Snuggle your head -- and everything within it -- inside a warm wool Klein Bottle Hat.

Complete with matching Mobius Scarf!


Klein bottle hats and scarves on Zoe and Danny Stoll many years ago

alt="Klein bottle hats and scarves on Zoe Stoll many years ago"

alt="Klein bottle hats and scarves"

Klein bottle hat and scarf

Pop an Acme Klein Bottle on your head!

It's ideal for skiing, sleigh-rides, snowball fights, midwinter colloquia, Antarctic beach parties, and alpine chess tournaments. A perfect gift for anyone with a zero-volume head. An important accessory to the one-sided mind. An essential headwarmer for your non-orientable friends who are temporarily immersed in our 3-dimensions.

This Klein Bottle is a hand knitted hat, so it's seamless and perfectly contoured. It's constructed of knit-purl-knit-purl, so the "outside" has the same pattern as the "inside". One sided? You betcha! (Purl is not to be confused with the computer language Perl, which shouldn't be confused with the oyster generated pearls)

Your Klein Bottle Hat is made of a scientifically balanced mix of 85 percent wool delicately shorn from contented Midwestern lambs, then blended with carefully selected 15 percent Mohair from grinning Angora goats in Texas (Goats have a lot to grin about in Texas). The special blend (called "Lamb's Pride" yarn) is spun and dyed in western Nebraska by Brown Sheep Company, yarn-makers of high repute.

Each Acme Klein Bottle Hat is lovingly hand knit by a team of professional knitters, who spend their winter evenings carefully constructing these manifolds using time proven 4-needle and circular needle techniques. Acme's dedicated knitters include several smiling grandmothers, a former librarian, a nurse, and a schoolteacher. Not one of them has studied orthogonal polynomials.

Imagine the brilliant ideas you'll enjoy after wrapping a genuine Acme Klein Bottle around your brain -- one of the most useful parts of your body.

These hats are sized for regular-sized heads. But you needn't worry if you have an especially big brain: the special weave stretches to fit any size human.

Acme Klein Bottle hats do not self-intersect. This lets you turn your hat inside out, by sliding the hat inside of itself. (This transformation requires a bit of care, but works well.) In this quick cross section, notice that the loop goes right through the outer shell, without any stitching. It slides through itself!

Cross section of our Klein Bottle Hat

Cross section of Acme's Knit Klein Bottle Hat

It's double walled, so it slides through itself.

Update, June 2018: My knitters have just made a new batch of Klein bottle hats and matching Mobius scarves. I'm delighted: they (the hats & scarves, as well as the knitters) look terrific and work perfectly! The hats stretch nicely - they fit snugly on your head and cover your ears. The Mobius scarves now have a machine-stitched seam, rather than a hand-knit seam. (This means that you can see the seam, perpendicular to the central axis of the scarf). A few changes: I no longer have any blue/green/white hat/scarfs, and I now send all headware with free shipping.

SPECIAL REFLEXIVE DEAL! Each Klein Bottle hat comes with a matching Mobius Scarf AND each Mobius Scarf comes with a matching Klein Bottle Hat! ? x ? X : x R x


Klein bottle hats and scarves on Zoe and Danny Stoll many years ago

Klein Bottle Hat with a matching Mobius Scarf

... both for only $50.

Two - YES TWO - matching manifolds for one low price! The Mobius Scarf works symbiotically with the matching Klein Bottle Hat to keep you toasty warm. Each is one-sided, but together, they protect both your outside and your inside from the chilly winds of winter.

Using all natural wool and all natural mathematics, Acme has designed specially matching hats and scarves which fight against thermodynamic equilibrium and promote healthy, warm heads even when camping on cold terrestial evenings, thinking wild wooly thoughts, or while wading through long, run-on sentences.

The Mobius scarf is also called an infinity scarf. If you try to knit one of these, you'll understand why -- it's easy to goof up the parity, get the wrong number of half-twists, and become infinitely frustated. (The Mobius scarves do not have hidden seams).

The photos include objects like bananas, oranges, apples, kids, books, and a white foam mannequin head. These are to help you judge the hats' color, size, and utility. Those objects (bananas, oranges, kids, etc) do not come with the hat, although there are days when I wouldn't mind sending off the kids...

Each hat and scarf is handmade from real wool from genuine sheep.  Three different color combinations allow you to match your manifold to your mood! Ready for same day shipping to you or your best friend. Just $50 keeps your head, neck, and shoulders snug and warm ... at a much lower cost than any single-payer public health care system.

Red Orange White Klein bottle hat and scarf <- click on a photo to enlarge

RED - ORANGE - WHITE Klein bottle hat with matching Mobius Scarf

Blue Teal White Klein bottle hat and scarf <- click on the photo to enlarge

BLUE - TEAL - WHITE Klein bottle hat with matching Mobius Scarf

Black Grey White Klein bottle hat and scarf <- click on the photo to enlarge

BLACK - GRAY - WHITE Klein bottle hat with matching Mobius Scarf (notice how I"ve learned to photo-mask!)

Three Klein BOttle hats. Nice and warm!

Warm in the winter? Yes, indeed! They may be single-sided but they're double-walled, so your head enjoys twice the insulation of a standard ski-hat. There's two layers of wool between your head and that cruel winter wind. Works down to minus 40 degrees (F or C, your choice) !

Exclusive features of your Acme's Klein Bottle Hat:

- Available in universally attractive color combinations - specially chosen to be visible during daylight.

- Genus 1 ... so there's exactly one topological hole. You can secure this hat with a Kryptonite Lock. Other hats, being genus zero, can't be locked.

- Stretchable ribbing allows this Klein Bottle hat to fit all sizes of heads. Keeps your ears warm, too!

- Unscientifically tested at Acme's Winter Proving Grounds in Buffalo, New York. Also, Danny Stoll is rigorously testing these at the University of Chicago's Low Temperature Terrestial Proving Grounds at Ryerson Hall. An Acme Mobius scarf and Klein bottle hat helps him survive Chicago's winter, as well as Complex Analysis.

- Easy to clean, as you need only wash one side.

- Zero topological volume ... fits in your pocket when not in use.

- Reversible! You can wear it with the loop pointing forwards, backwards, sidewards, or even downwards. Astonish the skeptics.

- Built in handle for enhanced portability - you can carry it on your head or hold it in your hand.

- Hat & Scarf together weigh about 200 grams (7 ounces) -- lighter on your head than a Canadian Goose.

- You can turn this hat inside-out, although it's kinda difficult to squeeze the bottom through the narrow loop.

- Unbreakable in normal use. Won't fracture, even if dropped onto a concrete floor. Works indoors and out!

- Perfectly flexible, just as semi-metric topological manifolds oughta be.

- Conserve scarce energy - wear one of these and turn off your furnace.

- Comfortably fits one head.

- Featured (with a photograph) in the 29 December 2001 issue of New Scientist

- Wrinkle resistant. Unlike people, wool sheds wrinkles and returns to its natural shape after a day's rest.

- Made with 100% pure yarn.

- For proper insulation properties to function properly, please wear on head. To remove hat, simply take it off your head.

- Protected by Acme's Unconditional Guarantee

- Covered by Acme's Lifetime Guarantee: We guarantee that you will live your entire lifetime.

Handwash in cool water, using a natural fiber shampoo. Don't use harsh detergents, bleach, or fuming nitric acid. Pat dry between towels - don't machine wash and don't machine dry. Never needs ironing, which is a good thing, considering that few mathematicians own irons (ever notice the rumpled suits at colloquia?).

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Cliff last updated this page on 2021-November-14