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https://mathworld.wolfram.com/ Wolfram MathWorld: The Web's Most Extensive Mathematics Resource Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples. wolfram mathworld the web extensive mathematics resource https://mathworld.wolfram.com/LucasPolynomial.html Lucas Polynomial -- from Wolfram MathWorld The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by... lucas polynomial wolfram mathworld https://mathworld.wolfram.com/Reflection.html Reflection -- from Wolfram MathWorld The operation of exchanging all points of a mathematical object with their mirror images (i.e., reflections in a mirror). Objects that do not change handedness... reflection wolfram mathworld https://mathworld.wolfram.com/Topos.html Topos -- from Wolfram MathWorld A category modeled after the properties of the category of sets. A category E is a topos if E has finite limits and every object of E has a power object (Barr... topos wolfram mathworld https://mathworld.wolfram.com/AtomicSpiral.html Atomic Spiral -- from Wolfram MathWorld atomic spiral wolfram mathworld https://mathworld.wolfram.com/SmallestQuarticCrossingNumberGraph.html Smallest Quartic Crossing Number Graph -- from Wolfram MathWorld The smallest quartic graphs with graph crossing number CN(G)=n have been termed "crossing number graphs" or n-crossing graphs by Pegg and Exoo (2009) in the... smallest quartic crossing number graph https://iris.cnr.it/handle/20.500.14243/84644 Mathworld. Una certezza matematica di interesse bibliografico. di interesse mathworld una certezza matematica https://mathworld.wolfram.com/SuzukiGraph.html Suzuki Graph -- from Wolfram MathWorld The Suzuki graph is an edge-transitive strongly regular graph on 1782 vertices with parameters (nu,k,lambda,mu)=(1782,416,100,96) and automorphism group Suz.2.... suzuki graph wolfram mathworld https://mathworld.wolfram.com/QuadraticFormIndex.html Quadratic Form Index -- from Wolfram MathWorld The index I associated to a symmetric, non-degenerate, and bilinear g over a finite-dimensional vector space V is a nonnegative integer defined by I=max_(W in... quadratic form index wolfram mathworld https://mathworld.wolfram.com/HyperbolicPolyhedron.html Hyperbolic Polyhedron -- from Wolfram MathWorld A polyhedron in a hyperbolic geometry. hyperbolic polyhedron wolfram mathworld https://mathworld.wolfram.com/TrivalentTree.html Trivalent Tree -- from Wolfram MathWorld trivalent tree wolfram mathworld https://mathworld.wolfram.com/PollardRhoFactorizationMethod.html Pollard rho Factorization Method -- from Wolfram MathWorld A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The... pollard rho factorization method wolfram https://mathworld.wolfram.com/KreiselConjecture.html Kreisel Conjecture -- from Wolfram MathWorld The Kreisel conjecture is a conjecture in proof theory that postulates that, if phi(x) is a formula in the language of arithmetic for which there exists a... kreisel conjecture wolfram mathworld https://mathworld.wolfram.com/257-gon.html 257-gon -- from Wolfram MathWorld 257 is a Fermat prime, and the 257-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. An illustration of the 257-gon... gon wolfram mathworld https://mathworld.wolfram.com/ExponentialMatrix.html Exponential Matrix -- from Wolfram MathWorld exponential matrix wolfram mathworld https://mathworld.wolfram.com/CriticalPoint.html Critical Point -- from Wolfram MathWorld A function y=f(x) has critical points at all points x_0 where f^'(x_0)=0 or f(x) is not differentiable. A function z=f(x,y) has critical points where the... critical point wolfram mathworld https://mathworld.wolfram.com/k-Tuple.html k-Tuple -- from Wolfram MathWorld k tuple wolfram mathworld https://mathworld.wolfram.com/IsospectralManifolds.html Isospectral Manifolds -- from Wolfram