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Online encyclopedia
PlanetMath is a free, collaborative, mathematics online encyclopedia. Intended to be comprehensive, the project is currently hosted by the University of
PlanetMath
Seven mathematical problems with a US$1 million prize for each solution
ISBN 978-0-8218-3679-8. This article incorporates material from Milllennium Problems on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Millennium_Prize_Problems
Natural number
Research, Inc. Retrieved 1 November 2026. CompositeFan. "Zeisel number". PlanetMath. Retrieved 1 November 2026. Weisstein, Eric W. (12 December 2002). "Zeisel
1000_(number)
Mnemonic device for calculating 3 by 3 matrix determinants
Elements of Linear Algebra. CRC Press. ISBN 978-0-412-55280-9. Sarrus' rule at Planetmath Linear Algebra: Rule of Sarrus of Determinants at khanacademy.org
Rule_of_Sarrus
Hyperbolic analogues of trigonometric functions
Encyclopedia of Mathematics, EMS Press, 2001 [1994] Hyperbolic functions on PlanetMath GonioLab: Visualization of the unit circle, trigonometric and hyperbolic
Hyperbolic_functions
Infinite series in mathematical analysis
Series, Vol. 32, No. 3 (Jul., 1931), pp. 600–622. "Dirichlet series". PlanetMath. "Dirichlet series", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
General_Dirichlet_series
Type of probability distribution
London: Springer. 2005. ISBN 978-1-85233-896-1. OCLC 262680588. "Joint continuous density function". PlanetMath. Mathworld: Joint Distribution Function
Joint probability distribution
Joint_probability_distribution
Large number defined as ten to the 100th power
the free dictionary. Weisstein, Eric W. "Googol". MathWorld. Googol at PlanetMath. Padilla, Tony; Symonds, Ria. "Googol and Googolplex". Numberphile. Brady
Googol
Middle quantile of a data set or probability distribution
Mechanics This article incorporates material from Median of a distribution on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Median
Branch of mathematics
[1994] Weisstein, Eric W. "Calculus". MathWorld. Topics on Calculus at PlanetMath. Calculus Made Easy (1914) by Silvanus P. Thompson Full text in PDF Calculus
Calculus
Mathematical model for deduction or proof systems
Daniel Richardson, Formal systems, logic and semantics Formal System at PlanetMath. Encyclopedia of Mathematics, Formal system Peter Suber, Formal Systems
Formal_system
Horizontal and vertical axes/coordinate numbers of a 2D coordinate system or graph
"Ordinate". MathWorld. Retrieved 14 July 2013. "Cartesian coordinates". PlanetMath. Archived from the original on 2025-02-21. Retrieved 2025-04-02. 'applicate'
Abscissa_and_ordinate
Topological space that is homeomorphic to a metric space
no. 2, 293–300. This article incorporates material from Metrizable on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Metrizable_space
Famous open problem in mathematics
"Swinnerton-Dyer Conjecture". MathWorld. "Birch and Swinnerton-Dyer Conjecture". PlanetMath. The Birch and Swinnerton-Dyer Conjecture: An Interview with Professor
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
Number in {..., –2, –1, 0, 1, 2, ...}
"Integer". MathWorld. This article incorporates material from Integer on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Integer
Simple curve of Euclidean geometry
"Circle". Encyclopedia of Mathematics. EMS Press. 2001 [1994]. Circle at PlanetMath. Weisstein, Eric W. "Circle". MathWorld. "Interactive Java applets". for
Circle
Part of a straight line that is bounded by two distinct end points
dictionary. Weisstein, Eric W. "Line segment". MathWorld. Line Segment at PlanetMath Copying a line segment with compass and straightedge Dividing a line segment
Line_segment
Copyleft license primarily for free software documentation
Last.fm – artist descriptions are under GFDL Marxists Internet Archive PlanetMath (now uses CC BY-SA license) Rosetta Code SourceWatch The specification
GNU Free Documentation License
GNU_Free_Documentation_License
Spiral with constant distance from itself
Weisstein, Eric W. "Archimedes' Spiral". MathWorld. archimedean spiral at PlanetMath. Page with Java application to interactively explore the Archimedean spiral
Archimedean_spiral
Coordinate system
(solid geometry) Orthant Ray (geometry) Wikimedia Commons has media related to Quadrants. Weisstein, Eric W. "Quadrant". MathWorld. Quadrant at PlanetMath.
