Pi day Countdown #12 – Pi and the Transcendental Number

Leonhard Euler, considered to be one of the best mathematicians of all time, had the honor of having a few Transcendental numbers named after him. The Euler’s number or 2.718281828459… is not only a beautiful and a powerful number, it also has a very interesting connection with \pi.

The Euler’s number e can be expressed in the Euler’s Identity as:

e^{ix} = \sin(x) + i \cos(x)

and with x = \pi the identity becomes

e^{i \pi} = \sin(\pi) + i \cos(\pi) = 1 or e^{i \pi} -1 = 0

Swiss Mathematician, Leonhard Euler (15 April 1707 – 18 September 1783), was famous for many discoveries in mathematics such as the Euler's number and graph theory
Swiss Mathematician, Leonhard Euler (15 April 1707 – 18 September 1783), was famous for many discoveries in mathematics such as the Euler’s number and graph theory

Which unites some of the most famous mathematical constants, not only just \pi. There is also i the number that was so controversial that it was named imaginary as a joke. The number 0 which represented the concept of nothingness, a concept that wasn’t accepted as a number for millennia. The number 1 that started it all, and not to forget \pi one of the most famous numbers in mathematics.

PS: For more Pi Day countdown articles, visit the fun corner