Breakthrough

I had an engineering breakthrough in my non-orientable manifold lab this past weekend and am pleased to announce a new and improved Klein Bottle construction technique. (That's quite alright, you can thank me later.) A key modification to the previous double-torus method virtually eliminates the need to reshape toruses and, consequently, to curse, and yields a Klein Bottle representation that permits hole-cutting tools to reach pretty much anywhere. (Ironically, in another breakthrough, I've overcome the need to cover the entire surface of my Klein Bottles with holes.)

The revised first step is to throw one classic torus and one torus with a collar. The diameter of the collar should be the same size as the diameter of the cross section of the first torus. Thank your subconscious for having made the hole of the first torus a little larger than the neck of the second torus, and promise you'll sing its praises for suggesting you use the first torus as a chuck to trim the second torus so that you don't squash the latter's neck.


Because you understand the importance of safety in the ceramics studio, do not assemble the Klein Bottle in your kitchen with a cat on your shoulders.