MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign.

MathWorld logo
Type of businessPrivate
Type of site
Internet encyclopedia project
Available inEnglish
OwnerWolfram Research, Inc. (for-profit)
Created byEric W. Weisstein[1] and other contributors
RegistrationNot required for viewing
LaunchedNovember 0, 1999 (available at another location since 1995[2])
Current statusActive
Content license
All rights reserved (copyright held by contributors and non-exclusively licensed to Wolfram Research, Inc., free for personal and educational use)[3][4]


Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled "CRC Concise Encyclopedia of Mathematics." The free online version became only partially accessible to the public. In 1999 Weisstein went to work for Wolfram Research, Inc. (WRI), and WRI renamed the Math Treasure Trove to MathWorld and hosted it on the company's website[5] without access restrictions.

CRC lawsuit

In 2000, CRC Press sued Wolfram Research Inc. (WRI), WRI president Stephen Wolfram, and author Eric Weisstein, due to what they considered a breach of contract: that the MathWorld content was to remain in print only. The site was taken down by a court injunction.[6]

The case was later settled out of court, with WRI paying an unspecified amount and complying with other stipulations. Among these stipulations is the inclusion of a copyright notice at the bottom of the website and broad rights for the CRC Press to produce MathWorld in printed book form. The site then became once again available free to the public.

This case made a wave of headlines in online publishing circles. The PlanetMath project was a result of MathWorld's being unavailable.[7]

See also


  1. ^ Eric Weisstein (2007). "Making MathWorld". Mathematica Journal. 10 (3).
  2. ^ "What is the history of MathWorld?". MathWorld Q&A. Wolfram Research, Inc. Retrieved 8 February 2011.
  3. ^ W., Weisstein, Eric. "Terms of Use".
  4. ^ W., Weisstein, Eric. "Wolfram MathWorld: The Web's Most Extensive Mathematics Resource".
  5. ^ The Value of a Good Idea: Protecting Intellectual Property in an Information Economy. Silver Lake Publishing. 2002. ISBN 9781563437458.
  6. ^ Corneli, Joseph (2011). "The PlanetMath Encyclopedia" (PDF). ITP 2011 Workshop on Mathematical Wikis (MathWikis 2011) Nijmegen, Netherlands, August 27, 2011.

External links

Ed Pegg Jr.

Ed Pegg Jr. (born December 7, 1963) is an expert on mathematical puzzles and is a self-described recreational mathematician. He wrote an online puzzle column called Ed Pegg Jr.'s Math Games for the Mathematical Association of America during the years 2003–2007. His puzzles have also been used by Will Shortz on the puzzle segment of NPR's Weekend Edition Sunday.

In 2000, he left NORAD to join Wolfram Research, where he collaborated on A New Kind of Science (NKS). In 2004 he started assisting Eric W. Weisstein at Wolfram MathWorld. He has made contributions to several hundred MathWorld articles. He was one of the chief consultants for Numb3rs.

Edge (geometry)

For edge in graph theory, see Edge (graph theory)In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.

Elementary cellular automaton

In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. As such it is one of the simplest possible models of computation. Nevertheless, there is an elementary cellular automaton (rule 110, defined below) which is capable of universal computation.

Enneagram (geometry)

In geometry, an enneagram is a nine-pointed plane figure. It is sometimes called a nonagram or nonangle.The name enneagram combines the numeral prefix, ennea-, with the Greek suffix -gram. The -gram suffix derives from γραμμῆς (grammēs) meaning a line.

Eric W. Weisstein

Eric Wolfgang Weisstein (born March 18, 1969) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld). He is the author of the CRC Concise Encyclopedia of Mathematics. He currently works for Wolfram Research, Inc.

Glossary of shapes with metaphorical names

Many shapes have metaphorical names, i.e., their names are metaphors: these shapes are named after a most common object that has it. For example, "U-shape" is a shape that resembles the letter U, a bell-shaped curve has the shape of the vertical cross-section of a bell, etc. These terms may variously refer to objects, their cross sections or projections.

Some of these names are "classical terms", i.e., words of Latin or Ancient Greek etymology. Others are English language constructs (although the base words may have non-English etymology). In some disciplines, where shapes of subjects in question are a very important consideration, the shape naming may be quite elaborate, see, e.g., the taxonomy of shapes of plant leaves in botany.


Aquiline, shaped like an eagle's beak (as in a Roman nose)

Bell-shaped curve

Biconic shape, a shape in a way opposite to the hourglass: it is based on two oppositely oriented cones or truncated cones with their bases joined; the cones are not necessarily the same

Bowtie shape, in two dimensions

Atmospheric reentry apparatus

Centerbody of an inlet cone in ramjets

Bow shape

Bow curve

Bullet Nose an open-ended hourglass

Butterfly curve

Cocked Hat curve, also known as Bicorn

Cone (from the Greek word for « pine cone »)

Donut shape

Egg-shaped, see "Oval", below

Fish bladder or Lens shape (the latter taking its name from the shape of the lentil seed)

Geoid (From Greek Ge (γη) for "Earth"), the term specifically introduced to denote the approximation of the shape of the Earth, which is approximately spherical, but not exactly so

