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Mathematical Constants
Many mathematical constants and expressions involving small integers occur time and again in numerical
calculations. The Constants class contains static fields for many
of these values.
The constants fall into four categories:
The following example shows a method that evaluates the probability density function of a normal distribution with
mean mean and standard deviation stdDev.
| C# | Copy Code |
|---|
using Extreme.Mathematics;
public double NormalPDF(double x, double mean, double stdDev)
{
double z = (x - mean) / stdDev;
return Constants.OneOverSqrtTwoPi / stdDev
* Math.Exp(-0.5*z*z);
} |
| Visual Basic | Copy Code |
|---|
Imports Extreme.Mathematics
Public Function NormalPDF(x As Double, mean As Double, stdDev As Double) As Double
Dim z As Double = (x - mean) / stdDev
Return Constants.OneOverSqrtTwoPi / stdDev _
* Math.Exp(-0.5*z*z)
End Function |
The tables below list the constants in each of the four categories.
| Fundamental constants |
| E
|
The base for the natural logarithm, e (2.718...). |
| EulersConstant
|
Euler's constant, which is important in number theory and some engineering calculations
(0.577...). |
| GoldenRatio
|
The Golden Ratio (1.618...). |
| Pi
|
The number Pi, the ratio between the circumference and the diameter of a circle
(3.1415...). |
Table 1. Fundamental constants.
Table 2. Expressions involving fundamental constants..
| Square Roots of Small Integers |
| Sqrt2
|
The square root of two (1.414...). |
| Sqrt3
|
The square root of three (1.732...). |
| Sqrt5
|
The square root of five (2.236...). |
| Sqrt7
|
The square root of seven (2.646...). |
| Sqrt17
|
The square root of seventeen (4.123...). |
Table 3. Square roots of small integers.
| Logarithms of Small Integers |
| Log2
|
The natural logarithm of two (0.693...). |
| Log3
|
The natural logarithm of three (1.098...). |
| Log10
|
The natural logarithm of ten (2.305...). |
| Log17
|
The natural logarithm of seventeen (2.833...). |
| InvLog10
|
The base-10 logarithm of E. |
Table 4. Logarithms of small integers.
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