Math Constants
Mathematical constants like Pi, e and i are builtin in SpeQ.
SpeQ has the following groups of builtin mathematical constants:
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  > 2.7e9 
BrunsPrimeQuadruplets  B_{4}  0.87058838 
BrunsTwinPrime  B_{2}  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  M_{1}  0.261497213 
Mills  θ  1.306377884 
Niven   1.70521114 
Porter   1.467078079 
RamanujanSoldner  K  1.451369235 
TwinPrime  C_{2}  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 NotaNumber and is the result of an operation on invalid input operands.
For example 0/0 and InfInf will return NaN as answer.
Name 
Value 
Inf 
Infinite 
NaN 
NotaNumber 
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 ^ (53)
Ans = 22.1671682968
3 * Exp(53)
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
See Also
Constants,
Physical constants,
Wikipedia
