Linked Questions

221
votes
9answers
22k views

John Nash's Mathematical Legacy

It would seem that John Nash and his wife Alicia died tragically in a car accident on May 23, 2015 (reference). My condolences to his family and friends. Maybe this is an appropriate time to ask a ...
23
votes
11answers
3k views

Creating high quality figures of surfaces

I am not sure if this question is suitable for mo, it is more about visualization than math. Anyway, here it is: What is the best way to visualize a 2-surface in Euclidean space with high quality? ...
21
votes
2answers
818 views

Eversion of the 6-sphere in 7-space

Say that $S^n$ "admits eversion" if the inclusion $S^n \rightarrow \mathbb{R}^{n+1}$ is regularly homotopic to the antipodal map (where a "regular" homotopy is a continuous path through immersions). ...
8
votes
2answers
321 views

Is there a $W^{2,2}$ isometric embedding of the flat torus into $\mathbb{R}^3$?

It is well known that there exists a $C^1$ isometric embedding of flat torus into $\mathbb{R}^3$, and that this embedding cannot be $C^2$. Is there a $W^{2,2}$ isometric embedding? (i.e an isometric ...
2
votes
1answer
785 views

embeddings of product of spheres in Euclidean spaces [closed]

I notice that $T^2=S^1\times S^1$ can be embedded in $\mathbb{R}^3$ as a hypersurface (submnaifolds of codimension 1). In general, (1). could the product of spheres $S^{m_1}\times\cdots\times S^{...
9
votes
1answer
694 views

Area of square to wrap a torus

The Nash-Kuiper $C^1$ isometric embedding of flat torus into $\mathbb{R}^3$ has recently been spectacularly visualized by the Hevea Project. This suggests two questions. Q1. What is the area of the ...
8
votes
1answer
190 views

Reference for a PL flat torus embedding in $\mathbb{R}^3$

A piecewise linear flat torus embedded in $\mathbb{R}^3$ is shown at http://www.mathcurve.com/polyedres/toreplat/toreplat.shtml. It is flat in the sense that the angle defect at the vertices is zero. ...