## Constants

This algorithm converts the digits of three popular constants into a sequence of numbers. Select the constant you'd like in Step A and the number of digits (precision) you'd like in Step B. For example, selecting the golden ratio with three digits of precision would yield the value 1.61. This would be interpreted as the sequence (1,6,1).

Constants are real or complex numbers that do not change. Lists of constants can be found in many texts and Web sites. Here is one online source:mathematical constants

Pi, known as Archimedes' constant, represents the ratio of a circle's circumference with its diameter. Pi is an infinite constant that is often expressed in the shorter form 3.14 or 22/7. The true value of pi has been elusive, because the decimal expansion after 3.14 never ends. Approximate values for pi have been sought by mathematicians through ancient history, from the Babylonians, Egyptians, Chinese and Greeks. The constant is named after Archimedes of Syracuse, because he used polygons in 3rd century B.C. to determine a close estimate for pi lying somewhere between 220/70 and 223/71. Pi is used in many areas of math: infinite series equations, integrals, number theory, probability functions, continued fractions, logarithms of imaginary numbers, and periodic functions. Since pi can not be expressed as the ratio of two whole numbers, it is called an irrational number. Pi is calculated from the Gauss-Legendre algorithm.

Phi is known as the golden ratio. It has ostensible mystical properties, because its presence is found in many environments such as nature, art, architecture, and music. Although it is ubiquitous, phi represents a ratio of very specific measurements of two lengths A and B. The ratio of the two lengths A and B equals phi, if, and only if, an identical ratio is found between the sum of the two lengths and the longest of the two (A or B). In other words, Phi is present when the ratio of A and B is equal to the ratio of A+B with A (if A is longer than B). Phi is also revealed as a ratio of adjacent integers of the Fibonacci series as the series unfolds. Phi can be found as the square root of 5 (+ 1) divided by 2.

(e), known as Euler's number, is a mathematical constant which represents the base of the natural logarithm function. (e) is an irrational number, which is also known as Napier's constant. (e) has several unique properties. For example it is its own derivative as an exponential function, and it is the sum of an infinite series using factorials. (e) is widely used in mathematics as a base for logarithms. Logarithms were introduced by John Napier in 1614, which led to practical calculations for navigation, astronomy, and surveying. In general terms, logarithms provide a means to manage quantities of units within a large range. Logarithmic scales are exponential (derived from multiplication), rather than linear (derived from addition). For example, logarithmic scales are represented in the Richter scale when measuring the magnitude of earthquakes, decibels for acoustic loudness, and the space between musical pitches.

The following examples will provide an understanding for how logarithms work:

log10(100) = 2 (since 10 squared = 100)

log2(8) = 3 (since 2 cubed = 8)

In a system of logarithms where 4 is the base:

log 4 = 1 since 4 raised to the first power = 4 (antilog 1 = 4)

log 16 = 2 since 4 squared = 16 (antilog 2= 16)

log 64 = 3 since 4 cubed = 64 (antilog 3 = 64)