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.
IN the published correspondence of Euler there is a note from him to Goldbach, or, the other way, from Goldbach to Euler, in which a very wonderful theorem is stated which has never been proved by ...
Check out this link: Ed Sandifer: How Euler Did It, March 2004 And here: Wikipedia: Basel Problem The Wikipedia link shows there actually does exist an "elementary" proof of the generalized Basel problem (the evaluation of the Riemann zeta function for positive even integers). Graham, Knuth, and Patashnik, in the text Concrete Mathematics, also give an outline of another elementary proof which ...
Robotics - Euler Angles from Linear Transformation Ask Question Asked 2 years ago Modified 1 year, 6 months ago
What is the geometrical importance of the Euler Line (ie, the line through the centroid, orthocenter, and circumcenter (and other points) of a non-equilateral triangle)? What is meant by importanc...
The graphic representation of the complex numbers, and therefore the realisation that Euler's formula can be interpreted as describing complex numbers in polar coordinates, is of more recent date, and was unknown to Euler.
I like the fact that your answer does not depend on knowing that sine is an odd function. It appears that when using Euler to prove sine is odd one must make use of complex conjugates. Correct?
19 I am rotating n 3D shape using Euler angles in the order of XYZ meaning that the object is first rotated along the X axis, then Y and then Z. I want to convert the Euler angle to Quaternion and then get the same Euler angles back from the Quaternion using some [preferably] Python code or just some pseudocode or algorithm.