#### Transcendental Numbers

Also known as irrational numbers, these occur in the natural world. They have the following properties:

- They have an infinite number of decimal places without repeating patterns

- They cannot be expressed as a fraction a/b where a and b are integers

Pi (π)

Probably the best known is Pi, this is the ratio of the circumference to the diameter of a circle, π begins 3.141592654.....
Euler's Number (e)

This is approx to 2.718... and can be calculated by the formula
e = (1 + 1/n)

Take the exponential function
^{n}f(x) = e

This is by definition the fixed point of the derivative operator, a function whose rate of increase at any given point equals its value at that given point. This represents natural non-linear change which we see throughout the natural world. Examples include population growth and the decay of a radioactive material. These are quantities that increase or decrease at a rate that is proportional to their current value.
^{x}Updated: 10/12/2023