In the mathematical field, Euler’s identity is widely regarded as the most beautiful equation in mathematics. Why? Euler’s identity takes five of the most fundamental and important constants (three of which are irrational numbers in mathematics) and makes a simple, yet profound equation:
Breaking down the equation:
In this equation you have five constants:
1. The number 1
2. The number 0
3. The constant e
4. The constant i
5. The constant pi
The constant e:
In mathematics, e approximately equals 2.71828182.... (e is an irrational constant and therefore never ends – it is infinite). Introduced into the mathematical society by Leonhard Euler, e is a constant that plays a fundamental role in calculus (being the base of natural logarithms). A logarithm is the inverse of an exponential function (a^x) - interestingly, when graphing the exponential function e^x, the gradient function of the curve is exactly the same as the original function.
The constant i:
The constant i is actually an imaginary number that is defined as the square root of -1. Technically, it’s impossible to take the square root of a negative number, as no number can be multiplied by itself to make a negative number, however, mathematicians are frequently forced to take the square of negative number hence the introduction of imaginary numbers.
The constant
Pi is a well known irrational constant, where pi = 3.14159265….. It is defined as the ratio of a circle’s circumference to its diameter.
References:
Coolman, R. (2015, July 1). Euler’s Identity: ‘The Most Beautiful Equation’. Livescience.Com. https://www.livescience.com/51399-eulers-identity.html
Wikipedia contributors. (2021, March 28). Euler’s identity. Wikipedia. https://en.wikipedia.org/wiki/Euler%27s_identity
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