Math Constants

Mathematical constants like Pi, e and i are built-in in SpeQ. SpeQ has the following groups of built-in mathematical constants: The values for the constants are taken from the Wikipedia, the free online encyclopedia. See Mathematical constants on Wikipedia for more information.

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General

Name Symbol Value Description
Aperyζ(3)1.202056903
Backhouse1.456074949
Cahen0.62946502
ee2.718281828The base of the natural logarithm function. Napier's constant, or Euler's number.
GoldenRatioφ1.618033989Two quantities a and b are said to be in the golden ratio if a+b is to a as a is to b, mathematically stated as: (a+b)/a = a/b = φ
iiSqrt(-1)The imaginary unit. You can read more about i on the page Complex Numbers.
LaplaceLimit0.662743419
Piπ3.141592654The ratio of a circle's circumference to its diameter.
PythagorasSqrt(2)1.414213562The square root of 2. Geometrically, Sqrt(2) is the length of a diagonal across a square with sides of one unit of length.
SierpinskiK2.58498176
TheodorusSqrt(3)1.732050808The square root of 3. Geometrically, Sqrt(3) is the length of a diagonal across a cube with sides of one unit of length.
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Number theory

Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular.
Name Symbol Value
AlladiGrinstead0.261497213
BruijnNewManΛ> -2.7e-9
BrunsPrimeQuadrupletsB40.87058838
BrunsTwinPrimeB21.902160582
EmbreeTrefethenβ*0.70258
ErdosBorweinEB1.606695152
EulerMascheroniγ0.577215665
GolombDickmanλ, μ0.624329988
HafnerSarnakMcCurleyD(1)0.353236372
Khinchin2.685452001
KhinchinLevy1.18656911
LandauRamanujanK0.764223654
LegendreB'L1
MeisselMertensM10.261497213
Millsθ1.306377884
Niven1.70521114
Porter1.467078079
RamanujanSoldnerK1.451369235
TwinPrimeC20.660161816
ViswanathK1.13198824
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Chaos theory

Chaos theory describes the behavior of certain nonlinear dynamical systems that act chaotic, but with certain deterministic properties.
Name Symbol Value
FeigenbaumAlphaα2.502907875
FeigenbaumDeltaδ4.669201609
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Combinatorics

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their properties.
Name Symbol Value
CatalanK0.915965594
GaussKuzminWirsingλ0.303663003
GolombDickmanλ, μ0.624329988
LengyelΛ1.098685805
Lieb1.539600718
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Analysis

Analysis is a branch of mathematics that studies continuous functions. Topics are limits, convergence, continuity, integration, differentiability.
Name Symbol Value
Bernsteinβ0.280169499
ee2.718281828
FransenRobinsonF2.807770242
iiSqrt(-1)
LandauL0.5
Piπ3.141592654
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Special values

There are a few special values: Inf and NaN. The constant Inf is returned if an overflow occures by evaluating an expression, for example 10^400. The second special value, NaN, means Not-a-Number and is the result of an operation on invalid input operands. For example 0/0 and Inf-Inf will return NaN as answer.
Name Value
Inf Infinite
NaN Not-a-Number
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Examples

'Examples of using Math constants

'Calculate the circumference and area
'for a circle with diameter 8.
diameter = 8; 'Define the diameter radius = 0.5*diameter; 'Calculate the radius Circumference = Pi * 2 * radius Circumference = 25.132741229 'Calculate the area Area = Pi * radius^2 Area = 50.265482457 'Don't forget to set angle mode 'to radians to get the right answer. Sin(.25 * Pi) Ans = 0.7071067812 3 * e ^ (5-3) Ans = 22.1671682968 3 * Exp(5-3) Ans = 22.1671682968 'a golden ratio example: a = 5; b = a / GoldenRatio; a / b Ans = 1.618033989 (a + b) / a Ans = 1.618033989 GoldenRatio Ans = 1.618033989 'The variable Inf is only used as result of an expression 'that gives an overflow of computer memory as result, 'for example: 50 ^ 1000 Ans = Inf
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See Also

Constants, Physical constants, Wikipedia