Affine geometry, the Glossary

Table of Contents

1. 134 relations: Abelian group, Absolute space and time, Addison-Wesley, Additive group, Affine connection, Affine group, Affine plane (incidence geometry), Affine space, Affine transformation, American Academy of Arts and Sciences, Angle, Area of a triangle, August Ferdinand Möbius, Axiom, Barycenter (astronomy), Bijection, Centre (geometry), Centroid, Ceva's theorem, Collinearity, Combinatorics, Cone, Configuration (geometry), Congruence (geometry), D. Reidel, David Hilbert, Desargues's theorem, Distance, Distributive property, Dover Publications, E. T. Whittaker, Edwin Bidwell Wilson, Emil Artin, Envelope (mathematics), Equivalence relation, Erlangen program, Euclidean geometry, Face (geometry), Felix Klein, Field (mathematics), Finite geometry, Forgetful functor, Four-dimensional space, Frame of reference, Function composition, General linear group, Geometric Algebra (book), Geometry, Gilbert N. Lewis, Group (mathematics), ... Expand index (84 more) »

Abelian group

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

See Affine geometry and Abelian group

Absolute space and time

Absolute space and time is a concept in physics and philosophy about the properties of the universe.

See Affine geometry and Absolute space and time

Addison-Wesley

Addison–Wesley is an American publisher of textbooks and computer literature.

See Affine geometry and Addison-Wesley

Additive group

An additive group is a group of which the group operation is to be thought of as addition in some sense.

See Affine geometry and Additive group

Affine connection

In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.

See Affine geometry and Affine connection

Affine group

In mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into itself.

See Affine geometry and Affine group

Affine plane (incidence geometry)

In geometry, an affine plane is a system of points and lines that satisfy the following axioms.

See Affine geometry and Affine plane (incidence 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.

See Affine geometry and Affine space

Affine transformation

In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.

See Affine geometry and Affine transformation

American Academy of Arts and Sciences

The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States.

See Affine geometry and American Academy of Arts and Sciences

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.

See Affine geometry and Angle

Area of a triangle

In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations.

See Affine geometry and Area of a triangle

August Ferdinand Möbius

August Ferdinand Möbius (17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer.

See Affine geometry and August Ferdinand Möbius

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.

See Affine geometry and Axiom

Barycenter (astronomy)

In astronomy, the barycenter (or barycentre) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit.

See Affine geometry and Barycenter (astronomy)

Bijection

A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the first set (the domain) is mapped to exactly one element of the second set (the codomain).

See Affine geometry and Bijection

Centre (geometry)

In geometry, a centre (British English) or center (American English) of an object is a point in some sense in the middle of the object.

See Affine geometry and Centre (geometry)

Centroid

In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure.

See Affine geometry and Centroid

Ceva's theorem

In Euclidean geometry, Ceva's theorem is a theorem about triangles.

See Affine geometry and Ceva's theorem

Collinearity

In geometry, collinearity of a set of points is the property of their lying on a single line.

See Affine geometry and Collinearity

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 Affine geometry and Combinatorics

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.

See Affine geometry and Cone

Configuration (geometry)

In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.

See Affine geometry and Configuration (geometry)

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 Affine geometry and Congruence (geometry)

D. Reidel

D.

See Affine geometry and D. Reidel

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 Affine geometry and David Hilbert

Desargues's theorem

In projective geometry, Desargues's theorem, named after Girard Desargues, states: Denote the three vertices of one triangle by and, and those of the other by and.

See Affine geometry and Desargues's theorem

Distance

Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are.

See Affine geometry and Distance

Distributive property

In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x \cdot (y + z).

See Affine geometry and Distributive property

Dover Publications

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

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E. T. Whittaker

Sir Edmund Taylor Whittaker (24 October 1873 – 24 March 1956) was a British mathematician, physicist, and historian of science.

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Edwin Bidwell Wilson

Edwin Bidwell Wilson (April 25, 1879 – December 28, 1964) was an American mathematician, statistician, physicist and general polymath.

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Emil Artin

Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.

See Affine geometry and Emil Artin

Envelope (mathematics)

In geometry, an envelope of a planar family of curves is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope.

See Affine geometry and Envelope (mathematics)

Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

See Affine geometry and Equivalence relation

Erlangen program

In mathematics, the Erlangen program is a method of characterizing geometries based on group theory and projective geometry.

See Affine geometry and Erlangen program

Euclidean geometry

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

See Affine geometry and Euclidean geometry

Face (geometry)

In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron.

See Affine geometry and Face (geometry)

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.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.

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Finite geometry

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

See Affine geometry and Finite geometry

Forgetful functor

In mathematics, in the area of category theory, a forgetful functor (also known as a stripping functor) 'forgets' or drops some or all of the input's structure or properties 'before' mapping to the output.

See Affine geometry and Forgetful functor

Four-dimensional space

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D).

See Affine geometry and Four-dimensional space

Frame of reference

In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points―geometric points whose position is identified both mathematically (with numerical coordinate values) and physically (signaled by conventional markers).

