It was just too irresistible... Klein Bottles

Rohit Khare (
Thu, 17 Jun 1999 09:06:54 -0700

Just had to have one... a Cliff Stoll enterprise... The sliced=20
bottles are way, way cool... Rohit


Welcome to the Land of Many Manifolds

Searching for a one-sided surface?
Need a zero-volume bottle?
Want the ultimate in non-orientability?


At last, Acme has conquered topological and engineering frontiers to=20
manufacture genuine glass Klein Bottles. These are the finest closed,=20
non-orientable, boundary-free manifolds sold anywhere in our three=20
spatial dimensions.

These elegant bottles make great gifts, fantastic displays, and=20
inferior mouse-traps. With its circle of singularities, an Acme Klein=20
Bottle can be said to exist inside of itself -- especially handy=20
during time-reversals

Specifications for ACME Klein Bottles

190 mm (7")
80 mm (3.5")
220gm (8 oz)
650ml (23 fl oz)
0.0ml (0 fl oz)
in stock

Half Pint
140 mm (5.5")
67 mm (2.7")
130gm (4.5oz)
300ml (10 fl oz)
0.0ml (0 fl oz)
April 99

Real Little
110 mm (4.5")
60 mm (2.5")
110gm (4 oz)
200ml (8 fl oz)
0.0ml (0 fl oz)
April 99

240 mm (9.5")
95 mm (4")
250gm (9 oz)
800ml (28 fl oz)
0.0ml (0 fl oz)
in stock

Top Erlen
160 mm (6.5")
95 mm (4")
225gm (8 oz)
750ml (26 fl oz)
0.0ml (0 fl oz)
in stock
No two Acme Klein Bottles are alike! Since Acme glassblowers=20
individually craft each one, dimensions will vary and you may find=20
occasional bubbles or streaks in the glass. These prove that your=20
Acme Klein Bottle was made by real, 3-dimensional humans, adding to=20
its unique status in a world of identical, machine made commodities.

Be careful with your Klein Bottle!

CAUTION! Acme Klein Bottles are crafted from glass, a supercooled,=20
inorganic liquid in a solid, non-crystalline state. If dropped, they=20
may shatter, possibly into paired single-sided M=F6bius loops. But then=20
again, they may not. Other shocks -- including fast decelerations and=20
Republican landslides -- may lead to similar fragmentation.
During earthquakes, your Acme Klein Bottle may jump off the table, in=20
a mistaken attempt to connect with the 4th dimension. So just before=20
major tremors, apply a dab of quake-putty to hold down your manifold=20
during the Big One.

WARNING!! Acme constructs each Klein Bottle from genuine Barionic=20
matter. Do not allow your Acme Klein Bottle to come in contact with=20
anti-matter or unpredictable results may occur. Acme cannot guarantee=20
the dimensionality of the result.
Although originating in the 4th dimension, Acme Klein Bottles are=20
immersed (not embedded) in 3 dimensions, using special techniques=20
known to students of advanced topology. We strongly recommend that=20
you do not attempt to evade the Pauli Exclusion Principle.
What with the decay of protons, Acme recognizes that our products=20
have a finite lifetime and may not outlast your physical universe. If=20
your application demands constant uninterrupted ceaseless unremitting=20
everlasting endless eternal persistent perpetual permanence, please=20
contact a qualified quantum mechanic.

=2E.. Because Acme makes the finest manifolds!


* Acme engineers use our familiar 3-dimensions. Result? You can=20
actually hold an Acme Klein Bottle in your hand. Those highfalutin'=20
4-dimensional ones can only be held in your mind.

* We select the finest quality genus-1 manifolds, so each Acme=20
Klein Bottle includes a built-in handle at no extra cost.

* With a carefully positioned center of gravity, your Acme=20
Klein Bottle stands on its own. No stands needed, nor cumbersome=20
space-time springhooks.

* Microwave safe, batteries not required, Y2K compliant.

* Our technicians painstakingly adjust each Acme Klein Bottle=20
for an Euler Characteristic very, very close to zero.

* With each Klein Bottle, Acme includes a manifold free of any=20
covering of coherently oriented coordinate neighborhoods. And an Acme=20
Klein Bottle allows a closed curve /s/ which is such that a small=20
oriented circle whose center traverses the curve continuously to=20
arrive at its starting point with its orientation reversed. If this=20
makes sense, then you simply must own an Acme Klein Bottle.

