Related (duplicate?): Simple proof of Euler Identity $\exp i\theta = \cos\theta+i\sin\theta$. Also, this possible duplicate has this answer, with a nice visual demonstration of the result. There are more instances of this question floating around Math.SE. Try searching for variations of "euler identity proof"; if no existing answers satisfy you, try to convey what it is about them that you ...
Euler's formula is quite a fundamental result, and we never know where it could have been used. I don't expect one to know the proof of every dependent theorem of a given result.
It was found by mathematician Leonhard Euler. In 1879, mathematician J.J.Sylvester coined the term 'totient' function. What is the meaning of the word 'totient' in the context? Why was the name coined for the function? I have received replies that 'tot' refers to 'that many, so many' in Latin. What about the suffix 'ient'?
The $3$ Euler angles (usually denoted by $\alpha, \beta$ and $\gamma$) are often used to represent the current orientation of an aircraft. Starting from the "parked on the ground with nose pointed North" orientation of the aircraft, we can apply rotations in the Z-X'-Z'' order: Yaw around the aircraft's Z axis by $ \alpha $ Roll around the aircraft's new X' axis by $ \beta $ Yaw (again) around ...
0 There is one difference that arises in solving Euler's identity for standard trigonometric functions and hyperbolic trigonometric functions. The difference is that the imaginary component does not exist in the solution to the hyperbolic trigonometric function.
The point is, Euler's Formula is a theorem about polyhedron, but not about graph drawn on paper. A planar graph satisfies Euler's is just because polyhedrons can be "stretched" to planar graphs and vice versa.
we arrive at Euler's identity. The $\pi$ itself is defined as the total angle which connects $1$ to $-1$ along the arch. Summarizing, we can say that because the circle can be defined through the action of the group of shifts which preserve the distance between a point and another point, the relation between π and e arises.
Well, the Euler class exists as an obstruction, as with most of these cohomology classes. It measures "how twisted" the vector bundle is, which is detected by a failure to be able to coherently choose "polar coordinates" on trivializations of the vector bundle.
I want to understand how to compute Euler classes, what are the canonical examples of vector bundles from which i can start, and are there any books or lectures which describe how to compute Euler