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Function composition

In mathematics, function composition is an operation that takes two functions and, and produces a function such that.

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General linear group

In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication.

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Geometric Algebra (book)

Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957.

See Affine geometry and Geometric Algebra (book)

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Affine geometry and Geometry

Gilbert N. Lewis

Gilbert Newton Lewis (October 23 or October 25, 1875 – March 23, 1946) was an American physical chemist and a dean of the college of chemistry at University of California, Berkeley.

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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.

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Group action

In mathematics, many sets of transformations form a group under function composition; for example, the rotations around a point in the plane.

See Affine geometry and Group action

Group theory

In abstract algebra, group theory studies the algebraic structures known as groups.

See Affine geometry and Group theory

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician.

See Affine geometry and Harold Scott MacDonald Coxeter

Height

Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is).

See Affine geometry and Height

Hermann Weyl

Hermann Klaus Hugo Weyl, (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher.

See Affine geometry and Hermann Weyl

Homography

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive.

See Affine geometry and Homography

Hyperbolic orthogonality

In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events.

See Affine geometry and Hyperbolic orthogonality

Hyperplane

In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension.

See Affine geometry and Hyperplane

Hyperplane at infinity

In geometry, any hyperplane H of a projective space P may be taken as a hyperplane at infinity.

See Affine geometry and Hyperplane at infinity

Internet Archive

The Internet Archive is an American nonprofit digital library founded in 1996 by Brewster Kahle.

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Introductio in analysin infinitorum

Introductio in analysin infinitorum (Latin: Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis.

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Invariant (mathematics)

In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations of a certain type are applied to the objects.

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Isaak Yaglom

Isaak Moiseevich Yaglom (Исаа́к Моисе́евич Ягло́м; 6 March 1921 – 17 April 1988) was a Soviet mathematician and author of popular mathematics books, some with his twin Akiva Yaglom.

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Jean Gallier

Jean Henri Gallier (born 1949) is a researcher in computational logic at the University of Pennsylvania, where he holds appointments in the Computer and Information Science Department and the Department of Mathematics.

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Katsumi Nomizu

was a Japanese-American mathematician known for his work in differential geometry.

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Kinematics

Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.

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Lebesgue measure

In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of higher dimensional Euclidean ''n''-spaces.

See Affine geometry and Lebesgue measure

Leonhard Euler

Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.

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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.

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Lorentz space

In mathematical analysis, Lorentz spaces, introduced by George G. Lorentz in the 1950s, are generalisations of the more familiar L^p spaces.

See Affine geometry and Lorentz space

Macmillan Publishers

Macmillan Publishers (occasionally known as the Macmillan Group; formally Macmillan Publishers Ltd in the UK and Macmillan Publishing Group, LLC in the US) is a British publishing company traditionally considered to be one of the 'Big Five' English language publishers (along with Penguin Random House, Hachette, HarperCollins and Simon & Schuster).

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Manifold

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

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Marshall Hall (mathematician)

Marshall Hall Jr. (17 September 1910 – 4 July 1990) was an American mathematician who made significant contributions to group theory and combinatorics.

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Mathematical physics

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

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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.

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Menelaus's theorem

In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry.

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Metric space

In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points.

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Midpoint

In geometry, the midpoint is the middle point of a line segment.

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Minkowski space

In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation.

See Affine geometry and Minkowski space

Moons of Jupiter

There are 95 moons of Jupiter with confirmed orbits.

See Affine geometry and Moons of Jupiter

Moulton plane

In incidence geometry, the Moulton plane is an example of an affine plane in which Desargues's theorem does not hold.

See Affine geometry and Moulton plane

Non-Desarguesian plane

In mathematics, a non-Desarguesian plane is a projective plane that does not satisfy Desargues' theorem (named after Girard Desargues), or in other words a plane that is not a Desarguesian plane.

See Affine geometry and Non-Desarguesian plane

Non-Euclidean geometry

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

See Affine geometry and Non-Euclidean geometry

Null vector

In mathematics, given a vector space X with an associated quadratic form q, written, a null vector or isotropic vector is a non-zero element x of X for which.

See Affine geometry and Null vector

Ordered pair

In mathematics, an ordered pair (a, b) is a pair of objects.

See Affine geometry and Ordered pair

Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.

See Affine geometry and Origin (mathematics)

Oswald Veblen

Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity.

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Pappus of Alexandria

Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς; AD) was a Greek mathematician of late antiquity known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry.

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Pappus's hexagon theorem

In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that.

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Parallel (geometry)

In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point.

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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 Affine geometry and Parallel postulate

Parallel transport

In differential geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold.

See Affine geometry and Parallel transport

Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

See Affine geometry and Parallelepiped

Parallelogram

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

See Affine geometry and Parallelogram

Perpendicular

In geometry, two geometric objects are perpendicular if their intersection forms right angles (angles that are 90 degrees or π/2 radians wide) at the point of intersection called a foot.

See Affine geometry and Perpendicular

Peter Cameron (mathematician)

Peter Jephson Cameron FRSE (born 23 January 1947) is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory.

