 Faster access than browser!

# Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. 

## Affine space

In mathematics, an affine space is a geometric structure that generalizes 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 Muslim mathematician and astronomer born in Mahan, (in today Kermān, Persia) and active in Baghdad, Abbasid Caliphate.

## Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

## Alexander Grothendieck

Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.

## Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

## Algebraic curve

In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.

## Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

## Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

## Algebraic surface

In mathematics, an algebraic surface is an algebraic variety of dimension two.

## Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

## Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry.

## Alphons

Alphons (Latinized Alphonsus, Adelphonsus, Adefonsus) is a male given name recorded from the 8th century (Alfonso I of Asturias, r. 739-757) in the Christian successor states of the Visigothic kingdom in the Iberian peninsula.

## Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

## Analytic–synthetic distinction

The analytic–synthetic distinction (also called the analytic–synthetic dichotomy) is a semantic distinction, used primarily in philosophy to distinguish propositions (in particular, statements that are affirmative subject–predicate judgments) into two types: analytic propositions and synthetic propositions.

## Ancient Egypt

Ancient Egypt was a civilization of ancient Northeastern Africa, concentrated along the lower reaches of the Nile River - geographically Lower Egypt and Upper Egypt, in the place that is now occupied by the countries of Egypt and Sudan.

## Ancient Egyptian mathematics

Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c. 300 BC, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt.

## Ancient Greece

Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 13th–9th centuries BC to the end of antiquity (AD 600).

## Angle

In plane 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.

New!!: Geometry and Angle · See more »

## Archimedean spiral

The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd century BC Greek mathematician Archimedes.

## Archimedes

Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

## Architecture

Architecture is both the process and the product of planning, designing, and constructing buildings or any other structures.

## Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

New!!: Geometry and Area · See more »

## Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

## Aryabhata

Aryabhata (IAST) 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 (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.

## Axiom

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

New!!: Geometry and Axiom · See more »

## Axiomatic system

In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.

## Babylonian mathematics

Babylonian mathematics (also known as Assyro-Babylonian mathematics) was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC.

## Bakhshali manuscript

The Bakhshali manuscript is a mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan).

## Basil Blackwell

Sir Basil Henry Blackwell (29 May 18899 April 1984) was born in Oxford, England.

## Bernhard Riemann

Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.

## Bible

The Bible (from Koine Greek τὰ βιβλία, tà biblía, "the books") is a collection of sacred texts or scriptures that Jews and Christians consider to be a product of divine inspiration and a record of the relationship between God and humans.

New!!: Geometry and Bible · See more »

## Book of Optics

The Book of Optics (Kitāb al-Manāẓir; Latin: De Aspectibus or Perspectiva; Italian: 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).

## Brahmagupta

Brahmagupta (born, died) was an Indian mathematician and astronomer.

## Brane

In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions.

New!!: Geometry and Brane · See more »

## Brāhmasphuṭasiddhānta

The Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is the main work of Brahmagupta, written c. 628.

## Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), 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.

## Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

## Celestial sphere

In astronomy and navigation, the celestial sphere is an abstract sphere with an arbitrarily large radius concentric to Earth.

## Circle

A circle is a simple closed shape.

## Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

## Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to 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 counting, both as a means and an end in obtaining results, and certain properties of finite structures.

## Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

## Compass (drawing tool)

A pair of compasses, also known simply as a bow compass, is a technical drawing instrument that can be used for inscribing circles or arcs.

## 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.

## Complex geometry

In mathematics, complex geometry is the study of complex manifolds and functions of several complex variables.

## Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

## Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.

## Computer graphics

Computer graphics are pictures and films created using computers.

## Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

## 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.

New!!: Geometry and Cone · See more »

## 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.

## Connectedness

In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece".

## Construction

Construction is the process of constructing a building or infrastructure.

## Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

## 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.

## Convex geometry

In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.

## Coordinate system

In geometry, a coordinate system is a system which 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.

## Coxeter group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).

## Cryptography

Cryptography or cryptology (from κρυπτός|translit.

## Crystallography

Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure).

## Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

## Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

## Curve

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

New!!: Geometry and Curve · See more »

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.

## David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.

## Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

## 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.

## Diffeomorphism

In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.

## Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

## Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

## Differential topology

In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.

## 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.

## Dimension theory

In mathematics, dimension theory is a branch of general topology dealing with dimensional invariants of topological spaces.

## Diophantine equation

In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).

## Discrete geometry

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.

## Discrete group

In mathematics, a discrete subgroup of a topological group G is a subgroup H such that there is an open cover of G in which every open subset contains exactly one element of H; in other words, the subspace topology of H in G is the discrete topology.

## Displacement (vector)

A displacement is a vector whose length is the shortest distance from the initial to the final position of a point P. It quantifies both the distance and direction of an imaginary motion along a straight line from the initial position to the final position of the point.

## Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.

## Duality (projective geometry)

In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept.

## Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

## Edwin Abbott Abbott

Edwin Abbott Abbott (20 December 1838 – 12 October 1926) was an English schoolmaster and theologian, best known as the author of the novella Flatland (1884).

## 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.

## Equation

In mathematics, an equation is a statement of an equality containing one or more variables.

## Erlangen program

The Erlangen program is a method of characterizing geometries based on group theory and projective geometry.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

## Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

## Euclidean distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.

## Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Eudoxus of Cnidus

Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato.

## Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.

## Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

## Finite geometry

A finite geometry is any geometric system that has only a finite number of points.

## 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.

## Fractal

In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.

## Frustum

In geometry, a frustum (plural: frusta or frustums) is the portion of a solid (normally a cone or pyramid) that lies between one or two parallel planes cutting it.

## 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 (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.

## General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

## General Relativity (book)

General Relativity is a popular textbook on Einstein's theory of general relativity written by Robert Wald.

## General topology

In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.

## Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

## 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 act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).

## Geometric topology

In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.

## Geometric transformation

A geometric transformation is any bijection of a set having some geometric structure to itself or another such set.

## Geometry of numbers

In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space.

## Gersonides

Levi ben Gershon (1288–1344), better known by his Graecized name as Gersonides or by his Latinized name Magister Leo Hebraeus 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.

## Girard Desargues

Girard Desargues (21 February 1591 &ndash; September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry.

## Glossary of arithmetic and diophantine geometry

This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry.

## Gröbner basis

In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring over a field.

## Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

## Gresham College

Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England.

## Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

## Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 &ndash; March 31, 2003) was a British-born Canadian geometer.

## Henri Poincaré

Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

## Heron's formula

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulae for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.

## Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

## Hodge conjecture

In mathematics, the Hodge conjecture is a major unsolved problem in the field of algebraic geometry that relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of it.

## Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

## Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry.

## Hyperbolic manifold

In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension.

## Ibn al-Haytham

Hasan Ibn al-Haytham (Latinized Alhazen; full name أبو علي، الحسن بن الحسن بن الهيثم) was an Arab mathematician, astronomer, and physicist of the Islamic Golden Age.

## Immanuel Kant

Immanuel Kant (22 April 1724 – 12 February 1804) was a German philosopher who is a central figure in modern philosophy.

## Incidence geometry

In mathematics, incidence geometry is the study of incidence structures.

## Indian mathematics

Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.

## Integer triangle

An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers.

## Internet Archive

The Internet Archive is a San Francisco–based nonprofit digital library with the stated mission of "universal access to all knowledge." It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and nearly three million public-domain books.

## Invariance of domain

Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space Rn.

## Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

## James Stewart (mathematician)

James Drewry Stewart, (March 29, 1941December 3, 2014) was a Canadian mathematician, violinist, and professor emeritus of mathematics at McMaster University.

## Jay Kappraff

Jay Kappraff is 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, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines.

## 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.

## Jeremy Gray

Jeremy John Gray (born 25 April 1947) is an English mathematician primarily interested in the history of mathematics.

## John Casey (mathematician)

John Casey (12 May 1820, Kilbehenny, Co. Limerick, Ireland – 3 January 1891, Dublin) was a respected Irish geometer.

## John Wallis

John Wallis (3 December 1616 – 8 November 1703) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus.

## Johns Hopkins University Press

The Johns Hopkins University Press (also referred to as JHU Press or JHUP) is the publishing division of Johns Hopkins University.

Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with a goal of creating a set of online tools that help educate students.

In geometry, a Lambert quadrilateral, named after Johann Heinrich Lambert, is a quadrilateral in which three of its angles are right angles.

## Latin

Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

New!!: Geometry and Latin · See more »

## Length

In geometric measurements, length is the most extended dimension of an object.

## Leonard Mlodinow

Leonard Mlodinow (born 1 January 1954) is an American theoretical physicist, screenwriter and author.

## Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

## Lie theory

In mathematics, the researcher 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)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

## Linear equation

In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.

## List of formulas in elementary geometry

This is a short list of some common mathematical shapes and figures and the formulas that describe them.

## List of geometers

A geometer is a mathematician whose area of study is geometry.

## 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.

## London

London is the capital and most populous city of England and the United Kingdom.

## M. C. Escher

Maurits Cornelis Escher (17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically-inspired woodcuts, lithographs, and mezzotints.

## Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

## Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

## Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

## Mathematical physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics.

## Mathematical sciences

The mathematical sciences are a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Mathematics in medieval Islam

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).

## Mean speed theorem

In the 14th-century, the Oxford Calculators of Merton College and French collaborators such as Nicole Oresme proved the mean speed theorem, also known as the Merton rule of uniform acceleration, or the Merton mean speed theorem.

## Mesopotamia

Mesopotamia is a historical region in West Asia situated within the Tigris–Euphrates river system, in modern days roughly corresponding to most of Iraq, Kuwait, parts of Northern Saudi Arabia, the eastern parts of Syria, Southeastern Turkey, and regions along the Turkish–Syrian and Iran–Iraq borders.

## Method of exhaustion

The method of exhaustion (methodus exhaustionibus, or méthode des anciens) 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.

## Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

## Middle Ages

In the history of Europe, the Middle Ages (or Medieval Period) lasted from the 5th to the 15th century.

## Millennium Prize Problems

The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.

## Moduli space

In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.

## Molecular geometry

Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule.

## Morse theory

"Morse function" redirects here.

## Moscow Mathematical Papyrus

The Moscow Mathematical Papyrus is an ancient Egyptian mathematical papyrus, also called the Golenishchev Mathematical Papyrus, after its first owner outside of Egypt, Egyptologist Vladimir Golenishchev.

## Nasir al-Din al-Tusi

Muhammad ibn Muhammad ibn al-Hasan al-Tūsī (محمد بن محمد بن حسن طوسی&lrm; 18 February 1201 – 26 June 1274), better known as Nasir al-Din Tusi (نصیر الدین طوسی; or simply Tusi in the West), was a Persian polymath, architect, philosopher, physician, scientist, and theologian.

## Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

## Neighbourhood (mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.

## 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 his fundamental study on Dirichlet integrals known as Lobachevsky integral formula.

## Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.

## Nubia

Nubia is a region along the Nile river encompassing the area between Aswan in southern Egypt and Khartoum in central Sudan.

New!!: Geometry and Nubia · See more »

## Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

## Omar Khayyam

Omar Khayyam (عمر خیّام; 18 May 1048 – 4 December 1131) was a Persian mathematician, astronomer, and poet.

## 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".

## OxfordDictionaries.com

OxfordDictionaries.com, originally titled Oxford Dictionaries Online (ODO) and rebranded Oxford Living Dictionaries in 2017, is an online dictionary produced by the Oxford University Press (OUP) publishing house, a department of the University of Oxford, which also publishes a number of print dictionaries, among other works.

## Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

## Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

## Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

## Pi

The number is a mathematical constant.

New!!: Geometry and Pi · See more »

## Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

## Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

## Plane curve

In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane.

## Planet

A planet is an astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.

## Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

## Playfair's axiom

In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.

## Plimpton 322

Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics.

## Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

## Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Projective geometry

Projective geometry is a topic in mathematics.

## Pseudo-Riemannian manifold

In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

## Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

## Pythagorean triple

A Pythagorean triple consists of three positive integers,, and, such that.

## Pythagoreanism

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.

## Ratio

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

New!!: Geometry and Ratio · See more »

## Real algebraic geometry

In mathematics, real algebraic geometry is the study of real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial mappings).

