Sliced Klein Bottles - see the inner Moebius loop - on sale right here!

Just made a few more of these--these are now in stock to send out today.

Sliced Klein bottle

To further advance your topological explorations, get a Klein Bottle cut right down the middle. You can then trace the built-in Möbius loop with your fingertip or crayon. In the photo, you can see the edge of the glass forms a nice Möbius loop.

In this all-too-asymetrical universe, Acme's topological technicians strive to preserve parity. By slicing an Acme Klein Bottle, they generate one left handed Möbius loop and a matching right-handed one. Unlike matter/antimatter couplets, these can be placed next to each other without fear of total annihilation. Indeed, they fit so well that you can glue 'em together to recreate the original.

These are great classroom demos - students immediately see (and feel) how two Möbius loops combine to make a Klein Bottle.

Put one of these on an overhead projector, and shine it at the chalkboard. A student can then use chalk to trace the edge -- showing that the edge does come back on itself (as a Möbius loop should!).

Sliced Klein bottle

Our Baby Klein Bottle sliced in two.

Sliced Klein bottle drawing

a computer generated image by Thomas Banchoff & Davide Cervone. Click here for an animation

We leave the edge semi-rough, like emery paper or the surface of Ramanujan's chalkboard.

Thanks to an advanced diamond band-saw, Acme's Slicer-meister can now cleave baby, medium, or big classical Klein bottles. (See how I do it - scroll to the bottom of this page)

Each half of a Baby Klein Bottle is about 110mm (4.5") tall; the matched set of two sides will set you back $100. 

A sliced Medium Klein Bottle is around 150mm (6") tall; both mirror-image halves cost $150.

The sliced Big Klein Bottle is a smidgen over 200mm (8") tall; the two matched halves cost $200.

Prices slightly higher north of the North Pole.

Klein Bottle sliced down the middle, with a pencil inside.  See the Moebius Strip along the edge.

How do you slice a Klein Bottle? Why, on a diamond band saw. The thin diamond band runs at about 40 miles per hour (it's driven by a hefty electric motor!). Meanwhile, the glass Klein Bottle must be pulled in an straight line, at a uniform slow rate. To move the Kleinbot without any wobble, I use a set of drawer-slides as linear bearings. The low-speed drive is a DeWalt saw turning a threaded 8/32 rod which is coupled to the Kleinbot through a set of wingnuts. The drill itself would turn much too fast, so I slow it down by a computer-controlled power supply that monitors its rotation speed through a magnetic reed switch. Oh - don't forget a syphon squirting water keeping the diamond saw wet.

Cliff Stoll's diamond bandsaw cutting a Klein bottle into two mobius loops

That's a Diamond Band Saw

Cutting a Klein bottle

Closeup of a baby Klein Bottle being cut. The bottle advances about 2mm per minute, and a water stream keeps the blade cool.

Sliced Klein bottle

A medium Klein Bottle sliced

Machine to cut a Klein bottle

A kludge? You bet! You can't do physics without pleny of C-Clamps, gaffer's tape, and paperclips.

Not shown is the honking 6 Amp regulated power supply and the Basic Stamp controller. But you can see the rotation sensor - a white reed-switch a few mm above the chuck of the drill. This senses each rotation so the computer will drive the drill at a constant (very slow) speed.

I last updated this 2022 March 11th after I purchased a new blade for my old diamond say - works like a champ!

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