How to prove Euler's formula: $e^{it}=\\cos t +i\\sin t$?
Aug 28, 2010 · 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.
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 …
How to calculate Euler angles of a line defined by two 3D vectors from ...
May 12, 2025 · I want to compute the Euler angles (RX, RY, RZ — pitch, yaw, roll) that would orient an object or camera to "look along" the line from A to B. In other words, I want to calculate the rotation …
$\\sin(x)$ infinite product formula: how did Euler prove it?
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 …
The "Euler Product formula" for general multiplicative functions
Jul 13, 2024 · The "Euler Product formula" for general multiplicative functions Ask Question Asked 1 year, 7 months ago Modified 1 year, 6 months ago
A sequence based on Euler's totient function that always converges to ...
Nov 8, 2025 · A sequence based on Euler's totient function that always converges to prime numbers Ask Question Asked 2 months ago Modified 2 months ago
general topology - Mismatching Euler characteristic of the Torus ...
Jun 10, 2024 · You should use Euler formula on a triangulation if you want to compute the euler characteristic. One easy triangulation of the torus can be obtained as following: Obtained by …
Euler-Lagrange equation in matrix form - Mathematics Stack Exchange
May 13, 2024 · The Euler-Lagrange equation seems fundamental, and mappings or vector functions are prevalent. Thus, I find it peculiar that I haven't seen so far a convenient matrix form of the E-L. See …
How to convert two vectors to three Euler angles
Mar 25, 2021 · I am trying to convert two vectors to Three Euler angles. My goal is to be able to type this formula in excel and be able to convert them to Euler angles. The first angle is "β" Which …
Proving Fermat's Last Theorem for n=3 using Euler's and Lamé's …
Euler's method of infinite descent for the case n = 3 (with a careful explanation of the gap in Euler's proof) is given and corrected in sections 2.2, 2.5 of this book.