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116 relations: A History of Vector Analysis, A New Era of Thought, Albert Einstein, Alfred A. Knopf, Algebra over a field, American Mathematical Society, An Experiment with Time, Andrew Forsyth, Angle, Archimedean solid, Array data structure, Artist, Associative algebra, August Ferdinand Möbius, Bernhard Riemann, Bicomplex number, Binocular vision, Bivector, Brain, Cambridge University Press, Cartesian product, Charles Howard Hinton, Coordinate system, Coxeter element, Cross product, Cross section (geometry), Cube, Cubinder, Cylinder, Dimension, Dot product, Duocylinder, Edwin Abbott Abbott, Eric Harold Neville, Euclidean distance, Euclidean geometry, Euclidean space, Euclidean vector, Exotic R4, Exterior algebra, Extrusion, Flatland, Four-dimensionalism, Fourth dimension in art, Fourth dimension in literature, Friedmann–Lemaître–Robertson–Walker metric, Frustum, General relativity, Graphical projection, Habilitation, ..., Harold Scott MacDonald Coxeter, Henry More, Hermann Minkowski, Hexahedron, Human eye, Hyperspace (book), Hypersurface, Internet Archive, Joseph-Louis Lagrange, Kite (geometry), Klein bottle, Knot (mathematics), Labyrinth, List of four-dimensional games, List of Martin Gardner Mathematical Games columns, Ludwig Schläfli, Martin Gardner, Mechanics, Minkowski space, Non-Euclidean geometry, Norm (mathematics), Orthogonality, Pairing, Perspective (graphical), Platonic solid, Point (geometry), Polygon, Polyhedron, Polytope, Quaternion, Real projective plane, Regular 4-polytope, Retina, Rudy Rucker, Schlegel diagram, Scientific American, Sensory neuron, Six-dimensional space, Space (mathematics), Spaceland (novel), Spacetime, Special relativity, Spherinder, Split-quaternion, Standard basis, Tesseract, The Time Machine, Three-dimensional space, Trapezoid, Tuple, Uniform 4-polytope, University of Dublin, University of Michigan, Vector calculus, Vector space, Victor Schlegel, Virtual reality, William Rowan Hamilton, 120-cell, 16-cell, 24-cell, 3-sphere, 4-manifold, 4-polytope, 5-cell, 600-cell. Expand index (66 more) »
A History of Vector Analysis
A History of Vector Analysis (1967) is a book on the history of vector analysis by Michael J. Crowe, originally published by the University of Notre Dame Press.
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A New Era of Thought
A New Era of Thought is a non-fiction work written by Charles Howard Hinton, published in 1888 and reprinted in 1900 by Swan Sonnenschein & Co.
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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).
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Alfred A. Knopf
Alfred A. Knopf, Inc. is a New York publishing house that was founded by Alfred A. Knopf Sr. and Blanche Knopf in 1915.
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Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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An Experiment with Time
An Experiment with Time is a book by the British soldier, aeronautical engineer and philosopher J. W. Dunne (1875–1949) on the subjects of precognitive dreams and a theory of time which he later called Serialism.
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Andrew Forsyth
Prof Andrew Russell Forsyth, FRS, FRSE (18 June 1858, Glasgow – 2 June 1942, South Kensington) was a British mathematician.
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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.
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Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.
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Array data structure
In computer science, an array data structure, or simply an array, is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key.
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Artist
An artist is a person engaged in an activity related to creating art, practicing the arts, or demonstrating an art.
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Associative algebra
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
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August Ferdinand Möbius
August Ferdinand Möbius (17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer.
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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.
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Bicomplex number
In abstract algebra, a bicomplex number is a pair of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate (w,z)^*.
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Binocular vision
In biology, binocular vision is a type of vision in which an animal having two eyes is able to perceive a single three-dimensional image of its surroundings.
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Bivector
In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors.
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Brain
The brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Charles Howard Hinton
Charles Howard Hinton (1853, United Kingdom – 30 April 1907, Washington D.C., United States) was a British mathematician and writer of science fiction works titled Scientific Romances.
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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.
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Coxeter element
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
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Cross product
In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.
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Cross section (geometry)
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces.
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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Cubinder
In four-dimensional geometry, the cubinder (otherwise known as cubical cylinder or hypercylinder) is one way to generalise the 3D cylinder to 4D.
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Cylinder
A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
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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.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Duocylinder
The duocylinder, or double cylinder, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r1 and r2: It is analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.
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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).
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Eric Harold Neville
Eric Harold Neville, known as E. H. Neville (1 January 1889 London, England – 22 August 1961 Reading, Berkshire, England) was an English mathematician.
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Euclidean distance
In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.
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Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
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Exotic R4
In mathematics, an exotic R4 is a differentiable manifold that is homeomorphic but not diffeomorphic to the Euclidean space R4.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Extrusion
Extrusion is a process used to create objects of a fixed cross-sectional profile.
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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.
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Four-dimensionalism
In philosophy, four-dimensionalism (also known as the doctrine of temporal parts) is an ontological position that an object's persistence through time is like its extension through space.
