#1 Most Beautiful Equation in Mathematics – Euler's Identity

Euler's Identity

Mathematics is a vast subject and is considered as the mother of all the science as it is a tool to solve problems in all other sciences. Mathematics is a subject with so many equations which can fill oceans.
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There are many wonderful equations in mathematics which really surprises us as to how can so many different things can be connected with a single equation.
One among such equation is the Euler’s identity, and it is considered as the most beautiful equation in mathematics especially Number theory. A poll of readers conducted by The Mathematical Intelligencer named Euler’s identity as the “most beautiful theorem in mathematics in 1990.
So, Euler’s identity is
euler identity

  1. e is the Euler’s number
  2. Π is the ratio of circumference to diameter of a circle
  3. i is the imaginary unit satisfying   i2 = −1

Now, let us know why is this equation so special. We know that Mathematics has Real numbers and Complex numbers which are two different things. Then Real numbers have rational numbers and irrational numbers which are two different parts of real numbers.
To understand its beauty we also have to know about transcendental numbers. These numbers are real or complex numbers which are not a solution of a non-zero polynomial equation.
Now, as we have good background let us know the specialty of this equation.
In this equation, three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation
The equation is considered as deep mathematical beauty because it connects very different things in mathematics and those are

  1. Two irrational and transcendental number that are e and Π
  2. The imaginary unit i
  3. Rational number 1 and 0

I hope you understand and feel the beauty of this mathematical equation.

  1. Euler’s Identity(Wikipedia)


  1. I have read your article, and marvel how often synchronicity on an apparently cosmic scale tends to tie things together – sometimes across great distances.
    I run a small research laboratory in the forests of the pacific northwest. Our lab is literally framed from giant timbers from the forests outside. People laugh at the greenness of our name – I have to explain there isn’t any ulterior motive. We design prototype demonstration-scale reactors deep in the rainforest.
    Over the past few days, we achieved a culmination of sorts, from more than a decade of effort – and strangely enough, for the first time, we discovered that the grounds behinds our past successes were due to the inadvertent presence of Euler’s Identity buried in the other equations and reams of data.
    Here is the reason this is noteworthy of your coverage and further study: It was discovered that the core structure of the entire Periodic Table of Elements, is *dominated* by the interwoven rotating phase behaviors of Pi and e. The entire system of periods and shells occurs in direct relationship to exchanges between polynomials of the two constants.
    Furthermore, much to our chagrin, we can find no prior literature from years of searching, that have approached this type of mathematical analysis in the matter we refined.
    Would you like to carry on this dialog further? I can send you a copy of our most recent work to study. I guarantee you, our topological graphics are unique – and amazingly effective, it would seem.
    W.A. (Bill) Harrington, Founder/CTO
    Rainforest Reactor Research, Seabeck WA 98380-0306 (360)830-0457


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