MathWorld Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter,... manifolds wolfram mathworld https://mathworld.wolfram.com/72Rule.html 72 Rule -- from Wolfram MathWorld rule wolfram mathworld https://mathworld.wolfram.com/MullersMethod.html Muller's Method -- from Wolfram MathWorld Generalizes the secant method of root finding by using quadratic 3-point interpolation q=(x_n-x_(n-1))/(x_(n-1)-x_(n-2)). (1) Then define A =... muller method wolfram mathworld https://mathworld.wolfram.com/GirardsSphericalExcessFormula.html Girard's Spherical Excess Formula -- from Wolfram MathWorld Let a spherical triangle Delta have angles A, B, and C. Then the spherical excess is given by Delta=A+B+C-pi. girard spherical excess formula wolfram https://mathworld.wolfram.com/news/2001-10-04/normal/ MathWorld News: New Class of Normal Numbers Discovered news new class of mathworld normal numbers https://mathworld.wolfram.com/MapesMethod.html Mapes' Method -- from Wolfram MathWorld A method for computing the prime counting function. Define the function... mapes method wolfram mathworld https://mathworld.wolfram.com/PartialEvaluation.html Partial Evaluation -- from Wolfram MathWorld Partial evaluation is a branch of computer science studying program transformation via specialization. Any function can be specialized by fixing one or more of... partial evaluation wolfram mathworld https://mathworld.wolfram.com/CenterFunction.html Center Function -- from Wolfram MathWorld center function wolfram mathworld https://mathworld.wolfram.com/KummerGraph.html Kummer Graph -- from Wolfram MathWorld The Kummer graph is the name apparently first adopted here for the Levi graph of Kummer's 16_6 configuration (Coxeter 1950), corresponding to the folded 6-cube... kummer graph wolfram mathworld https://mathworld.wolfram.com/NonhamiltonianCubicGraph.html Nonhamiltonian Cubic Graph -- from Wolfram MathWorld cubic graph wolfram mathworld https://mathworld.wolfram.com/UniformDifferenceDistribution.html Uniform Difference Distribution -- from Wolfram MathWorld The difference X_1-X_2 of two uniform variates on the interval [0,1] can be found as P_(X_1-X_2)(u) = int_0^1int_0^1delta((x-y)-u)dxdy (1) = 1-u+2uH(-u), (2)... uniform difference distribution wolfram mathworld https://mathworld.wolfram.com/Surjective.html Surjective -- from Wolfram MathWorld wolfram mathworld https://www.wolframalpha.com/input/?i=MathWorld+subject+chaos MathWorld subject chaos - Wolfram|Alpha mathworld subject chaos wolfram alpha https://mathworld.wolfram.com/ParabolicHornCyclide.html Parabolic Horn Cyclide -- from Wolfram MathWorld A parabolic cyclide formed by inversion of a horn torus when the inversion sphere is tangent to the torus. parabolic horn wolfram mathworld https://mathworld.wolfram.com/StabilityIndex.html Stability Index -- from Wolfram MathWorld The stability index Z^_(G) of a graph G is defined by Z^_=sum_(k=0)^(|_n/2_|)|c_(2k)|, where c_k is the kth coefficient of the characteristic polynomial and... stability index wolfram mathworld https://mathworld.wolfram.com/SystemofDifferentialEquations.html System of Differential Equations -- from Wolfram MathWorld differential equations system wolfram mathworld https://mathworld.wolfram.com/OrthocentricLine.html Orthocentric Line -- from Wolfram MathWorld The common axis of the three altitude planes of a trihedron. line wolfram mathworld https://mathworld.wolfram.com/topics/Noe.html Noe -- from Wolfram MathWorld noe wolfram mathworld https://mathworld.wolfram.com/StandardizedScore.html Standardized Score -- from Wolfram MathWorld standardized score wolfram mathworld https://mathworld.wolfram.com/topics/Wallis.html Wallis -- from Wolfram MathWorld wallis wolfram mathworld https://mathworld.wolfram.com/SphericalTetrahedron.html Spherical Tetrahedron -- from Wolfram MathWorld spherical tetrahedron wolfram mathworld