## Real analysis

In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions.

## Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

## René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

## Rhind Mathematical Papyrus

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of Egyptian mathematics.

## Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

## 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 that varies smoothly from point to point.

## Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

## 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 or line gauge, is a device with equally spaced markings along its length, used in geometry, technical drawing, engineering and building to measure distances or to rule straight lines.

New!!: Geometry and Ruler · See more »

A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base.

## Sanskrit

Sanskrit is the primary liturgical language of Hinduism; a philosophical language of Hinduism, Sikhism, Buddhism and Jainism; and a former literary language and lingua franca for the educated of ancient and medieval India.

## Scheme (mathematics)

In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.

## Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

## Seven Bridges of Königsberg

The Seven Bridges of Königsberg is a historically notable problem in mathematics.

## Shatapatha Brahmana

The Shatapatha Brahmana (IAST:, "Brāhmaṇa of one hundred parts") is a prose text describing Vedic rituals, history and mythology associated with the Śukla Yajurveda.

## Shulba Sutras

The Shulba Sutras or Śulbasūtras (Sanskrit: "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction.

## Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

## Singularity theory

In mathematics, singularity theory studies spaces that are almost manifolds, but not quite.

## Solid geometry

In mathematics, solid geometry is the traditional name for the geometry of three-dimensional Euclidean space.

## Sophus Lie

Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician.

## Space

Space is the boundless three-dimensional extent in which objects and events have relative position and direction.

New!!: Geometry and Space · See more »

## Spacetime

In physics, spacetime is any 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, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

## Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

## Star

A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity.

New!!: Geometry and Star · See more »

## 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.

## Surface (mathematics)

In mathematics, a surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero.

## Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

## Surface of revolution

A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) around an axis of rotation.

## Surveying

Surveying or land surveying is the technique, profession, and science of determining the terrestrial or three-dimensional positions of points and the distances and angles between them.

## Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.

## Symmetry group

In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.

## Synthetic geometry

Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.

## Syracuse, Sicily

Syracuse (Siracusa,; Sarausa/Seragusa; Syrācūsae; Συράκουσαι, Syrakousai; Medieval Συρακοῦσαι) is a historic city on the island of Sicily, the capital of the Italian province of Syracuse.

## Thales of Miletus

Thales of Miletus (Θαλῆς (ὁ Μιλήσιος), Thalēs; 624 – c. 546 BC) was a pre-Socratic Greek philosopher, mathematician, and astronomer from Miletus in Asia Minor (present-day Milet in Turkey).

## Thales's theorem

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, then the angle ∠ABC is a right angle.

## Thābit ibn Qurra

(ثابت بن قره, Thebit/Thebith/Tebit; 826 – February 18, 901) was a Syrian Arab Sabian mathematician, physician, astronomer, and translator who lived in Baghdad in the second half of the ninth century during the time of Abbasid Caliphate.

## Theorem

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.

## Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

## Topological manifold

In topology, a branch of mathematics, a topological manifold is a topological space (which may also be a separated space) which locally resembles real n-dimensional space in a sense defined below.

## Topological space

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

## Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

## 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.

## Trapezoid

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English but as a trapezium in English outside North America.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

## Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

## Unit circle

In mathematics, a unit circle is a circle with a radius of one.

## Universe

The Universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy.

## University of St Andrews

The University of St Andrews (informally known as St Andrews University or simply St Andrews; abbreviated as St And, from the Latin Sancti Andreae, in post-nominals) is a British public research university in St Andrews, Fife, Scotland.

## 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

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

## Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

## Vitello

Witelo (also Erazmus Ciołek Witelo; Witelon; Vitellio; Vitello; Vitello Thuringopolonis; Vitulon; Erazm Ciołek); born ca.

## Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

## 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.

## William Kingdon Clifford

William Kingdon Clifford FRS (4 May 1845 – 3 March 1879) was an English mathematician and philosopher.

## Yuri Burago

Yuri Dmitrievich Burago (Ю́рий Дми́триевич Бура́го) (born 1936) is a Russian mathematician.

## References

Hey! We are on Facebook now! »