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

* * * SOLD OUT * * * I expect to make more in later summer. Send email if you want one of these * * *

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 Mobius 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 Mobius loop should!).

Our Baby Klein Bottle sliced in two.

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 will be about 110mm (4.5") tall; both halves will set you back $100. (I'm sorry, I have sold out of the baby Klein bottles sliced in half. I will make more in late 2017)

A sliced Medium Klein Bottle is about 140mm (5.5") tall and the two halves cost $125. (Out of stock. I will cut several more in late 2017)

The sliced Big Klein Bottle is 190mm (7") tall; the two halves cost $150. In stock, ready to send today. (Out of stock - I expect to cut more of these in late 2017)

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.

That's a Diamond Band Saw

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

A medium Klein Bottle sliced

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 page on June 16, 2017 (but it won't change much, so don't expect frequent updates)

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