Why is it Euler's 'Totient' Function? - Mathematics Stack Exchange
Dec 13, 2018 · The function ϕ(n) ϕ (n) calculates the number of positive integers k ⩽ n , gcd(k, n) = 1 k ⩽ n , gcd (k, n) = 1. It was found by mathematician Leonhard Euler. In 1879, mathematician …
How can I prove Euler's formula using mathematical induction
Mar 18, 2019 · Using Euler's formula in graph theory where r − e + v = 2 r e + v = 2 I can simply do induction on the edges where the base case is a single edge and the result will be 2 vertices. A …
rotations - Computing Euler angles between two 3D points from …
Computing Euler angles between two 3D points from Cartesian coordinates Ask Question Asked 3 years, 2 months ago Modified 3 years, 2 months ago
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, 2 months ago Modified 9 years, 1 month ago
The interconnection between Hyperbolic functions and Euler's Formula
Jul 16, 2018 · There is one difference that arises in solving Euler's identity for standard trigonometric functions and hyperbolic trigonometric functions. The difference is that the imaginary component …
rotations - Are Euler angles the same as pitch, roll and yaw ...
From wiki, I know that Euler angles are used to represent the rotation from three axes independently, which seems like pitch, roll and yaw. But from this wiki, it seems that they are two different things.
Euler angles and gimbal lock - Mathematics Stack Exchange
Jan 22, 2017 · Can someone show mathematically how gimbal lock happens when doing matrix rotation with Euler angles for yaw, pitch, roll? I'm having a hard time understanding what is going …
Proof of the formula for Euler's totient function
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 …
number theory - Modular exponentiation using Euler’s theorem ...
This is if you're doing it by hand, for this case. In general, algorithmically, you would just use repeated squaring to exponentiate numbers. You don't gain much by using Euler's theorem, since finding …
Why does the sum of inverse squares equal $\\pi^2/6$?
Oct 5, 2016 · This was the famous "problem of Basilea", what makes that a young Euler was recognized internationality as a great mathematician.