Get the latest tech news
The Deceptively Asymmetric Unit Sphere
The deficiencies of the Unit Sphere, and how Lie groups can solve many of these deficiencies
In their search for a minimal set of axioms, differential geometers have taken great care to remove this dependence on an ambient space; they describe *smooth manifolds* as objects existing in their own right. Note that unlike our visualization of \\(\mathbb{R}^n,\\) we have chosen to explicitly display a tangent space of unit circle, since it takes a different shape than the underlying manifold. > In this post, we’ll continue with the embedded and overlapping view to aid intuition, but don’t be surprised if you see the tangent bundle drawn differently in other resources.
Or read this on Hacker News