Proof of Euler's formula? - Mathematics Stack Exchange
Feb 27, 2025 · I have been searching for a satisfying proof of Euler's formula. Namely: $$ e^{ix}= \\cos{x} + i\\sin{x} $$ There are 3 proofs mentioned in Wikipedia: Using differentiation Using power …
Extrinsic and intrinsic Euler angles to rotation matrix and back
Extrinsic and intrinsic Euler angles to rotation matrix and back Ask Question Asked 10 years, 8 months ago Modified 9 years, 7 months ago
Does Euler's formula give $e^ {-ix}=\cos (x) -i\sin (x)$?
Apr 13, 2018 · 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. …
Did Euler guess the Basel problem’s solution to be
Mar 2, 2025 · So, is it even possible for Euler, or anyone for that matter, to guess the sum to be π2 6 π 2 6 from the approximation 1.6449340668482264 1.6449340668482264? The only way I could see it …
How to convert Euler angles to Quaternions and get the same Euler ...
Oct 29, 2018 · 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 …
Euler formula and $\sin^3$ - Mathematics Stack Exchange
Jun 29, 2011 · Euler formula and $\sin^3$ Ask Question Asked 14 years, 7 months ago Modified 14 years, 3 months ago
Where to find English translations of Euler's collected works?
Jun 15, 2020 · I will highly appreciate if someone can provide me the link to the book or link to the paper where I can find the following papers $(90-94)$ with English translation. Any help would be appreciated.
$\\sin(x)$ infinite product formula: how did Euler prove it?
I know that sin(x) sin (x) can be expressed as an infinite product, and I've seen proofs of it (e.g. Infinite product of sine function). I found How was Euler able to create an infinite product for sinc by using its …
Who came up with the Euler-Lagrange equation first?
Euler himself much preferred Lagrange's derivation and gave it the name "calculus of variations," and it is essentially Lagrange's technique that is used today. The name of the equation, then, is very …
reference request - Euler's errors? - Mathematics Stack Exchange
Seeing as Euler's conjecture turned out to be false, it in an indicator for the existence of this mathemagician's coefficient of humanity - he did not have some completely infallible looking glass …