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.

Related (duplicate?): Simple proof of Euler Identity $\exp i\theta = \cos\theta+i\sin\theta$. Also, this possible duplicate has this answer, with a nice visual demonstration of the result. There are more …

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 …

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 question (in my …

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 coherently choose …

Jul 23, 2021 · What is the geometrical importance of the Euler Line (ie, the line through the centroid, orthocenter, and circumcenter (and other points) of a non-equilateral triangle)? What is meant by …

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 describe how to …

Nov 28, 2010 · Then you should try to understand Euler's formula better first. (For one thing, there is a slight subtlety in the definition of f that you should be aware of.) Try playing around with examples …

Oct 4, 2021 · @Jonas: Another property of the Euler class listed in Milnor & Stasheff is that the Euler class reduces mod 2 to the corresponding Stiefel-Whitney class. Maybe including this as an axiom …

Extrinsic and intrinsic Euler angles to rotation matrix and back Ask Question Asked 10 years, 7 months ago Modified 9 years, 6 months ago