Special numbers, once called transcendental numbers,
are a group of irrational numbers defined by a special
ratio or limit function.
Two of the most mathematically important special numbers are the logarithmic
e and trigonometric
pi. The number pi
is a consistent ratio taking from the diameter of
any circle and dividing
it by its circumference. The ancient Greeks named
the pi ratio after the 16th letter in the Greek
alphabet. Trigonometry uses pi with a unit of
measure called radians where two pi
radians equals a 360 degree circle. Natural logarithm
and exponential functions
use a special number formed by limits. The number
e is the limit of the expression one plus
the quantity one over n, all taken to the power
of n (any constant number), as n
approaches infinity. Another interesting special
number is the number phi, the least known
of these three special numbers. It is a ratio arrived at by dividing a line,
so that the length of the whole line as a ratio to the length of the long
section is equal to the length of the long section as a ratio to the length
of the short section. This is also known as the golden
ratio. Since all these special numbers are irrational numbers they
have infinite, nonrepeating decimals.