What is Euler's formula?

Swiss mathematician from the 18th century Leonhard Euler developed two equations that became known as Euler's formula. One of these equations concerns the number of peaks, surfaces and edges on polyhedron. The second formula connects the five most common mathematical constants to each other. These two equations were placed on the second and the first or first mathematical results according to "The Mathematical Intelligencer". It states that the number of facials and the number of peaks, minus the number of edges per polyhedron is always equal to two. It is written as F + V - E = 2. The cube has six areas, eight vertices and 12 edges. It connects to the Euler formula, 6 + 8 - 12 actually equals two.

There are exceptions to this formula because it applies only to Polyhedron, which intersects itself. Well -known geometric shapes including spheres, chicks, tetrahedra and octagons are all non -intestorting polyhedra. However, the intersecting polyhedron would be created if someone should connect to the two vertices of the non -radiant polyhedron. This would result in the fact thatE would have the same number of faces and edges, but one less vertica, so it is clear that the formula is no longer true.

On the other hand, the more general version of the Euler formula that intersects is used on the polyhedra. This formula is often used in topology, which is a study of spatial properties. In this version of the formula, F + V - E equals the number called Euler's characteristic, which is often symbolized by the Greek letter Chi. For example, both donut -shaped and mobius strip have Euler's zero characteristic. Euler's characteristic can also be less than zero.

The formula of the second Euler includes the Mathematical Constants E, I, π, 1 and 0. Imaginary number I is defined as a second root -1. Pi (π), the relationship between the diameter and the circuit of the circle is approximately 3.14, but like E, is an irrational numbero.

This formula is written as e ^{(i*π) + 1 = 0. Euler found that if π has been replaced x in trigonometric identity e In addition to the relationship of these five basic constants, the formula may also show that increasing the irrational number to the strength of an imaginary irrational number can result in a real number.}