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.

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. …

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 …

Aug 22, 2023 · How to understand Euler's criterion for exactness of differential equation as presented in the book "Physical chemistry" by Silbey, Alberty, Bawendy?

Extrinsic and intrinsic Euler angles to rotation matrix and back Ask Question Asked 10 years, 9 months ago Modified 9 years, 8 months ago

Feb 20, 2015 · I read on a forum somewhere that the totient function can be calculated by finding the product of one less than each of the number's prime factors. For example, to find $\\phi(30)$, you …

The $3$ Euler angles (usually denoted by $\alpha, \beta$ and $\gamma$) are often used to represent the current orientation of an aircraft. Starting from the "parked on the ground with nose pointed …

Nov 8, 2025 · A sequence based on Euler's totient function that always converges to prime numbers Ask Question Asked 4 months ago Modified 3 months ago

Aug 4, 2024 · This is again a kind of "inclusion-exclusion" argument, and it's a useful computational tool but it doesn't by itself imply any kind of deep relationship to the topological Euler characteristic, which …

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 …