MaplePrimes - answers and comments on Question, boys surface - is it one surface

Self-crossing surface

Markiyan Hirnyk — Thu, 22 Nov 2012 01:31:42 Z

The functions x, y, and z are continuous in u and v. This is a self-crossing surface as it is seen in

partially

Christopher2222 — Thu, 22 Nov 2012 18:51:54 Z

Okay that partially works. My idea was to get rid of the self crossing surfaces. The grid is still slightly noticeable crossing the space with the transparency option. Originally I had thought this klein bottle post http://www.mapleprimes.com/maplesoftblog/95570-Klein-Bottle-Plot did not have self crossing surfaces but on closer inspection it does as well.

Would it be much trouble getting rid of those self crossing surfaces?

A flythrough would also be quite neat.

crossing surfaces

Christopher2222 — Sat, 24 Nov 2012 05:59:39 Z

For the klein surface we could create 2 sections. I borrowed these equations for two surfaces but the point is that one surface crosses through the other. I thought maybe a cutout option? The point is I want a solid surface with which we can fly through in maple without coming up on any crossing walls. I think the klein surface might be easier to deal with than boys surface so maybe we can take care of that first?

Anyways here is what this plot yields.

Download klein_bottle_surfac.mw

If you read the Whitney theorem,

Markiyan Hirnyk — Sat, 24 Nov 2012 12:52:37 Z

maybe you will understand that this is impossible.

One surface

Markiyan Hirnyk — Thu, 22 Nov 2012 02:20:39 Z

The image of a connected set under a continuous map is a connected set (for example, see lect2.pdf ).

Reference

Markiyan Hirnyk — Thu, 22 Nov 2012 03:02:57 Z

See http://en.wikipedia.org/wiki/Boy%27s_surface