What Is Euler's Formula?

On any regular spherical map, use R to record the number of regions, V to record the number of vertices, and E to record the number of boundaries. Then R + V- E = 2 is the Euler theorem. It was first given by Descartes in 1640. Proof. Later, Euler gave the proof independently in 1752. We call it Euler's theorem, and some people call it Descartes theorem abroad. ^[1]

The value of the formula is 0 when r = 0 or 1, the value is 1 when r = 2, and the value is a + b + c when r = 3. ^[4]

A formula that associates a complex exponential function with a trigonometric function,

^[5]

Let ABC

Topology is also called "continuous geometry".

A branch of geometry. Investigate the properties that geometric figures can maintain after continuous deformation. Including point set topology, algebraic topology, differential topology and other branches. ^[7]

As we all know, friction exists in life, and Euler's measurement calculated the relationship between friction and the number of turns of the rope around the pile. Here is a valuable formula of Euler:

Among them, f is the force we applied, F is the force against it, e is the base of natural logarithm, k is the coefficient of friction between rope and pile, and a is the winding angle, that is, the arc length and radius Ratio.