Quadrant_(plane_geometry)
Coordinate system using perpendicular axes
system", Encyclopedia of Mathematics, EMS Press "Cartesian coordinates". planetmath.org. Retrieved 25 August 2024. Hughes-Hallett, McCallum & Gleason 2013
Cartesian_coordinate_system
Method of solution to differential equations
for differential operator at PlanetMath. Green's function at PlanetMath. Green functions and conformal mapping at PlanetMath. Introduction to the Keldysh
Green's_function
British mathematician
the European Mathematical Society (33): 8–9. "William Timothy Gowers". PlanetMath. Listen to Timothy Gowers on The Forum from BBC World Service Radio Timothy
Timothy_Gowers
Statement that is taken to be true
dictionary. Wikisource has the text of the 1911 Encyclopædia Britannica article "Axiom". Axiom at PhilPapers Axiom at PlanetMath. Metamath axioms page
Axiom
Unique positive real number which when multiplied by itself gives 3
pivotal role in studies of three-phase electric power. "square root of 3". planetmath.org. Retrieved 2025-07-23. Komsta, Łukasz (December 2013). "Computations
Square_root_of_3
Open problem on 3x+1 and x/2 functions
Weisstein, Eric W. "Collatz Problem". MathWorld. Collatz Problem at PlanetMath. Nochella, Jesse. "Collatz Paths". Wolfram Demonstrations Project. Eisenbud
Collatz_conjecture
Polynomial of the elements of a matrix
Mathematical Monthly, 72 (6): 577–591, doi:10.2307/2313846, JSTOR 2313846 Permanent at PlanetMath. Van der Waerden's permanent conjecture at PlanetMath.
Permanent_(mathematics)
90° angle (π/2 radians)
Heath p. 181 Wentworth p. 9 Heath pp. 200–201 for the paragraph "octant". PlanetMath.org. 2013-03-22. Retrieved 2024-10-21. Wentworth, G.A. (1895). A Text-Book
Right_angle
Ancient Egyptian texts
College, London A Kahun Mathematical Fragment[link removed], a paper by John A.R. Legon Kahun Papyrus and Arithmetic Progressions at PlanetMath. v t e
Kahun_Papyri
Pair of logical equivalences
Weisstein, Eric W. "de Morgan's Laws". MathWorld. de Morgan's laws at PlanetMath. Duality in Logic and Language, Internet Encyclopedia of Philosophy.
De_Morgan's_laws
Geometric figure which has infinite surface area but finite volume
60–65. doi:10.5951/MT.82.1.0060. JSTOR 27966098. Torricelli's trumpet at PlanetMath Weisstein, Eric W. "Gabriel's Horn". MathWorld. "Gabriel's Horn" by John
Gabriel's_horn
Software for converting LaTeX to XML and other formats
as to render the web pages on the peer produced mathematics website, PlanetMath. Since July, 2015, it was adopted by Authorea for their advanced LaTeX
LaTeXML
Distance from zero to a number
"Absolute value". Encyclopedia of Mathematics. EMS Press. 2001 [1994]. absolute value at PlanetMath. Weisstein, Eric W. "Absolute Value". MathWorld.