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Fourth dimension in art
New possibilities opened up by the concept of four-dimensional space (and difficulties involved in trying to visualize it) helped inspire many modern artists in the first half of the twentieth century.
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Fourth dimension in literature
The idea of a fourth dimension has been a factor in the evolution of modern art, but use of concepts relating to higher dimensions has been little discussed by academics in the literary world.
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Friedmann–Lemaître–Robertson–Walker metric
The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding or contracting universe that is path connected, but not necessarily simply connected.
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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.
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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.
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Graphical projection
Graphical projection is a protocol, used in technical drawing, by which an image of a three-dimensional object is projected onto a planar surface without the aid of numerical calculation.
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Habilitation
Habilitation defines the qualification to conduct self-contained university teaching and is the key for access to a professorship in many European countries.
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Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
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Henry More
Henry More (12 October 1614 – 1 September 1687) was an English philosopher of the Cambridge Platonist school.
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Hermann Minkowski
Hermann Minkowski (22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen.
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Hexahedron
A hexahedron (plural: hexahedra) is any polyhedron with six faces.
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Human eye
The human eye is an organ which reacts to light and pressure.
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Hyperspace (book)
Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension (1994) is a book by Michio Kaku, a theoretical physicist from the City College of New York.
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Hypersurface
In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.
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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.
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Joseph-Louis Lagrange
Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.
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Kite (geometry)
In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
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Klein bottle
In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.
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Knot (mathematics)
In mathematics, a knot is an embedding of a circle S^1 in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).
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Labyrinth
In Greek mythology, the Labyrinth (Greek: Λαβύρινθος labyrinthos) was an elaborate, confusing structure designed and built by the legendary artificer Daedalus for King Minos of Crete at Knossos.
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List of four-dimensional games
This is a list of four-dimensional games.
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List of Martin Gardner Mathematical Games columns
Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive "Mathematical Games" columns for Scientific American magazine.
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Ludwig Schläfli
Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces.
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Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.
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Mechanics
Mechanics (Greek μηχανική) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.
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Minkowski space
In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.
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Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
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Pairing
In mathematics, a pairing is an R-bilinear map of modules, where R is the underlying ring.
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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.
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Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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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.
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
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Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers.
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Real projective plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.
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Regular 4-polytope
In mathematics, a regular 4-polytope is a regular four-dimensional polytope.
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Retina
The retina is the innermost, light-sensitive "coat", or layer, of shell tissue of the eye of most vertebrates and some molluscs.
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Rudy Rucker
Rudolf von Bitter Rucker (born March 22, 1946) is an American mathematician, computer scientist, science fiction author, and one of the founders of the cyberpunk literary movement.
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Schlegel diagram
In geometry, a Schlegel diagram is a projection of a polytope from R^d into R^ through a point beyond one of its facets or faces.
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Scientific American
Scientific American (informally abbreviated SciAm) is an American popular science magazine.
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Sensory neuron
Sensory neurons also known as afferent neurons are neurons that convert a specific type of stimulus, via their receptors, into action potentials or graded potentials.
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Six-dimensional space
Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location in this space.
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Space (mathematics)
In mathematics, a space is a set (sometimes called a universe) with some added structure.
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Spaceland (novel)
Spaceland is a science fiction novel written by the Silicon Valley mathematician and computer scientist Rudy Rucker, and published in 2002 by Tor Books.
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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.
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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.
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Spherinder
In four-dimensional geometry, the spherinder, or spherical cylinder or spherical prism, is a geometric object, defined as the Cartesian product of a 3-ball (or solid 2-sphere), radius r1 and a line segment of length 2r2: Like the duocylinder, it is also analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.
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Split-quaternion
In abstract algebra, the split-quaternions or coquaternions are elements of a 4-dimensional associative algebra introduced by James Cockle in 1849 under the latter name.
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Standard basis
In mathematics, the standard basis (also called natural basis) for a Euclidean space is the set of unit vectors pointing in the direction of the axes of a Cartesian coordinate system.
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Tesseract
In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.
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The Time Machine
The Time Machine is a science fiction novella by H. G. Wells, published in 1895 and written as a frame narrative.
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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).
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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.
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Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
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Uniform 4-polytope
In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
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University of Dublin
The University of Dublin (Ollscoil Átha Cliath), corporately designated the Chancellor, Doctors and Masters of the University of Dublin, is a university located in Dublin, Ireland.
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University of Michigan
The University of Michigan (UM, U-M, U of M, or UMich), often simply referred to as Michigan, is a public research university in Ann Arbor, Michigan.
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Vector calculus
Vector calculus, or vector analysis, is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3.
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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.
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Victor Schlegel
Victor Schlegel (1843–1905) was a German mathematician.
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Virtual reality
Virtual reality (VR) is an interactive computer-generated experience taking place within a simulated environment, that incorporates mainly auditory and visual, but also other types of sensory feedback like haptic.
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William Rowan Hamilton
Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.
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120-cell
In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.
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16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
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24-cell
In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
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4-manifold
In mathematics, a 4-manifold is a 4-dimensional topological manifold.
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4-polytope
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.
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5-cell
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
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600-cell
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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References
[1] https://en.wikipedia.org/wiki/Four-dimensional_space
