What is the metric on the $n$-sphere in stereographic projection ...
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Understanding the formula for stereographic projection of a point.
2018年2月16日 · Solving stereographic projection for central latitude $\phi_1$ and central longitude $\lambda_0$ Related. 3.
calculus - Stereographic Projection and Diffeomorphism
Oct 26, 2020 at 17:13. 1. The last component is extraneous. Remember that we are projecting onto the plane. Writing. f(x, y, z) =(x 1 − z, y 1 − z) f (x, y, z) = (x 1 − z, y 1 − z) Would be correct. As for differentiability, see here. It would help us to answer your question if you showed some of the stuff you've tried so far so we can ...
differential geometry - Smoothness of streographic projection ...
For the question to make sense one needs to have a differentiable structure on the sphere. One common way to equip the sphere with a manifold structure is to fix an atlas given by the stereographic projection from the north and south pole. With this atlas, the question becomes trivial, because the map $\pi$ becomes the identity on the local chart.
general topology - Showing that stereographic projection is a ...
2015年1月28日 · (This map is called stereographic projection.) It can be described geometrically as follows: ...
Formula for Stereographic Projection of Ball of Radius $R$
2019年7月11日 · 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.
differential geometry - Stereographic projection calculating the ...
2017年3月6日 · Stereographic projection calculating the Transition function. Ask Question Asked 7 years, 8 months ago.
How differentiate the stereographic projection map
2021年2月17日 · How differentiate the stereographic projection map. Ask Question Asked 3 years, 8 months ago.
functions - The stereographic projection is bijective - Mathematics ...
2020年11月21日 · 1. I want to prove that the stereographic projection: f: { (x, y):x2 +y2 = 1} → R f: { (x, y): x 2 + y 2 = 1} → R where f f is defined as: f(x, y) = x 1 − y f (x, y) = x 1 − y. is bijective to the real number. I have already shown that f f is one-to-one, but I am struggling on showing this is onto. I also tried to find an inverse for f ...
geometry - Proving geometrically that stereographic projection ...
2016年12月30日 · I am aware of a few analytical calculations showing that the stereographic projection sends circles on the sphere to circles on the equatorial plane. There are related questions here. What about a