That's from a website called Mathematical Imagery by Jos Leys. No, I don't know how I found that. Internet surfing lands us in the strangest places. :-)
KLEIN BOTTLE MATHS (for those who like Maths, and beware, this is about your run-of-the-mill Klein bottle, not the .... thing in the photograph above ...... ) :
The "figure 8" immersion (Klein bagel) of the Klein bottle has a particularly simple parameterization. It is that of a "figure-8" torus with a 180 degree "Möbius" twist inserted:
The parameterization of the 3-dimensional immersion of the bottle itself is much more complicated. Here is a simplified version:
In this parameterization, u follows the length of the bottle's body while v goes around its circumference.
Off topic: This webpage (The Best NYC Pastrami Sandwich restaurants) is wrong. The best hot-pastrami-on-rye sandwich on Earth can be found at Harold's New York Deli Restaurant in Edison, New Jersey. ;-p
Important note: Like the website says, all in CAPS, sorry: HAROLD JAFFE, OWNER OF HAROLD'S NY DELI IN EDISON NEW JERSEY IS NOT IN ANY WAY AFFILIATED WITH
HAROLD'S DELI IN PARSIPPANY NJ OR ANY OTHER LOCATION
Trust me, he's not kidding, cuz I've eaten at both. Go to Edison, or don't go at all. The Parsippany Pastrami ain't bad, but it ain't as good as Jaffe's restaurant in Edison, unless "average" or "OK" turns you on. IMO, which I'm entitled to.