https://mathworld.wolfram.com/topics/GeneralizedHypergeometricFunctions.html Generalized Hypergeometric Functions -- from Wolfram MathWorld generalized hypergeometric functions wolfram mathworld https://mathworld.wolfram.com/IVP.html IVP -- from Wolfram MathWorld ivp wolfram mathworld https://mathworld.wolfram.com/topics/ProjectiveGeometry.html Projective Geometry -- from Wolfram MathWorld projective geometry wolfram mathworld https://mathworld.wolfram.com/n-ColoredGraph.html n-Colored Graph -- from Wolfram MathWorld n colored graph wolfram mathworld https://mathworld.wolfram.com/DawsonsFunction.html Dawson's Function -- from Wolfram MathWorld dawson function wolfram mathworld https://mathworld.wolfram.com/Bauspiel.html Bauspiel -- from Wolfram MathWorld A construction for the rhombic dodecahedron. bauspiel wolfram mathworld https://mathworld.wolfram.com/Watson-NicholsonFormula.html Watson-Nicholson Formula -- from Wolfram MathWorld watson nicholson formula wolfram mathworld https://mathworld.wolfram.com/UnilateralLaplaceTransform.html Unilateral Laplace Transform -- from Wolfram MathWorld A one-sided (singly infinite) Laplace transform, L_t[f(t)](s)=int_0^inftyf(t)e^(-st)dt. This is the most common variety of Laplace transform and it what is... laplace transform unilateral wolfram mathworld https://mathworld.wolfram.com/MultidimensionalContinuedFractionAlgorithm.html Multidimensional Continued Fraction Algorithm -- from Wolfram MathWorld multidimensional continued fraction algorithm wolfram https://mathworld.wolfram.com/AdditivelyClosed.html Additively Closed -- from Wolfram MathWorld A mathematical object S is said to be additively closed if a,b in S implies that a+b in S. closed wolfram mathworld https://mathworld.wolfram.com/topics/BinarySequences.html Binary Sequences -- from Wolfram MathWorld binary sequences wolfram mathworld https://mathworld.wolfram.com/LagrangianCoefficient.html Lagrangian Coefficient -- from Wolfram MathWorld Coefficients which appear in Lagrange interpolating polynomials where the points are equally spaced along the abscissa. lagrangian coefficient wolfram mathworld https://mathworld.wolfram.com/SiegelDiskFractal.html Siegel Disk Fractal -- from Wolfram MathWorld A Julia set with c=-0.390541-0.586788i. The fractal somewhat resembles the better known Mandelbrot set. siegel disk fractal wolfram mathworld https://mathworld.wolfram.com/AugmentedDodecahedron.html Augmented Dodecahedron -- from Wolfram MathWorld The augmented dodecahedron is Johnson solid J_(58), which is formed from augmentation of one of the faces of the regular dodecahedron by an equilateral... augmented dodecahedron wolfram mathworld https://mathworld.wolfram.com/GroemerPacking.html Groemer Packing -- from Wolfram MathWorld A honeycomb-like packing that forms hexagons. packing wolfram mathworld https://mathworld.wolfram.com/CoversedSine.html Coversed Sine -- from Wolfram MathWorld sine wolfram mathworld https://mathworld.wolfram.com/classroom/Quadrilateral.html Quadrilateral -- from the MathWorld Classroom from the quadrilateral mathworld classroom https://mathworld.wolfram.com/topics/WheelGraphs.html Wheel Graphs -- from Wolfram MathWorld wheel graphs wolfram mathworld https://mathworld.wolfram.com/SmallInvertedRetrosnubIcosicosidodecahedron.html Small Inverted Retrosnub Icosicosidodecahedron -- from Wolfram MathWorld small inverted wolfram mathworld https://mathworld.wolfram.com/GyroelongatedPentagonalBicupola.html Gyroelongated Pentagonal Bicupola -- from Wolfram MathWorld The gyroelongated pentagonal bicupola is the Johnson solid J_(46), which consists of two pentagonal cupolas, one twisted with respect to the other, adjoined to... pentagonal wolfram mathworld https://mathworld.wolfram.com/CameronGraph.html Cameron Graph -- from Wolfram MathWorld The 231-Cameron graph is a strongly regular Hamiltonian graph on 231 vertices