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Following is a list of some mathematically well-defined shapes. See also list of polygons, polyhedra and polytopes and list of geometric shapes. For other meanings of mathematics or math, see mathematics (disambiguation). ...
In mathematics, the term well-defined is used to specify that a certain concept (a function, a property, a relation, etc. ...
In geometry, two sets have the same shape if one can be transformed to another by a combination of translations, rotations and uniform scalings. ...
This is a list of polygons, polyhedra and polytopes, by Wikipedia page. ...
This is a list of geometric shapes. ...
0D with no surface
1D with 0D surface A spatial point is an entity with a location in space but no extent (volume, area or length). ...
In mathematics, interval is a concept relating to the sequence and set-membership of one or more numbers. ...
A line, or straight line, can be described as an (infinitely) thin, (infinitely) long, perfectly straight curve (the term curve in mathematics includes straight curves). In Euclidean geometry, exactly one line can be found that passes through any two points. ...
2D with 1D surface In the mathematical subfield of numerical analysis a Bézier curve is a parametric curve important in computer graphics. ...
In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. ...
The ellipse and some of its mathematical properties. ...
Wikisource has an original article from the 1911 Encyclopædia Britannica about: Parabola A parabola The parabola (from the Greek: παÏαβολή) is a conic section generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. ...
A graph of a hyperbola. ...
Two intersecting planes in R3 In mathematics, a plane is a fundamental two-dimensional object. ...
Look up Polygon in Wiktionary, the free dictionary. ...
In geometry, a chiliagon (pronounced /ˈkɪli. ...
An image of a Regular Decagon In geometry, a decagon is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and all angles equal to 144°. Its Schläfli symbol is {10}. The area of a regular decagon...
A regular enneagon. ...
A googol is the large number 10100, that is, the digit 1 followed by one hundred zeroes. ...
A hectagon is a polygon with 100 edges. ...
In geometry, a heptagon is a polygon with seven sides and seven angles. ...
Categories: Math stubs | Polygons ...
A regular hexagon In geometry, a hexagon is a polygon with six edges and six vertices. ...
A myriagon is a polygon with 10,000 sides. ...
A regular octagon. ...
A regular pentagon A pentagram enclosed in a pentagon In geometry, a pentagon is any five-sided polygon. ...
In geometry, a quadrilateral is a polygon with four sides and four vertices. ...
For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...
In mathematics, several functions or groups of functions are important enough to deserve their own names. ...
3D with 1D surface A helix (pl: helices), from the Greek word Îλικας/Îλιξ, is a twisted shape like a spring, screw or a spiral staircase. ...
A plot of the trajectory Lorenz system for values r=28, σ = 10, b = 8/3 The Lorenz attractor, introduced by Edward Lorenz in 1963, is a non-linear three-dimensional deterministic dynamical system derived from the simplified equations of convection rolls arising in the dynamical equations of the atmosphere. ...
3D with 2D surface A cubic Bézier triangle is a surface with the equation where α3, β3, γ3, α2β, αβ2, β2γ, βγ2, αγ2, α2γ and αβγ are the control points of the triangle. ...
A negative number is a number that is less than zero, such as −3. ...
A right circular cylinder In mathematics, a cylinder is a quadric, i. ...
A hyperplane is a concept in geometry. ...
A Möbius strip made with a piece of paper and tape. ...
In solid geometry and some ancient physical theories, a Platonic solid is a convex polyhedron with: All its faces being congruent regular polygons The same number of faces meeting at each of its vertices These are in contrast to: The Kepler-Poinsot solids, which are not convex The Archimedean and...
A dodecahedron is literally a polyhedron with 12 faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. ...
A hexahedron is a polyhedron with 6 faces. ...
An icosahedron [ËŒaıkÉ™sÉ™hiËdrÉ™n] noun (plural: -drons, -dra [-drÉ™]) is a polyhedron having 20 faces, but usually a regular icosahedron is meant, which has faces which are equilateral triangles. ...
An octahedron (plural: octahedra) is a polyhedron with eight faces. ...
A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ...
A torus. ...
Ellipsoid Elliptic Paraboloid Hyperbolic Paraboloid Hyperboloid of One Sheet Hyperboloid of Two Sheets Cone Elliptic Cylinder Hyperbolic Cylinder Parabolic Cylinder In mathematics a quadric, or quadric surface, is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates). ...
This article needs to be cleaned up to conform to a higher standard of quality. ...
A right circular cylinder In mathematics, a cylinder is a quadric, i. ...
3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ...
In mathematics, a spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ...
