ECUATION EULER´S

Introduction:

Euler's identity is considered the most beautiful equation in mathematics (according to readers of Matematical Intelligencer, 1978), either because of its simplicity or elegance. The formula below is known as Euler's Identity:

e^iπ+1=0

Euler's identity:

Created by Leonhard Euler, it was published in his book "Introduction in Analtsin Infinitorum" in 1748. He defined it as an exponential function for complex numbers and discovered its relationship with trigonometric functions, for any real number (R) can be established with the following formula:

e^iπ=cos⁡(π)+i sen (π)

This formula is simplified, so when we solve it (since from what we know (sen (π)=0 and cos(π)= -1) it stays the way we know it:

e^iπ+1=0

It can also be seen that it relates the five fundamental numbers and the concepts of "addition (a+b)", "product (ab)", "exponentiation (a^b)", "identity (a=b)", as it is made up of the following values:

·         1: Used in arithmetic. This number is the main base of the others, since with this one all the other numbers can be formed when adding them up: 1+1=2, 1+1+1=3..., in a more poetic way there is always a pillar by which to start

·         0: used in arithmetic, the one that leads to nothing, moreover it separates in the line of the real numbers (R), the positive ones from the negative ones. In a simpler way nothingness is not negligible

·        π: This is an irrational transcendent number, this is the proportion between the circumference and the diameter of a circle (π=(Cincurferencia )/(Diametro )), this does not depend on the size of the circle. It is approximately equivalent to 3.14159256....

·         e: It is a transcendent irrational number with infinite quantities, which is used to analyze the growths among others, the formula used for this is the following: 

〖(1+1/n)〗^n

·       i: This is simply the root of -1. (i=√(-1))

    Conclusion:

      This equation is useful for trigonometry, thermodynamics and mechanics. As to define logarithms of negative numbers or complex numbers.
This equation expresses with a few mathematical symbols an infinite beauty of a genius like Euler.