Euler's Identity

 

Image source: File: Euler's formula.png - Wikimedia Commons

 

There is a single equation that connects five mathematical constants in a simple equality. The equation is known as Euler’s Identity (or Euler’s Equation):

The five constants include:

The base of the natural logarithm, e (2.718…), also know as Euler’s number

The square root of -1, i (the imaginary unit)

The ratio of a circle’s circumference to its diameter, p (3.141...)

The additive identity, 0, and

The multiplicative identity, 1.

 

The basis of Euler’s Identity, is the more general formula, Euler’s Formula, which is:

When x = p, then:

Since cos p = -1 and sin p = 0, the equation becomes:

Or 

Other blog posts and links about Euler:

Math Vacation: Euler Characteristic of Polyhedra (jamesmacmath.blogspot.com)

Math Vacation: Project Euler (jamesmacmath.blogspot.com)

Math Vacation: Using Random Numbers to Estimate Pi (jamesmacmath.blogspot.com)

Math Vacation: Perfect Number Generator (jamesmacmath.blogspot.com)

More on Euler’s Identity: Euler's identity - Wikipedia

More on Euler: Leonhard Euler - Wikipedia