# Category: Mathematical constants

Khinchin's constant
In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x, coefficients ai of the continued fraction expansion of x have a finite geometric mean that is independent of
Prouhet–Thue–Morse constant
In mathematics, the Prouhet–Thue–Morse constant, named for , Axel Thue, and Marston Morse, is the number—denoted by τ—whose binary expansion 0.01101001100101101001011001101001... is given by the Thue–
In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle L at a point P on an algebraic variety. It was introduced by Demailly to measure a certain rate of growth, of the ten
Erdős–Tenenbaum–Ford constant
The Erdős–Tenenbaum–Ford constant is a mathematical constant that appears in number theory. Named after mathematicians Paul Erdős, Gérald Tenenbaum, and Kevin Ford, it is defined as where is the natur
Meissel–Mertens constant
The Meissel–Mertens constant (named after Ernst Meissel and Franz Mertens), also referred to as Mertens constant, Kronecker's constant, Hadamard–de la Vallée-Poussin constant or the prime reciprocal c
Magic angle
The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, P2(cos θ) = 0, and so any interaction which
Favard constant
In mathematics, the Favard constant, also called the Akhiezer–Krein–Favard constant, of order r is defined as This constant is named after the French mathematician Jean Favard, and after the Soviet ma
List of mathematical constants
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it
Sierpiński's constant
Sierpiński's constant is a mathematical constant usually denoted as K. One way of defining it is as the following limit: where r2(k) is a number of representations of k as a sum of the form a2 + b2 fo
Gelfond's constant
In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is eπ, that is, e raised to the power π. Like both e and π, this constant is a transcendental number. This was first established by G
Silver ratio
In mathematics, two quantities are in the silver ratio (or silver mean) if the ratio of the smaller of those two quantities to the larger quantity is the same as the ratio of the larger quantity to th
E (mathematical constant)
The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828, which can be characterized in many ways: * It is the base of the natural logarithms * It is the
Brun's constant
No description available.
Catalan's constant
In mathematics, Catalan's constant G, is defined by where β is the Dirichlet beta function. Its numerical value is approximately (sequence in the OEIS) G = 0.915965594177219015054603514932384110774…Un
Chvátal–Sankoff constants
In mathematics, the Chvátal–Sankoff constants are mathematical constants that describe the lengths of longest common subsequences of random strings. Although the existence of these constants has been
97.5th percentile point
In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations. The approximate value of this number is 1.96, mea
List of scientific constants named after people
This is a list of physical and mathematical constants named after people.Eponymous constants and their influence on scientific citations have been discussed in the literature. * Apéry's constant – Ro
Omega constant
The omega constant is a mathematical constant defined as the unique real number that satisfies the equation It is the value of W(1), where W is Lambert's W function. The name is derived from the alter
Legendre's constant
Legendre's constant is a mathematical constant occurring in a formula conjectured by Adrien-Marie Legendre to capture the asymptotic behavior of the prime-counting function . Its value is now known to
Mathematical constant
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it
Linnik's constant
No description available.
Apéry's constant
In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number where ζ is the Riemann zeta function. It has an approximate value of ζ(3) = 1
Ramanujan–Soldner constant
In mathematics, the Ramanujan–Soldner constant (also called the Soldner constant) is a mathematical constant defined as the unique positive zero of the logarithmic integral function. It is named after
Supergolden ratio
In mathematics, two quantities are in the supergolden ratio if the quotient of the larger number divided by the smaller one is equal to which is the only real solution to the equation . It can also be
Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , wher
Reciprocal Fibonacci constant
The reciprocal Fibonacci constant, or ψ, is defined as the sum of the reciprocals of the Fibonacci numbers: The ratio of successive terms in this sum tends to the reciprocal of the golden ratio. Since
Square root of 6
The square root of 6 is the positive real number that, when multiplied by itself, gives the natural number 6. It is more precisely called the principal square root of 6, to distinguish it from the neg
Conic constant
In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by where e is t
Porter's constant
In mathematics, Porter's constant C arises in the study of the efficiency of the Euclidean algorithm. It is named after J. W. Porter of University College, Cardiff. Euclid's algorithm finds the greate
De Bruijn–Newman constant
The de Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is a mathematical constant defined via the zeros of a certain function H(λ, z), where λ is
Niven's constant
In number theory, Niven's constant, named after Ivan Niven, is the largest exponent appearing in the prime factorization of any natural number n "on average". More precisely, if we define H(1) = 1 and
Fransén–Robinson constant
The Fransén–Robinson constant, sometimes denoted F, is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive x axis. That is,
Lemniscate constant
In mathematics, the lemniscate constant ϖ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of π for t
Stieltjes constants
In mathematics, the Stieltjes constants are the numbers that occur in the Laurent series expansion of the Riemann zeta function: The constant is known as the Euler–Mascheroni constant.
