How to prove Eulers formula: $e^{it}=\\cos t +i\\sin t$? Euler's formula generalizes to quaternions, and this in turn can be thought of as describing the exponential map from the Lie algebra $\mathbb{R}^3$ (with the cross product) to $\text{SU}(2)$ (which can then be sent to $\text{SO}(3)$) This is one reason it is convenient to use quaternions to describe 3-d rotations in computer graphics; the
What is the geometrical importance of the Euler Line? Centers $2-5$, $20-30$ (a lot of important points), $140$, $186$, $199$, $235$, $237$, $297$, $376-379$, $381-384$, $401-475$ (a lot of points), $546-550$, $631-632$ (and others) lie on the Euler line and there are many other points defined using the Euler line, or satisfying properties related to the Euler line
rotations - Are Euler angles the same as pitch, roll and yaw . . . You can say that Euler angle representation (rep) is ZYX representation whereas roll-pitch-yaw is XYZ representation If $\alpha$ is rotation about Z axis, $\beta$ is rotation about Y axis, and $\gamma$ is rotation about X axis:
Euler Product formula for Riemann zeta function proof $\begingroup$ The book "Gamma: Exploring Euler's Constant by Julian Havil" -- I am pretty sure that you will read not only the easiest but also the most rigorous proof of the theorem $\endgroup$ – user231343
Does Eulers formula give $e^{-ix}=\\cos(x) -i\\sin(x)$? Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
ordinary differential equations - Respective advantages and . . . Forwards Euler is the most simple method, just take the linear Taylor polynomial As such it is often used for abstract theoretical contemplation and to derive reaction or interaction models, translating them from some discrete-time intuition to the continuous model Implicit or backwards Euler is very stable, works also with rather large step
Euler Formula for planar graphs - Mathematics Stack Exchange Let us look into a tetrahedron It has 4 faces, 4 vertices, 6 edges It does satisfy the Euler's Formula The point is, Euler's Formula is a theorem about polyhedron, but not about graph drawn on paper A planar graph satisfies Euler's is just because polyhedrons can be "stretched" to planar graphs and vice versa Come back to the question