with parameters (nu,k,lambda,mu)=(231,30,9,3). It is distance-regular with... cameron graph wolfram mathworld https://mathworld.wolfram.com/Pantograph.html Pantograph -- from Wolfram MathWorld A linkage invented in 1630 by Christoph Scheiner for making a scaled copy of a given figure. The linkage is pivoted at O; hinges are denoted circledot . By... pantograph wolfram mathworld https://mathworld.wolfram.com/Sum-of-DivisorsTransform.html Sum-of-Divisors Transform -- from Wolfram MathWorld sum divisors transform wolfram mathworld https://mathworld.wolfram.com/MethodofFalsePosition.html Method of False Position -- from Wolfram MathWorld An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best... method false position wolfram mathworld https://mathworld.wolfram.com/topics/Points.html Points -- from Wolfram MathWorld points wolfram mathworld https://mathworld.wolfram.com/Coprime.html Coprime -- from Wolfram MathWorld wolfram mathworld https://mathworld.wolfram.com/SphericalTriangle.html Spherical Triangle -- from Wolfram MathWorld A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle... spherical triangle wolfram mathworld https://mathworld.wolfram.com/ApexGraph.html Apex Graph -- from Wolfram MathWorld An apex graph is a graph possessing at least one vertex whose removal results in a planar graph. The set of vertices whose removal results in a planar graph is... apex graph wolfram mathworld https://mathworld.wolfram.com/Polynomial.html Polynomial -- from Wolfram MathWorld A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a... polynomial wolfram mathworld https://mathworld.wolfram.com/GraphKroneckerProduct.html Graph Kronecker Product -- from Wolfram MathWorld graph kronecker product wolfram mathworld https://mathworld.wolfram.com/WeylsCriterion.html Weyl's Criterion -- from Wolfram MathWorld criterion wolfram mathworld https://mathworld.wolfram.com/KautzGraph.html Kautz Graph -- from Wolfram MathWorld kautz graph wolfram mathworld https://mathworld.wolfram.com/?source=footer Wolfram MathWorld: The Web's Most Extensive Mathematics Resource Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples. wolfram mathworld the web extensive mathematics resource https://mathworld.wolfram.com/EuclidsFifthAxiom.html Euclid's Fifth Axiom -- from Wolfram MathWorld euclid fifth axiom wolfram mathworld https://mathworld.wolfram.com/CatalanRuledSurface.html Catalan Ruled Surface -- from Wolfram MathWorld A Catalan ruled surface is a ruled surface whose generators are all parallel to the same plane. The general form of such a surface generated by a space curve... catalan ruled surface wolfram mathworld https://mathworld.wolfram.com/SimplexGraph.html Simplex Graph -- from Wolfram MathWorld The simplex graph kappa(G) of an undirected graph G is the graph with vertices given by the cliques of G and edges between pairs of cliques that differ by... simplex graph wolfram mathworld https://mathworld.wolfram.com/ReciprocalPrimeConstant.html Reciprocal Prime Constant -- from Wolfram MathWorld reciprocal prime constant wolfram mathworld https://mathworld.wolfram.com/BaranyaisTheorem.html Baranyai's Theorem -- from Wolfram MathWorld If k|n, then the complete k-uniform hypergraph on n vertices decomposes into 1-factors, where a 1-factor is a set of n/k pairwise disjoint k-sets. Brouwer and... theorem wolfram mathworld https://mathworld.wolfram.com/SimpleCurve.html Simple Curve -- from Wolfram MathWorld A curve is simple if it does not cross itself. simple curve wolfram mathworld https://mathworld.wolfram.com/ConfidenceRegion.html Confidence Region -- from Wolfram MathWorld confidence region wolfram mathworld https://mathworld.wolfram.com/LocalDegree.html Local Degree -- from Wolfram MathWorld local degree wolfram mathworld https://mathworld.wolfram.com/Second.html Second -- from Wolfram MathWorld second wolfram mathworld