (mathematics)
Mechanics
Mechanics (from Ancient Greek: μηχανική, mēkhanikḗ, "of machines") is the area of physics concerned with the relationships between force, matter, and motion among physical objects.
Medical imaging
Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology).
See Geometry and Medical imaging
Mesopotamia
Mesopotamia is a historical region of West Asia situated within the Tigris–Euphrates river system, in the northern part of the Fertile Crescent.
Method of exhaustion
The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.
See Geometry and Method of exhaustion
Metric space
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points.
Michelangelo
Michelangelo di Lodovico Buonarroti Simoni (6 March 1475 – 18 February 1564), known mononymously as Michelangelo, was an Italian sculptor, painter, architect, and poet of the High Renaissance.
Middle Ages
In the history of Europe, the Middle Ages or medieval period (also spelt mediaeval or mediæval) lasted from approximately 500 to 1500 AD.
Millennium Prize Problems
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000.
See Geometry and Millennium Prize Problems
Minimum spanning tree
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.
See Geometry and Minimum spanning tree
Mirror symmetry (string theory)
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds.
See Geometry and Mirror symmetry (string theory)
Model
A model is an informative representation of an object, person or system.
Molecular geometry
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule.
See Geometry and Molecular geometry
Moscow Mathematical Papyrus
The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra.
See Geometry and Moscow Mathematical Papyrus
Nasir al-Din al-Tusi
Muhammad ibn Muhammad ibn al-Hasan al-Tusi (1201 – 1274), also known as Nasir al-Din al-Tusi (نصیر الدین الطوسی; نصیر الدین طوسی) or simply as (al-)Tusi, was a Persian polymath, architect, philosopher, physician, scientist, and theologian.
See Geometry and Nasir al-Din al-Tusi
Natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.
See Geometry and Natural number
Navigation
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.
Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
See Geometry and Neighbourhood (mathematics)
Neusis construction
In geometry, the neusis (νεῦσις;; plural: label) is a geometric construction method that was used in antiquity by Greek mathematicians.
See Geometry and Neusis construction
Nikolai Lobachevsky
Nikolai Ivanovich Lobachevsky (a; –) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, known as the Lobachevsky integral formula.
See Geometry and Nikolai Lobachevsky
Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.
See Geometry and Non-Euclidean geometry
Nubia
Nubia (Nobiin: Nobīn) is a region along the Nile river encompassing the area between the first cataract of the Nile (south of Aswan in southern Egypt) and the confluence of the Blue and White Niles (in Khartoum in central Sudan), or more strictly, Al Dabbah.
Number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.
See Geometry and Number theory
Omar Khayyam
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīsābūrī (18 May 1048 – 4 December 1131), commonly known as Omar Khayyam (عمر خیّام), was a Persian polymath, known for his contributions to mathematics, astronomy, philosophy, and poetry.
Outline of geometry
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
See Geometry and Outline of geometry
Oxford Calculators
The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford; for this reason they were dubbed "The Merton School".
See Geometry and Oxford Calculators
Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
Parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.
See Geometry and Parallel postulate
Paul Cézanne
Paul Cézanne (19 January 1839 – 22 October 1906) was a French Post-Impressionist painter whose work introduced new modes of representation and influenced avant-garde artistic movements of the early 20th century.
Perspective (graphical)
Linear or point-projection perspective is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection.
See Geometry and Perspective (graphical)
Physics
Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.
Pi
The number (spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.
See Geometry and Pi
Pierre de Fermat
Pierre de Fermat (between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.
See Geometry and Pierre de Fermat
Plane (mathematics)
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely.
See Geometry and Plane (mathematics)
Plane curve
In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane.
Planet
A planet is a large, rounded astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself.
Plato
Plato (Greek: Πλάτων), born Aristocles (Ἀριστοκλῆς; – 348 BC), was an ancient Greek philosopher of the Classical period who is considered a foundational thinker in Western philosophy and an innovator of the written dialogue and dialectic forms.
Platonic solid
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.
See Geometry and Platonic solid
Plimpton 322
Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics.
Poincaré conjecture
In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
See Geometry and Poincaré conjecture
Point (geometry)
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces.
See Geometry and Point (geometry)
Polygon
In geometry, a polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
Polynomial
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.
