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
- e is the Euler’s number
- Π is the ratio of circumference to diameter of a circle
- 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
- Two irrational and transcendental number that are e and Π
- The imaginary unit i
- Rational number 1 and 0
I hope you understand and feel the beauty of this mathematical equation.