Intuitive explanation of Euler's formula $e^{it}=\\cos(t)+i\\sin(t)$
Thinking in polar coordinates helps—multiplying a number by i i rotates its position by 90° 90 °, ie π 4 π 4, cos cos and sin sin calculate the co-ordinates, multiplying by a fractional power of i i …
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, 8 months ago Modified 9 years, 6 months ago
Prove that $e^{i\\pi} = -1$ - Mathematics Stack Exchange
The identity is a special case of Euler's formula from complex analysis, which states that eix e i x = cos x + i ⋅ sin x cos x + i sin x for any real number x x. (Note that the variables of the …
Simple Proof of the Euler Identity - Mathematics Stack Exchange
Jun 25, 2016 · How can I explain this relation (intrinsically)in a simple way to a high-school student, they is any physical interpretation of this formula ? or we can give another equivalent …
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 …
calculating Euler classes - Mathematics Stack Exchange
Feb 12, 2023 · I want to understand how to compute Euler classes, what are the canonical examples of vector bundles from which i can start, and are there any books or lectures which …
ordinary differential equations - What's the difference between ...
Sep 8, 2016 · The Euler method is an explicit method in that the expression for y1 y 1 depends only on x0 x 0 and y0 y 0. On the other hand, backward Euler is an implicit method, since the …
The interconnection between Hyperbolic functions and Euler's …
Jul 16, 2018 · 0 There is one difference that arises in solving Euler's identity for standard trigonometric functions and hyperbolic trigonometric functions. The difference is that the …
How to interpret the Euler class? - Mathematics Stack Exchange
Well, the Euler class exists as an obstruction, as with most of these cohomology classes. It measures "how twisted" the vector bundle is, which is detected by a failure to be able to …
Equivalent definitions of the Euler class of an oriented vector bundle
Oct 4, 2021 · If is an odd-rank bundle such that has nonzero Euler class, then must be nonzero. I think you can construct such an example by adapting this answer of Qiaochu Yuan, replacing …