Absolute_value
Natural number
Encyclopedia of Integer Sequences. OEIS Foundation. "Leyland number". planetmath.org. Retrieved 2025-05-20. "The Planck Scale". School of Physics, University
10,000,000
Branch of mathematics
Algebraic Geometry by Ravi Vakil, 808 pp. Algebraic geometry entry on PlanetMath English translation of the van der Waerden textbook Dieudonné, Jean (March
Algebraic_geometry
National encyclopedia of Canada
Encyclopedia Encyclopedia of Canadian Biography Encyclopaedia Metallum PlanetMath List of online encyclopedias National historic significance Events of
The_Canadian_Encyclopedia
article incorporates material from Isomorphism-closed subcategory on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Isomorphism-closed subcategory
Isomorphism-closed_subcategory
Set of philosophical problems
Philosophy. This article incorporates material from Zeno's paradox on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Zeno's_paradoxes
Online mathematics reference work
This case made a wave of headlines in online publishing circles. The PlanetMath project was a result of MathWorld's being unavailable. List of online
MathWorld
significantly different from the so-called authority model previously adopted by PlanetMath. Only registered users could create and edit their own entries, or contribute
PlanetPhysics
Function space of all functions whose derivatives are rapidly decreasing
article incorporates material from Space of rapidly decreasing functions on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Schwartz_space
Additional mathematical object
1170–1173. doi:10.1126/science.260.5111.1170. PMID 17806355. "Structure". PlanetMath. (provides a model theoretic definition.) Mathematical structures in computer
Mathematical_structure
Mathematical operation
This article incorporates material from Mellin's inverse formula on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Inverse_Laplace_transform
Algebraic structure of set algebra
York. https://doi.org/10.1007/978-1-4757-2545-2 "Algebra of sets", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Sigma Algebra from PlanetMath.
Σ-algebra
Algebraic structure with an associative operation and an identity element
S2CID 56410568. Zbl 0865.06010. "Monoid", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Weisstein, Eric W. "Monoid". MathWorld. Monoid at PlanetMath.
Monoid
Mathematics web site
resource in history of mathematics". Mathematics Genealogy Project MathWorld PlanetMath Hughes, Barnabas (July 2007), "St Andrews History of Mathematics Archive"
MacTutor History of Mathematics Archive
MacTutor_History_of_Mathematics_Archive
Formula for systems of linear equations
Wikibooks has a book on the topic of: Linear Algebra/Cramer's Rule Proof of Cramer's Rule at PlanetMath. Weisstein, Eric W. "Cramer's rule". MathWorld.
Cramer's_rule
Average uncertainty in variable's states
ISBN 978-1-4757-4321-0. This article incorporates material from Shannon's entropy on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Entropy_(information_theory)
Theorem on modular exponentiation
Elementary Number Theory, New York: Chelsea Weisstein, Eric W. "Euler's Totient Theorem". MathWorld. Euler-Fermat Theorem at PlanetMath Portal: Mathematics
Euler's_theorem
Arithmetic operation
Archived 2019-08-17 at the Wayback Machine Retrieved October 23, 2018 Planetmath division Division on a Japanese abacus selected from Abacus: Mystery of
Division_(mathematics)
Generalization of metric spaces in mathematics
Pseudometric space on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License. "Example of pseudometric space". PlanetMath.
Pseudometric_space
Geometric relation between a triangle's side lengths and cevian length
Cochran "Proposition II" Russell 1905, p. 3 Proof of Stewart's Theorem at PlanetMath. Coxeter, H.S.M.; Greitzer, S.L. (1967), Geometry Revisited, New Mathematical
Stewart's_theorem
Two matrices placed in the diagonal of a larger matrix
McGraw-Hill Education. ISBN 9781260011449. Direct sum of matrices at PlanetMath. Abstract nonsense: Direct Sum of Linear Transformations and Direct Sum
Direct_sum_of_matrices
Geometric concept of a 2D space with "points at infinity" adjoined
Small Order, (2003) Ch. Weibel: Survey of Non-Desarguesian Planes Weisstein, Eric W., "Projective plane", MathWorld "Projective plane" at PlanetMath.
Projective_plane
Sequence of numbers ((2n) choose (n))
Koshy, Thomas (2008), Catalan Numbers with Applications, Oxford University Press, ISBN 978-0-19533-454-8. Central binomial coefficient at PlanetMath.
Central_binomial_coefficient
Natural number
constant". arXiv:2309.13520 [11K16]. Mravinci. "Copeland-Erdős constant". PlanetMath. Retrieved 2026-10-15. Weisstein, Eric W. "Smarandache-Wellin Number"
2000_(number)
Subset of incomparable elements
connected", SIAM Journal on Computing, 12 (4): 777–788, doi:10.1137/0212053, MR 0721012 Weisstein, Eric W. "Antichain". MathWorld. "Antichain". PlanetMath.