Square root of 7
The square root of 7 is the positive real number that, when multiplied by itself, gives the prime number 7. It is more precisely called the principal square root of 7, to distinguish it from the negat
Gelfond–Schneider constant
The Gelfond–Schneider constant or Hilbert number is two to the power of the square root of two: 2√2 = 2.6651441426902251886502972498731... which was proved to be a transcendental number by Rodion Kuzm
Backhouse's constant
Backhouse's constant is a mathematical constant named after Nigel Backhouse. Its value is approximately 1.456 074 948. It is defined by using the power series such that the coefficients of successive
Feller–Tornier constant
In mathematics, the Feller–Tornier constant CFT is the density of the set of all positive integers that have an even number of distinct prime factors raised to a power larger than one (ignoring any pr
Sophomore's dream
In mathematics, the sophomore's dream is the pair of identities (especially the first) discovered in 1697 by Johann Bernoulli. The numerical values of these constants are approximately 1.291285997...
Laplace limit
In mathematics, the Laplace limit is the maximum value of the eccentricity for which a solution to Kepler's equation, in terms of a power series in the eccentricity, converges. It is approximately 0.6
Universal parabolic constant
The universal parabolic constant is a mathematical constant. It is defined as the ratio, for any parabola, of the arc length of the parabolic segment formed by the latus rectum to the focal parameter.
Erdős–Borwein constant
The Erdős–Borwein constant is the sum of the reciprocals of the Mersenne numbers. It is named after Paul Erdős and Peter Borwein. By definition it is:
Square root of 3
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as or . It is more precisely called the principal square root of 3 to
Landau–Ramanujan constant
In mathematics and the field of number theory, the Landau–Ramanujan constant is the positive real number b that occurs in a theorem proved by Edmund Landau in 1908, stating that for large , the number
Prime constant
The prime constant is the real number whose th binary digit is 1 if is prime and 0 if is composite or 1. In other words, is the number whose binary expansion corresponds to the indicator function of t
Copeland–Erdős constant
The Copeland–Erdős constant is the concatenation of "0." with the base 10 representations of the prime numbers in order. Its value, using the modern definition of prime, is approximately 0.23571113171
Euler product
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers. The original such product was given for the sum of all positive integers rai
Liouville number
In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exists a pair of integers (p, q) with q > 1 such that . Liouville numbers are "almos
Particular values of the gamma function
The gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known fo
Lieb's square ice constant
Lieb's square ice constant is a mathematical constant used in the field of combinatorics to quantify the number of Eulerian orientations of grid graphs. It was introduced by Elliott H. Lieb in 1967.
Euler's constant
Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (γ). It is defined as the limiting difference betw
Feigenbaum constants
In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after t
Square root of 2
The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as or , and is an algebraic number. Technic
In mathematics, Somos' quadratic recurrence constant, named after Michael Somos, is the number This can be easily re-written into the far more quickly converging product representation which can then
Degree (angle)
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. It is not an SI un
Random Fibonacci sequence
In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation , where the signs + or − are chosen at random with equal probability
Look-and-say sequence
In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, ... (sequence in the OEIS). To genera
Schnirelmann density
In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is. It is named after Russian mathematician Lev Schnirelmann, who was the firs
Lévy's constant
In mathematics Lévy's constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions.In 193
Beraha constants
The Beraha constants are a series of mathematical constants by which the Beraha constant is given by Notable examples of Beraha constants include is , where is the golden ratio, is the silver constant
Komornik–Loreti constant
In the mathematical theory of non-standard positional numeral systems, the Komornik–Loreti constant is a mathematical constant that represents the smallest base q for which the number 1 has a unique r
Ramanujan's constant
No description available.