Polynomial ring
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
See Geometry and Polynomial ring
Position (geometry)
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space.
See Geometry and Position (geometry)
Projection (linear algebra)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P.
See Geometry and Projection (linear algebra)
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.
See Geometry and Projective geometry
Proportionality (mathematics)
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.
See Geometry and Proportionality (mathematics)
Pseudo-Riemannian manifold
In mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate.
See Geometry and Pseudo-Riemannian manifold
Pythagoras
Pythagoras of Samos (Πυθαγόρας; BC) was an ancient Ionian Greek philosopher, polymath and the eponymous founder of Pythagoreanism.
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
See Geometry and Pythagorean theorem
Pythagorean triple
A Pythagorean triple consists of three positive integers,, and, such that.
See Geometry and Pythagorean triple
Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans.
See Geometry and Pythagoreanism
Quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices).
See Geometry and Quadrilateral
Quantum information
Quantum information is the information of the state of a quantum system.
See Geometry and Quantum information
Quasi-isometry
In mathematics, a quasi-isometry is a function between two metric spaces that respects large-scale geometry of these spaces and ignores their small-scale details.
See Geometry and Quasi-isometry
Ratio
In mathematics, a ratio shows how many times one number contains another.
Real analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions.
See Geometry and Real analysis
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
Regular polygon
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
See Geometry and Regular polygon
René Descartes
René Descartes (or;; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science.
See Geometry and René Descartes
Rhind Mathematical Papyrus
The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057, pBM 10058, and Brooklyn Museum 37.1784Ea-b) is one of the best known examples of ancient Egyptian mathematics.
See Geometry and Rhind Mathematical Papyrus
Riemann integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.
See Geometry and Riemann integral
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold.
See Geometry and Riemann surface
Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point).
See Geometry and Riemannian geometry
Riemannian manifold
In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined.
See Geometry and Riemannian manifold
Rigour
Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness.
Routledge
Routledge is a British multinational publisher.
Ruler
A ruler, sometimes called a rule, scale or a line gauge, is an instrument used to make length measurements, whereby a user estimates a length by reading from a series of markings called "rules" along an edge of the device.
Saccheri quadrilateral
A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base.
See Geometry and Saccheri quadrilateral
Sanskrit
Sanskrit (attributively संस्कृत-,; nominally संस्कृतम्) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages.
Scheme (mathematics)
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.
See Geometry and Scheme (mathematics)
Section (fiber bundle)
In the mathematical field of topology, a section (or cross section) of a fiber bundle E is a continuous right inverse of the projection function \pi.
See Geometry and Section (fiber bundle)
Series (mathematics)
In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
See Geometry and Series (mathematics)
Set (mathematics)
In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
See Geometry and Set (mathematics)
Shatapatha Brahmana
The Shatapatha Brahmana (lit,, abbreviated to 'SB') is a commentary on the Śukla Yajurveda.
See Geometry and Shatapatha Brahmana
Sheaf (mathematics)
In mathematics, a sheaf (sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them.
See Geometry and Sheaf (mathematics)
Shing-Tung Yau
Shing-Tung Yau (born April 4, 1949) is a Chinese-American mathematician.
See Geometry and Shing-Tung Yau
Shulba Sutras
The Shulva Sutras or Śulbasūtras (Sanskrit: शुल्बसूत्र;: "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction.
See Geometry and Shulba Sutras
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.
See Geometry and Similarity (geometry)
Solid geometry
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space).
See Geometry and Solid geometry
Sophus Lie
Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician.
Space
Space is a three-dimensional continuum containing positions and directions.
Space (mathematics)
In mathematics, a space is a set (sometimes known as a universe) with a definition (structure) of relationships among the elements of the set.
See Geometry and Space (mathematics)
Spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
Special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time.
See Geometry and Special relativity
Sphere
A sphere (from Greek) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.
Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
See Geometry and Sphere packing
Spherical geometry
A sphere with a spherical triangle on it. Spherical geometry or spherics is the geometry of the two-dimensional surface of a sphere or the -dimensional surface of higher dimensional spheres.
See Geometry and Spherical geometry
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
See Geometry and Springer Science+Business Media
Stack (mathematics)
In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets.