Antichain
Non-orientable mathematical surface
October 2022. This article incorporates material from Klein bottle on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Klein_bottle
Approximation for factorials
n! Weisstein, Eric W., "Stirling's Approximation", MathWorld{{cite web}}: CS1 maint: overridden setting (link) Stirling's approximation at PlanetMath.
Stirling's_approximation
Plane curve
at Wikiquote Media related to Ellipses at Wikimedia Commons ellipse at PlanetMath. Weisstein, Eric W. "Ellipse". MathWorld. Weisstein, Eric W. "Ellipse
Ellipse
General theory of mathematical structures
channel on YouTube, a channel about category theory. Category theory at PlanetMath.. Video archive of recorded talks relevant to categories, logic and the
Category_theory
Family of second-order differential equations
York: Springer. pp. 254–257. ISBN 0-387-97443-1. "Liénard equation", Encyclopedia of Mathematics, EMS Press, 2001 [1994] LienardSystem at PlanetMath.
Liénard_equation
Infinite products of functions indexed by primes
1000-digit values This article incorporates material from Euler product on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Euler_product
Theorem in topology
Theorem for Triangles at cut-the-knot Brouwer fixed-point theorem at PlanetMath. Reconstructing Brouwer at MathPages Brouwer Fixed Point Theorem at Math
Brouwer_fixed-point_theorem
Zbl 0061.39807. This article incorporates material from Development on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Development_(topology)
Non-zero element of a matrix selected by an algorithm
row echelon form. This article incorporates material from Pivoting on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Pivot_element
Number of subsets of a given size
Retrieved 2013-09-03. This article incorporates material from the following PlanetMath articles, which are licensed under the Creative Commons Attribution/Share-Alike
Binomial_coefficient
American mathematician and encyclopedist (born 1969)
MathWorld on November 6, 2001. This ultimately led to the creation of PlanetMath. Wolfram Research, Stephen Wolfram, and Eric Weisstein settled with the
Eric_W._Weisstein
Right inverse of a fiber bundle map
ISBN 0-201-10096-7. Husemöller, Dale (1994), Fibre Bundles, Springer Verlag, ISBN 0-387-94087-1 Fiber Bundle, PlanetMath Weisstein, Eric W. "Fiber Bundle". MathWorld.
Section_(fiber_bundle)
Mathematical concept in algebra
Second Course in Linear Algebra (1st ed.), Cambridge University Press, ISBN 978-1-107-10381-8 Nilpotent matrix and nilpotent transformation on PlanetMath.
Nilpotent_matrix
Decomposition of periodic functions
This article incorporates material from example of Fourier series on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Fourier_series
Relates the tangent of half of an angle to trigonometric functions of the entire angle
of Mathematics, EMS Press, 2001 [1994] Tangent half-angle formula at PlanetMath. Mathematics. United States, NAVEDTRA [i.e. Naval] Education and Training
Tangent_half-angle_formula
Concept in number theory
Mathematics book series. Vol. 1467. Springer. doi:10.1007/BFb0098246. ISBN 978-3-540-47374-9. S2CID 118143570. Dirichlet's Approximation Theorem at PlanetMath.
Dirichlet's approximation theorem
Dirichlet's_approximation_theorem
American mathematician (1931–2018)
1090/s0273-0979-99-00792-2. This article incorporates material from Elias Stein on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Elias_M._Stein
Pair of diametrically opposite points on a circle, sphere, or hypersphere
Guillemin; A. Pollack (1974). Differential topology. Prentice-Hall. "Antipodes", Encyclopedia of Mathematics, EMS Press, 2001 [1994] "antipodal". PlanetMath.
