Drinking Mug Klein Bottles - for the Thirsty Topologist
This looks like a glass cup. But wait -- it has two big chambers connected by a hollow handle. In fact, it's actually a Klein Bottle.
Hot ziggitty -- a Klein Bottle that delivers liquid straight to your waiting lips. Yep - you heard me right. You can drink right from this cup. Pour in beer and it's a Klein Stein. Would you believe Einstein's Klein Stein?
This cheezy diagram shows a cross section through the Acme Klein Bottle Drinking Mug. With a single hole, it's a true genus-1 manifold and topologically identical to our other Klein Bottles.
The handle does triple duty: It connects the inner and outer chambers, provides a topological hole, and gives you a way to conveniently grasp the mug. We've designed the handle to be fully ambidexterous -- yes, your Acme Drinking Mug Klein Bottle fits either hand. Indeed, it's possible to hold it with both hands simultaneously. And since it has no preferred angular momentum vector, you can swish your drink either clockwise or counterclockwise.
And if that's not enough, the outer chamber (which is topologically the inner chamber) insulates the inner chamber (which topologically is also the outer chamber). The 7 mm air space separates the inside from the outside, so ice water won't cause condensation. This extends the life of hot or cold drinks, saves energy, and helps stave off the dreaded local thermodynamic equilibrium and subsequent heat death of the universe. Even better, thanks to the exclusive Acme Concave Mug Bottom, no extraneous feet are needed!
But be careful. As a day-to-day cup, well, this isn't practical. It's hard to get liquids in and out of the outer chamber. A length of flexible tubing can relieve the obvious airlock; otherwise, it's a lot of tilt-and-pour. And once wet, the chamber is difficult to dry -- surface tension holds water up at the very top. (Alcohol is useful in drying, as is an aquarium style air pump). So treat this as a topological novelty - not as a utilitarian drinking mug. (you can tape over the hole in the side, and use it as a regular cup, but that kinda defeats the whole idea, eh?)
Again my warning: THIS IS NOT A GOOD DRINKING GLASS! It's difficult to get liquids in. Difficult to get liquids out. It's difficult to clean. (it's also difficult to make, if that's any consolation. ) Please treat it as a mathematical curiousity rather than a practical cup.
This Klein Stein is ideal for the mathematical physicist who needs a glass of water while accepting her Nobel Prize. Perfect for the Silicon Valley programmer swigging Jolt on an allnighter. Just the thing to quench the thirst of the multibillionaire following a leveraged buyout of the US government. Indeed, think of all the seminars, colloquia, interviews, and funerals that would be jazzed up with an Acme Klein Bottle Mug at your side.
Now, thanks to the wonders of modern technology, this multipurpose Klein Bottle is available for a mere $95 -- cheaper than sending a spaceprobe most of the way to Mars!
Here's a Klein Stein with the slightly wider diameter handle. That's Rose Wine in the outer chamber, and water in the inner chamber.
Same Klein Stein, except against a black background, so you can see the calibration label. It's hard to photograph these darn things!
Acme - the most trusted manufacturer of onesided, zero volume, locally Euclidean, Riemannian, affine, borosilicate glass manifolds that are fully immersed in 3-space!
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