See Affine geometry and Peter Cameron (mathematician)

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. It is equivalent to Euclid's parallel postulate in the context of Euclidean geometry and was named after the Scottish mathematician John Playfair.

See Affine geometry and Playfair's axiom

Point at infinity

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

See Affine geometry and Point at infinity

Primitive notion

In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts.

See Affine geometry and Primitive notion

Project Gutenberg

Project Gutenberg (PG) is a volunteer effort to digitize and archive cultural works, as well as to "encourage the creation and distribution of eBooks." It was founded in 1971 by American writer Michael S. Hart and is the oldest digital library.

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Projective geometry

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.

See Affine geometry and Projective geometry

Projective space

In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity.

See Affine geometry and Projective space

Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

See Affine geometry and Pyramid (geometry)

Rafael Artzy

Rafael Artzy (23 July 1912 – 22 August 2006) was an Israeli mathematician specializing in geometry.

See Affine geometry and Rafael Artzy

Rapidity

Rapidity is a measure for relativistic velocity.

See Affine geometry and Rapidity

Ratio

In mathematics, a ratio shows how many times one number contains another.

See Affine geometry and Ratio

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.

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Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.

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Rotation (mathematics)

Rotation in mathematics is a concept originating in geometry.

See Affine geometry and Rotation (mathematics)

Russian language

Russian is an East Slavic language, spoken primarily in Russia.

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Scripta Mathematica

Scripta Mathematica was a quarterly journal published by Yeshiva University devoted to the Philosophy, history, and expository treatment of mathematics.

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Semidirect product

In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product.

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Shear mapping

In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed distance from a given line parallel to that direction.

See Affine geometry and Shear mapping

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 Affine geometry and Special relativity

Special right triangle

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.

See Affine geometry and Special right triangle

Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant that is exactly equal to). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.

See Affine geometry and Speed of light

Squeeze mapping

In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is not a rotation or shear mapping.

See Affine geometry and Squeeze mapping

Symmetry

Symmetry in everyday life refers to a sense of harmonious and beautiful proportion and balance.

See Affine geometry and Symmetry

Synthetic geometry

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

See Affine geometry and Synthetic geometry

The American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

See Affine geometry and The American Mathematical Monthly

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 Affine geometry and Three-dimensional space

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 Affine geometry and Transformation geometry

Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.

See Affine geometry and Translation (geometry)

Unit cube

A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.

See Affine geometry and Unit cube

University of London

The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom.

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University of Pennsylvania

The University of Pennsylvania, commonly referenced as Penn or UPenn, is a private Ivy League research university in Philadelphia, Pennsylvania, United States.

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University of Toronto Press

The University of Toronto Press is a Canadian university press.

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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''.

See Affine geometry and Vector space

Velocity

Velocity is the speed in combination with the direction of motion of an object.

See Affine geometry and Velocity

Vertex (geometry)

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

See Affine geometry and Vertex (geometry)

Volume

Volume is a measure of regions in three-dimensional space.

See Affine geometry and Volume

WebCite

WebCite is an intermittently available archive site, originally designed to digitally preserve scientific and educationally important material on the web by taking snapshots of Internet contents as they existed at the time when a blogger or a scholar cited or quoted from it.

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Wiley (publisher)

John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.

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World line

The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime.

See Affine geometry and World line

References

[1] https://en.wikipedia.org/wiki/Affine_geometry

Also known as Affine-geometric.

, Group action, Group theory, Harold Scott MacDonald Coxeter, Height, Hermann Weyl, Homography, Hyperbolic orthogonality, Hyperplane, Hyperplane at infinity, Internet Archive, Introductio in analysin infinitorum, Invariant (mathematics), Isaak Yaglom, Jean Gallier, Katsumi Nomizu, Kinematics, Lebesgue measure, Leonhard Euler, Linear algebra, Lorentz space, Macmillan Publishers, Manifold, Marshall Hall (mathematician), Mathematical physics, Mathematics, Menelaus's theorem, Metric space, Midpoint, Minkowski space, Moons of Jupiter, Moulton plane, Non-Desarguesian plane, Non-Euclidean geometry, Null vector, Ordered pair, Origin (mathematics), Oswald Veblen, Pappus of Alexandria, Pappus's hexagon theorem, Parallel (geometry), Parallel postulate, Parallel transport, Parallelepiped, Parallelogram, Perpendicular, Peter Cameron (mathematician), Playfair's axiom, Point at infinity, Primitive notion, Project Gutenberg, Projective geometry, Projective space, Pyramid (geometry), Rafael Artzy, Rapidity, Ratio, Real number, Representation theory, Rotation (mathematics), Russian language, Scripta Mathematica, Semidirect product, Shear mapping, Special relativity, Special right triangle, Speed of light, Squeeze mapping, Symmetry, Synthetic geometry, The American Mathematical Monthly, Three-dimensional space, Transformation geometry, Translation (geometry), Unit cube, University of London, University of Pennsylvania, University of Toronto Press, Vector space, Velocity, Vertex (geometry), Volume, WebCite, Wiley (publisher), World line.