A sphere (< Greek σφαίÏα) is a perfectly symmetrical geometrical object. ...
Hyperboloid of one sheet Hyperboloid of two sheets In mathematics, a hyperboloid is a quadric, a type of surface in three dimensions, described by the equation: (hyperboloid of one sheet), or (hyperboloid of two sheets) If, and only if, , it is a hyperboloid of revolution. ...
Paraboloid of revolution Hyperbolic paraboloid In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation: (elliptic paraboloid), or (hyperbolic paraboloid). ...
A sphere (< Greek σφαίÏα) is a perfectly symmetrical geometrical object. ...
4D with 2D surface The Klein bottle immersed in three-dimensional space. ...
In mathematics, the real projective plane is a two-dimensional manifold, that is, a surface, that has basic applications to geometry, but which cannot be embedded in our usual three-dimensional space. ...
4D with 3D surface The duocylinder is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of radius r: // Geometry Bounding 3-manifolds The duocylinder is bounded by two mutually perpendicular 3-manifolds with torus-like surfaces, described by the equations: and The duocylinder is so...
In mathematics, a hypersphere is a sphere which has dimension 3 or higher. ...
In geometry, a four-dimensional polytope is sometimes called a polychoron (plural: polychora) (from Greek poly meaning many and choros meaning room or space), 4-polytope, or polyhedroid. ...
In geometry, the 120-cell, or hecatonicosachoron, is the convex, regular polychoron (a 4-dimensional polytope) with 120 cells (or facets). ...
In mathematics, the 600-cell is the 4-dimensional convex regular polytope with 600 facets. ...
In geometry, a cross-polytope, or orthoplex, is a regular, convex polytope that exists in any number of dimensions. ...
In mathematics, the 24-cell is the 4-dimensional convex regular polytope with 24 facets. ...
The pentachoron, also called a pentatope or 4-simplex, is the simplest convex regular polychoron (a type of four-dimensional geometric figure). ...
In geometry, a simplex (plural: simplices) or n-simplex is an n-dimensional analogue of a triangle. ...
Stereographic projection In geometry, the tesseract is the 4-dimensional analog of the (3-dimensional) cube, where motion along the fourth dimension is often a representation for bounded transformations of the cube through time. ...
In geometry, a spherical cone is the figure in the 4-dimensional Euclidean space represented by the equation It is a quadric surface, and is one of the possible 3-manifolds which are 4-dimensional equivalents of the conical surface in 3 dimensions. ...
5D with 4D surfaces In geometry, a simplex (plural: simplices) or n-simplex is an n-dimensional analogue of a triangle. ...
In geometry, a cross-polytope, or orthoplex, is a regular, convex polytope that exists in any number of dimensions. ...
In geometry, a measure polytope is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). ...
6D
7D
8D
The boundary of the Mandelbrot set is a famous example of a fractal. ...
In mathematics, an Apollonian gasket or Apollonian net is a fractal generated from three circles, any two of which are tangent to one another. ...
The Cantor set, introduced by German mathematician Georg Cantor, is a remarkable construction involving only the real numbers between zero and one. ...
A dragon curve is the generic name for a member of a family of self similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems. ...
The first four iterations of the Koch snowflake The Koch curve is a mathematical curve, and one of the earliest fractal curves to have been described. ...
In mathematics, the Lévy C curve is a self similar fractal that was first described and whose differentiability properties were analysed by E.Cesaro in 1906 and G. Farber in 1910, but now bears the name of French mathematician Paul Lévy, who was the first to describe its...
Standard Lyapunov logistic fractal with iteration sequence AB Generalized Lyapunov logistic fractal with iteration sequence AABAB In mathematics Lyapunov fractals (also known as Markus-Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches...
A rendering of the Mandelbrot set In mathematics, the Mandelbrot set is defined as the connectedness locus of the family of complex quadratic polynomials. ...
The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński. ...
Intuitively, a continuous curve in the 2-dimensional plane or in the 3-dimensional space can be thought of as the path of a continuously moving point. To eliminate the inherent vagueness of this notion, Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the...
Sierpinski triangle The Sierpinski triangle, also called the Sierpinski gasket, is a fractal, named after Wacław Sierpiński who described it in 1916. ...
Etymology Esoteric is an adjective originating during Hellenic Greece under the domain of the Roman Empire; it comes from the Greek esôterikos, from esôtero, the comparative form of esô: within. It is a word meaning anything that is inner and occult, a latinate word meaning hidden (from which...
3D analogy to a wormhole. ...
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