Math Constants

Mathematical constants like Pi, e and i are built-in in SpeQ. SpeQ has the following groups of built-in mathematical constants:

General
Number theory
Chaos theory
Combinatorics
Analysis
Special values

The values for the constants are taken from the Wikipedia, the free online encyclopedia. See Mathematical constants on Wikipedia for more information.

General

Name	Symbol	Value	Description
Apery	ζ(3)	1.202056903
Backhouse		1.456074949
Cahen		0.62946502
e	e	2.718281828	The base of the natural logarithm function. Napier's constant, or Euler's number.
GoldenRatio	φ	1.618033989	Two 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
i	i	Sqrt(-1)	The imaginary unit. You can read more about i on the page Complex Numbers.
LaplaceLimit		0.662743419
Pi	π	3.141592654	The ratio of a circle's circumference to its diameter.
Pythagoras	Sqrt(2)	1.414213562	The square root of 2. Geometrically, Sqrt(2) is the length of a diagonal across a square with sides of one unit of length.
Sierpinski	K	2.58498176
Theodorus	Sqrt(3)	1.732050808	The square root of 3. Geometrically, Sqrt(3) is the length of a diagonal across a cube with sides of one unit of length.

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
AlladiGrinstead		0.261497213
BruijnNewMan	Λ	> -2.7e-9
BrunsPrimeQuadruplets	B₄	0.87058838
BrunsTwinPrime	B₂	1.902160582
EmbreeTrefethen	β^*	0.70258
ErdosBorwein	E_B	1.606695152
EulerMascheroni	γ	0.577215665
GolombDickman	λ, μ	0.624329988
HafnerSarnakMcCurley	D(1)	0.353236372
Khinchin		2.685452001
KhinchinLevy		1.18656911
LandauRamanujan	K	0.764223654
Legendre	B'_L	1
MeisselMertens	M₁	0.261497213
Mills	θ	1.306377884
Niven		1.70521114
Porter		1.467078079
RamanujanSoldner	K	1.451369235
TwinPrime	C₂	0.660161816
Viswanath	K	1.13198824

Chaos theory

Chaos theory describes the behavior of certain nonlinear dynamical systems that act chaotic, but with certain deterministic properties.

Name	Symbol	Value
FeigenbaumAlpha	α	2.502907875
FeigenbaumDelta	δ	4.669201609

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
Catalan	K	0.915965594
GaussKuzminWirsing	λ	0.303663003
GolombDickman	λ, μ	0.624329988
Lengyel	Λ	1.098685805
Lieb		1.539600718

Analysis

Analysis is a branch of mathematics that studies continuous functions. Topics are limits, convergence, continuity, integration, differentiability.

Name	Symbol	Value
Bernstein	β	0.280169499
e	e	2.718281828
FransenRobinson	F	2.807770242
i	i	Sqrt(-1)
Landau	L	0.5
Pi	π	3.141592654

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

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