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 …
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 …
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
$\\sin(x)$ 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 …
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 …
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.
How to find Euler's angles? - Mathematics Stack Exchange
I have read about Euler's angles and matrices, including zxz, zyz z x z, z y z, etc . I am not obliged to use a specific rotation but rather I want to figure out what angles I need to use for alpha,theta, …