https://mathworld.wolfram.com/EquiproductPoint.html Equiproduct Point -- from Wolfram MathWorld A point, such as interior points of a disk, such that (px)(py)=[const], where p is the chord length. point wolfram mathworld https://mathworld.wolfram.com/CubefreeWord.html Cubefree Word -- from Wolfram MathWorld A cubefree word contains no cubed words as subwords. The number of binary cubefree words of length n=1, 2, ... are 2, 4, 6, 10, 16, 24, 36, 56, 80, 118, ...... word wolfram mathworld https://mathworld.wolfram.com/Lg.html Lg -- from Wolfram MathWorld There are several conflicting meanings associated with the notation lgx. In German and Russian literature, the notation lgx is used to mean the common... lg wolfram mathworld https://mathworld.wolfram.com/ModularPrimeCountingFunction.html Modular Prime Counting Function -- from Wolfram MathWorld By way of analogy with the prime counting function pi(x), the notation pi_(a,b)(x) denotes the number of primes of the form ak+b less than or equal to x... modular prime counting function wolfram https://mathworld.wolfram.com/topics/GoldenRatio.html Golden Ratio -- from Wolfram MathWorld golden ratio wolfram mathworld https://mathworld.wolfram.com/OpenProblems.html Open Problems -- from Wolfram MathWorld open problems wolfram mathworld https://mathworld.wolfram.com/TrivialKnot.html Trivial Knot -- from Wolfram MathWorld trivial knot wolfram mathworld https://mathworld.wolfram.com/PasechnikGraph.html Pasechnik Graph -- from Wolfram MathWorld The n-Pasechnik graph is a strongly regular graph on (4n-1)^2 vertices constructed from a skew Hadamard matrix of order 4n. It has regular parameters . The... graph wolfram mathworld https://mathworld.wolfram.com/classroom/ChromaticNumber.html Chromatic Number -- from the MathWorld Classroom from the chromatic number mathworld classroom https://mathworld.wolfram.com/LommelPolynomial.html Lommel Polynomial -- from Wolfram MathWorld The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of... lommel polynomial wolfram mathworld https://mathworld.wolfram.com/MedialAxis.html Medial Axis -- from Wolfram MathWorld The boundaries of the cells of a Voronoi diagram. medial axis wolfram mathworld https://mathworld.wolfram.com/PermutationGraph.html Permutation Graph -- from Wolfram MathWorld For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1... permutation graph wolfram mathworld https://mathworld.wolfram.com/CliqueEdgeCoverNumber.html Clique Edge Cover Number -- from Wolfram MathWorld clique edge cover number wolfram https://mathworld.wolfram.com/topics/TheCuriousIncidentoftheDogintheNight-Time.html The Curious Incident of the Dog in the Night-Time -- from Wolfram MathWorld night time curious incident dog https://mathworld.wolfram.com/RhomboidalDodecahedron.html Rhomboidal Dodecahedron -- from Wolfram MathWorld dodecahedron wolfram mathworld https://mathworld.wolfram.com/topics/Keller-Ressel.html Keller-Ressel -- from Wolfram MathWorld keller wolfram mathworld https://mathworld.wolfram.com/AltitudeTriangle.html Altitude Triangle -- from Wolfram MathWorld altitude triangle wolfram mathworld https://mathworld.wolfram.com/Snake.html Snake -- from Wolfram MathWorld A snake is an Eulerian path in the d-hypercube that has no chords (i.e., any hypercube edge joining snake vertices is a snake edge). Klee (1970) asked for the... snake wolfram mathworld https://mathworld.wolfram.com/Kneser-SommerfeldFormula.html Kneser-Sommerfeld Formula -- from Wolfram MathWorld Let J_nu(z) be a Bessel function of the first kind, N_nu(z) a Bessel function of the second kind, and j_(nu,n)(z) the zeros of z^(-nu)J_nu(z) in order of... sommerfeld formula wolfram mathworld https://mathworld.wolfram.com/EulerAngles.html Euler Angles -- from Wolfram MathWorld According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and... euler angles wolfram mathworld