Tuesday, May 12, 2026

My Klein bottle




(Klein bottles only exist in four-dimensional space, but a self-intersecting model of a Klein bottle can be made in 3D.)

Sometime in my teen years, I read the Time-Life book Mathematics. One photo caught my eye: Princeton math professor Albert W. Tucker's Klein bottle: 


I wrote to him asking where he had got it.  He wrote back and said the University glassblower had made it for him, but had found it very difficult, and wasn't going to do it again! 

But in 1999, a story in the San Jose Mercury News said someone in Berkeley was selling these. I bought the small one pictured at the top of this piece. I exchanged a few emails with the seller, Cliff Stoll, and realized I had read his book The Cuckoo's Egg.

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