Antipodal_point
Point which a function/system returns to after some time or iterations
mappings This article incorporates material from hyperbolic fixed point on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Periodic_point
Probability Measures on Polish Spaces. STOCHASTICS MONOGRAPHS. London: CRC Press. p. 13. ISBN 0415273870. "Measurable projection theorem", PlanetMath
Projection_(measure_theory)
Result in combinatorics and graph theory
article incorporates material from proof of Hall's marriage theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Hall's_marriage_theorem
Mathematical term
the Stone–Čech compactification of the natural numbers. "Banach limit". PlanetMath. Conway, Theorem III.7.1 Balcar-Štěpánek, 8.34 Balcar, Bohuslav; Štěpánek
Banach_limit
Sum of an (infinite) geometric progression
Weisstein, Eric W. "Geometric Series". MathWorld. Geometric Series at PlanetMath. Peppard, Kim. "College Algebra Tutorial on Geometric Sequences and Series"
Geometric_series
Axioms for the natural numbers
Commentary on Dedekind's work. This article incorporates material from PA on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Peano_axioms
Theorem for proving more complex theorems
a Thousand Theorems This article incorporates material from Lemma on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Lemma_(mathematics)
Mathematical constants related to chaotic behavior
solution of the Feigenbaum-Cvitanovic equation) Feigenbaum constant – PlanetMath Hofstätter, Harald (25 October 2015). "Calculation of the Feigenbaum Constants"
Feigenbaum_constants
American foundation
website This article incorporates material from Millennium Problems on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Clay_Mathematics_Institute
3D generalization of the Leibniz integral rule
Introduction to Fluid Mechanics. Georgia Tech. Archived from the original on March 27, 2008. "Reynolds transport theorem". planetmath.org. Retrieved 2024-04-22.
Reynolds_transport_theorem
Probability distribution
populations Seeing Around Corners (Artificial societies turn up Zipf's law) PlanetMath article on Zipf's law Distributions de type "fractal parabolique" dans
Zipf's_law
Result from multiplying no factors
equal to 1 we can do away with the exception: 'If n is a positive integer, then n is a finite product of primes.' PlanetMath article on the empty product
Empty_product
to provide fixes and information on all PC games 45,508 CC NC-SA 3.0 PlanetMath Misc – Mathematics Free wiki-style mathematical encyclopedia Proteopedia
List_of_wikis
Counting technique in combinatorics
article incorporates material from principle of inclusion–exclusion on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Inclusion–exclusion_principle
Algorithm for computing greatest common divisors
MathWorld. Euclid's Algorithm at cut-the-knot Euclid's algorithm at PlanetMath. The Euclidean Algorithm at MathPages Euclid's Game at cut-the-knot Music
Euclidean_algorithm
System of mathematical set theory
Theory", Journal of Formalized Mathematics. Metamath: "Proof Explorer Home Page." Scroll down to "Grothendieck's Axiom." Tarski's Axiom at PlanetMath.
Tarski–Grothendieck set theory
Tarski–Grothendieck_set_theory
Every natural number can be represented as the sum of four integer squares
four squares in Lagrange's theorem" (PDF). Integers. 18A: A15. Proof at PlanetMath.org Another proof An applet decomposing numbers as sums of four squares
Lagrange's four-square theorem
Lagrange's_four-square_theorem
Class of generalisations of the derivative
ISBN 978-1-4348-4161-2. This article incorporates material from Dini derivative on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Dini_derivative
Disjoint, equal-size subsets of a group's underlying set
"Coset in a group", Encyclopedia of Mathematics, EMS Press Coset at PlanetMath. Illustrated examples "Coset". groupprops. The Group Properties Wiki.
Coset
Concept in General Topology
Rinehart and Winston (1970). ISBN 0030794854. Willard, Stephen (2004). General Topology. Dover Publications. ISBN 0-486-43479-6. "Box topology". PlanetMath.
Box_topology
ISBN 3-7643-2931-9. This article incorporates material from Conjugate index on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Conjugate_index
Natural number
Research, Inc. Retrieved 2026-10-20. PrimeFan. "Lucas-Carmichael number". PlanetMath. Retrieved 2026-10-20. Numberphile (2015-01-15). Something special about
399_(number)
Orthonormalization of a set of vectors
of n vectors of order m routine Proof: Raymond Puzio, Keenan Kidwell. "proof of Gram-Schmidt orthogonalization algorithm" (version 8). PlanetMath.org.
Gram–Schmidt_process
Theorem in complex analysis
New York. This article incorporates material from Hardy's theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike
Hardy's_theorem
Spectroscopic technique based on change of nuclear spin state
mention of Jeener's suggestion.) Two-dimensional Fourier Transforms at PlanetMath. "Multinuclear NMR". chem.ch.huji.ac.il. Archived from the original on
Nuclear_magnetic_resonance
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