Some women like to wear diamond necklaces, I prefer Euler’s Identity.
Commonly referred to as the most beautiful relationship in all of mathematics, Euler’s Identity holds a gloriousness of incredible magnitude. This elegantly simple identity acts as the wardrobe of mathematics, bridging what is real and what is imaginary, while incorporating all of the most important numbers in mathematics.
Ahhhh. I’ll let you take it in.
I would like to set aside a minute spotlight each of the elements that take part in this alluring conclusion.
First, we’ll take a look at the constant e, also known as Euler's number, which is equal to about 2.72. e is most famous for being the base of natural logarithms. e is also one of two irrational numbers in this identity, which means that it cannot be written as a simple fraction. This constant is particularly fascinating because it manages to pop up all over the place. Whether you are computing integrals, discussing compound interest, or looking at population growth, e always seems to find its way into the conversation.
Next, let’s take a peek into the imaginary. The number i is defined as the square root of negative one, in other words, i squared is equal to negative one. Since one cannot take the square root of a negative number in the real world, i acts as the gateway into the world of imaginary numbers.
Our next number is undoubtedly the most delicious out of the bunch, π. π, just like e, is an irrational number, and is equal to about 3.14. π is most commonly used for angle measurements in radians, and can be defined as the angle of half of a circle, or the ratio of a circle’s circumference to its diameter.
Our next number is undoubtedly the most delicious out of the bunch, π. π, just like e, is an irrational number, and is equal to about 3.14. π is most commonly used for angle measurements in radians, and can be defined as the angle of half of a circle, or the ratio of a circle’s circumference to its diameter.
These last two numbers you are definitely familiar with; 1 and 0, so I won’t do too much explaining. 1 is the first positive whole number, or integer. While 0 characterizes the boundary between positive and negative numbers.
Now, I am sure you are beginning to see what is so awe-inspiring about this equation. Euler’s Identity is incredibly humbling in its elegant ability to bring together all corners of the mathematical world so beautifully. In mathematical application, Euler’s Identity can be used to express complex waves using the iteration,
where the specific angle, π is generalized as θ. This identity is particularly useful for quantifying the behavior of AC (alternating current) circuits. But beyond mathematical application, Euler’s Identity reveals that all aspects of our world have a deeply rooted and profound connection. Euler’s Identity teaches us that no matter how unrelated two things may seem, they all have the same greater force acting upon them, which is a beautiful realization all in itself.
Sources:
https://www.mathsisfun.com/numbers/e-eulers-number.html
https://i.pinimg.com/originals/f1/9e/da/f19eda292493ee511068d994a2d4e28d.jpg