MRB constant
The MRB constant is a mathematical constant, with decimal expansion 0.187859… (sequence in the OEIS). The constant is named after its discoverer, Marvin Ray Burns, who published his discovery of the c
Cahen's constant
In mathematics, Cahen's constant is defined as the value of an infinite series of unit fractions with alternating signs: Here denotes Sylvester's sequence, which is defined recursively by Combining th
Champernowne constant
In mathematics, the Champernowne constant C10 is a transcendental real constant whose decimal expansion has important properties. It is named after economist and mathematician D. G. Champernowne, who
Twelfth root of two
The twelfth root of two or (or equivalently ) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio
Kepler–Bouwkamp constant
In plane geometry, the Kepler–Bouwkamp constant (or polygon inscribing constant) is obtained as a limit of the following sequence. Take a circle of radius 1. Inscribe a regular triangle in this circle
Square root of 5
The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negat
6174 (number)
6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule: 1. * Take any four-digit number, using at least two different digit
Plastic number
In mathematics, the plastic number ρ (also known as the plastic constant, the plastic ratio, the minimal Pisot number, the platin number, Siegel's number or, in French, le nombre radiant) is a mathema
Dottie number
In mathematics, the Dottie number is a constant that is the unique real root of the equation , where the argument of is in radians. The decimal expansion of the Dottie number is . Since is decreasing
Foias constant
In mathematical analysis, the Foias constant is a real number named after Ciprian Foias. It is defined in the following way: for every real number x1 > 0, there is a sequence defined by the recurrence
Hermite constant
In mathematics, the Hermite constant, named after Charles Hermite, determines how short an element of a lattice in Euclidean space can be. The constant γn for integers n > 0 is defined as follows. For
Natural logarithm of 2
The decimal value of the natural logarithm of 2 (sequence in the OEIS)is approximately The logarithm of 2 in other bases is obtained with the formula The common logarithm in particular is (OEIS: ) The
Imaginary unit
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation . Although there is no real number with this property, i can be used to extend the real numbers to what are call
Bernstein's constant
Bernstein's constant, usually denoted by the Greek letter β (beta), is a mathematical constant named after Sergei Natanovich Bernstein and is equal to 0.2801694990... .
Mills' constant
In number theory, Mills' constant is defined as the smallest positive real number A such that the floor function of the double exponential function is a prime number for all natural numbers n. This co
Heath-Brown–Moroz constant
The Heath-Brown–Moroz constant C, named for Roger Heath-Brown and , is defined as where p runs over the primes.
Golden angle
In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the leng
Hafner–Sarnak–McCurley constant
The Hafner–Sarnak–McCurley constant is a mathematical constant representing the probability that the determinants of two randomly chosen square integer matrices will be relatively prime. The probabili
Particular values of the Riemann zeta function
In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ(s) and is named after the mathematician Bernhard Riemann. W
Period (algebraic geometry)
In algebraic geometry, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of periods remain periods, so the periods form a r
Glaisher–Kinkelin constant
In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted A, is a mathematical constant, related to the K-function and the Barnes G-function. The constant appears in a n
Feller's coin-tossing constants
Feller's coin-tossing constants are a set of numerical constants which describe asymptotic probabilities that in n independent tosses of a fair coin, no run of k consecutive heads (or, equally, tails)
Golomb–Dickman constant
In mathematics, the Golomb–Dickman constant arises in the theory of random permutations and in number theory. Its value is (sequence in the OEIS) It is not known whether this constant is rational or i