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.
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.
One way to express the Euler-Maclaurin formula is ($a<b$ and $L \geq 1$ are integers, and let us assume that $f$ is at least $2L$ times continuously ...
It has all the five constants and all the addition, multiplication, and exponentiation operators. Indeed it does ! Unfortunately, it is not particularly meaningful, as has already been pointed out. But why are Euler's identity and formula considered meaningful in the first place ?, you might legitimately ask me in return. To which I would like to respond by referring you to the following seven ...
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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...
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.