See Geometry and Stack (mathematics)
Star
A star is a luminous spheroid of plasma held together by self-gravity.
String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.
See Geometry and String theory
Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings.
See Geometry and Superstring theory
Surface (mathematics)
In mathematics, a surface is a mathematical model of the common concept of a surface.
See Geometry and Surface (mathematics)
Surface (topology)
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold.
See Geometry and Surface (topology)
Surface of revolution
A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints).
See Geometry and Surface of revolution
Surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them.
Symmetry
Symmetry in everyday life refers to a sense of harmonious and beautiful proportion and balance.
Symmetry group
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition.
See Geometry and Symmetry group
Synthetic geometry
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates.
See Geometry and Synthetic geometry
Syracuse, Sicily
Syracuse (Siracusa; Sarausa) is a historic city on the Italian island of Sicily, the capital of the Italian province of Syracuse.
See Geometry and Syracuse, Sicily
Tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps.
Thales of Miletus
Thales of Miletus (Θαλῆς) was an Ancient Greek pre-Socratic philosopher from Miletus in Ionia, Asia Minor.
See Geometry and Thales of Miletus
Thales's theorem
In geometry, Thales's theorem states that if,, and are distinct points on a circle where the line is a diameter, the angle is a right angle.
See Geometry and Thales's theorem
Thābit ibn Qurra
Thābit ibn Qurra (full name:, أبو الحسن ثابت بن قرة بن زهرون الحراني الصابئ, Thebit/Thebith/Tebit; 826 or 836 – February 19, 901), was a polymath known for his work in mathematics, medicine, astronomy, and translation.
See Geometry and Thābit ibn Qurra
Theorem
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven.
Theorema Egregium
Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces.
See Geometry and Theorema Egregium
Three-dimensional space
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point.
See Geometry and Three-dimensional space
Topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.
See Geometry and Topological space
Topology
Topology (from the Greek words, and) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
Transformation geometry
In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them.
See Geometry and Transformation geometry
Trapezoid
In geometry, a trapezoid in North American English, or trapezium in British English, is a quadrilateral that has one pair of parallel sides.
Travelling salesman problem
The travelling salesman problem, also known as the travelling salesperson problem (TSP), asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research.
See Geometry and Travelling salesman problem
Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.
Triangulation (geometry)
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices.
See Geometry and Triangulation (geometry)
Trigonometry
Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
Unit circle
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1.
Universe
The universe is all of space and time and their contents.
University of St Andrews
The University of St Andrews (Oilthigh Chill Rìmhinn; abbreviated as St And, from the Latin Sancti Andreae, in post-nominals) is a public university in St Andrews, Scotland.
See Geometry and University of St Andrews
Uta Merzbach
Uta Caecilia Merzbach (February 9, 1933 – June 27, 2017) was a German-American historian of mathematics who became the first curator of mathematical instruments at the Smithsonian Institution.
Vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.
Velocity
Velocity is the speed in combination with the direction of motion of an object.
Vertex (geometry)
In geometry, a vertex (vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect.
See Geometry and Vertex (geometry)
Vitello
Vitello (Witelon; Witelo; – 1280/1314) was a Polish friar, theologian, natural philosopher and an important figure in the history of philosophy in Poland.
Vitruvius
Vitruvius (–70 BC – after) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work titled De architectura.
Volume
Volume is a measure of regions in three-dimensional space.
Whitehead's point-free geometry
In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point.
See Geometry and Whitehead's point-free geometry
Wiles's proof of Fermat's Last Theorem
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves.
See Geometry and Wiles's proof of Fermat's Last Theorem
William Kingdon Clifford
William Kingdon Clifford (4 May 18453 March 1879) was a British mathematician and philosopher.
See Geometry and William Kingdon Clifford
Worldsheet
In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime.
Yuri Burago
Yuri Dmitrievich Burago (Ю́рий Дми́триевич Бура́го; born 21 June 1936) is a Russian mathematician.
Zenodorus (mathematician)
Zenodorus (Ζηνόδωρος; c. 200 – c. 140 BC) was an ancient Greek mathematician.
See Geometry and Zenodorus (mathematician)
Zero of a function
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is a solution to the equation f(x).
See Geometry and Zero of a function
References
[1] https://en.wikipedia.org/wiki/Geometry
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