Heart shape, long been used for its varied symbolism

Hourglass shape or hourglass figure, the one that resembles an hourglass; nearly symmetric shape wide at its ends and narrow in the middle; some flat shapes may be alternatively compared to the figure eight or hourglass

Dog bone shape, an hourglass with rounded ends

Hourglass corset


Hourglass Nebula

Inverted bell

Lune, from the Latin word for the Moon

Maltese Cross curve

Mushroom shape, which became infamous as a result of the mushroom cloud

Oval (from the Latin "ovum" for egg), a descriptive term applied to several kinds of "rounded" shapes, including the egg shape

Pear shaped, in reference to the shape of a pear, i.e., a generally rounded shape, tapered towards the top and more spherical/circular at the bottom

Rod, a 3-dimensional, solid (filled) cylinder

Rod shaped bacteria

Scarabaeus curve resembling a scarab

Serpentine, shaped like a snake

Stadium, two half-circles joined by straight sides

Stirrup curve

Star a figure with multiple sharp points



Jean Gaston Darboux

Jean-Gaston Darboux FAS MIF FRS FRSE (14 August 1842 – 23 February 1917) was a French mathematician.

List of mathematical constants

A mathematical constant is a number, which has a special meaning for calculations. For example, the constant π means the ratio of the length of a circle's circumference to its diameter. This value is always the same for any circle.

Mathematical constant

A mathematical constant is a special number that is "significantly interesting in some way". Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, and calculus.

What it means for a constant to arise "naturally", and what makes a constant "interesting", is ultimately a matter of taste, and some mathematical constants are notable more for historical reasons than for their intrinsic mathematical interest. The more popular constants have been studied throughout the ages and computed to many decimal places.

All mathematical constants are definable numbers and usually are also computable numbers (Chaitin's constant being a significant exception).

Order-7 square tiling

In geometry, the order-7 square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,7}.

Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets. The Petrie polygon of a regular polygon is the regular polygon itself; that of a regular polyhedron is a skew polygon such that every two consecutive side (but no three) belongs to one of the faces.For every regular polytope there exists an orthogonal projection onto a plane such that one Petrie polygon becomes a regular polygon with the remainder of the projection interior to it. The plane in question is the Coxeter plane of the symmetry group of the polygon, and the number of sides, h, is Coxeter number of the Coxeter group. These polygons and projected graphs are useful in visualizing symmetric structure of the higher-dimensional regular polytopes.

Petrie polygons can be defined more generally for any embedded graph. They form the faces of another embedding of the same graph, usually on a different surface, called the Petrie dual.


PlanetMath is a free, collaborative, online mathematics encyclopedia. The emphasis is on rigour, openness, pedagogy, real-time content, interlinked content, and also community of about 24,000 people with various maths interests. Intended to be comprehensive, the project is currently hosted by the University of Waterloo. The site is owned by a US-based nonprofit corporation, ", Ltd".PlanetMath was started when the popular free online mathematics encyclopedia MathWorld was temporarily taken offline for 12 months by a court injunction as a result of the CRC Press lawsuit against the Wolfram Research company and its employee (and MathWorld's author) Eric Weisstein.


In geometry, the rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.

It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.

Smarandache–Wellin number

In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin.

The first decimal Smarandache–Wellin numbers are:

2, 23, 235, 2357, 235711, 23571113, 2357111317, 235711131719, 23571113171923, 2357111317192329, ... (sequence A019518 in the OEIS).

Snub triapeirogonal tiling

In geometry, the snub triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of sr{∞,3}.


A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry.

If the ellipse is rotated about its major axis, the result is a prolate (elongated) spheroid, shaped like an American football or rugby ball. If the ellipse is rotated about its minor axis, the result is an oblate (flattened) spheroid, shaped like a lentil. If the generating ellipse is a circle, the result is a sphere.

Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography the Earth is often approximated by an oblate spheroid instead of a sphere. The current World Geodetic System model uses a spheroid whose radius is 6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles.

The word spheroid originally meant "an approximately spherical body", admitting irregularities even beyond the bi- or tri-axial ellipsoidal shape, and that is how the term is used in some older papers on geodesy (for example, referring to truncated spherical harmonic expansions of the Earth).


A tetromino is a geometric shape composed of four squares, connected orthogonally. This, like dominoes and pentominoes, is a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected orthogonally.

A popular use of tetrominoes is in the video game Tetris, which refers to them as tetriminos. The tetrominoes used in the game are specifically the one-sided tetrominoes. Tetrominoes also appeared in Zoda's Revenge: StarTropics II but were called tetrads instead.

Transcendental number

In mathematics, a transcendental number is a real number or complex number that is not an algebraic number—that is, not a root (i.e., solution) of a nonzero polynomial equation with integer coefficients. The best-known transcendental numbers are π and e.

Though only a few classes of transcendental numbers are known (in part because it can be extremely difficult to show that a given number is transcendental), transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers compose a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set. All real transcendental numbers are irrational numbers, since all rational numbers are algebraic. The converse is not true: not all irrational numbers are transcendental. For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2 − 2 = 0. The golden ratio (denoted or ) is another irrational number that is not transcendental, as it is a root of the polynomial equation x2x − 1 = 0.

Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.


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