* Your Acme Klein Bottle is hand crafted in low expansion=20
borosilicate glass by happy glassblowers, ceramicists & one gourmet=20
cook. Triple sealed with an oxy-hydrogen torch, annealed, then=20
individually inspected by PhD astrophysicists with advanced degrees=20
in radiative transfer.

* You can convert your Acme Klein Bottle into an astonishing=20
amount of energy, over 1023 ergs! Enough to power a small city for=20
years. To get you started, we'll supply the necessary equation for=20

* Acme Klein Bottles are made on a planet rich in silicon=20
dioxide -- we never clearcut rainforests, stripmine Kentucky towns,=20
or smash oil tankers into arctic shores.

* All manifolds are homogeneous, that is, every small piece=20
looks like a piece of Euclidean space of the same dimension. Immersed=20
in 3 dimensions, a Klein bottle's surface must intersect itself at=20
the nexus, and Acme cleverly uses an elegant transverse puncture.=20
Inferior 4-D Klein Bottles lack this self-intersection feature.

* You can actually fill your Acme Klein Bottle with colored=20
water! (In Britain, use coloured water) Impress your friends, astound=20
your professors, and baffle next year's graduating class!

* Every Acme Klein Bottle comes with a free topological=20
fundamental group which can be homomorphically mapped onto the=20
Baumslag-Solitar group. Perfect for dorm parties.

* Acme Klein Bottles incorporate NO MAGNETIC MONOPOLES and=20
strictly obey Gauss's Law. And our low coefficient of expansion=20
insures that the bottle's size remains almost invariant with=20

* Worried about Lorentz contractions? No problem with an Acme=20
Klein Bottle! It's designed to work in any frame of reference.

* Buy with confidence -- your Acme Klein Bottle comes with a=20
unconditional guarantee which includes about seven conditions.

* Your money back if not satisfied! (However, we suspect that=20
we will be quite satisfied with your money)

* Acme uses no expensive palladium compounds so there's minimal=20
danger of cold-fusion byproducts.

* Your Acme Klein Bottle is transparent to most forms of=20
visible radiation, yet blocks harmful extreme ultraviolet rays.

* They're rustproof, even in Wisconsin.

* Run-of-the-mill Klein Bottles are homeomorphic to a sphere=20
with two crosscaps. Thanks to the Acme's exclusive transverse=20
puncture, Acme Klein Bottles are homeomorphic to a disc with two=20
crosscaps. Especially useful during the extreme weather conditions=20
encountered in the palagonite plains around Utopia Planitia.

* Acme Klein Bottles are designed using advanced numerical=20
models done on a high speed Curta calculator.

* We employ skilled craftsfolk from around the Earth, including=20
the USA and the People's Republic of Berkeley. We also employ=20
unskilled workers, but they mainly spend their time surfing the web.

* Tired of point set topology and semi-metric space? Imagine=20
the look on your instructor's face when you pop out an Acme Klein=20

* Acme's glassblowers select from the finest borosilicate glass=20
-- including Pyrex, Kimax, Simax, Bomex -- so you can be sure to=20
receive exactly what they choose. With its Poisson ratio of 0.2, you=20
won't be tempted to crush your bottle to save space. Just as nice --=20
the glass has a bulk density of 2.23 gm/cm3. (Of course, a Klein=20
Bottle's density is undefined since it has zero volume.)

* At any time -- day or night -- you can easily check on the=20
Euler Characteristic of your Acme Klein Bottle. Just add the number=20
of vertices to the number of faces, then subtract the number of=20
edges. So simple, even a grad student can do it!

* Low Coefficient of Expansion -- our special blend of=20
borosilicate glass expands just 0.000326% per degree C, so your Acme=20
Klein Bottle will shrink only a few microns if you trek from Nogales=20
to Nome

* No reason to worry about the incorrect number of=20
perforations. Acme's Department of Holes and Handles checks each=20
Klein Bottle to make sure it contains exactly one hole.

* Your manifold is shipped to you in a box made from genuine=20
organic materials, specially padded to reduce shock and vibration.=20
Ecologically friendly packaging can be recycled.

* Acme donates a portion of its profits to a college fund for=20
the owner's children.

Seeking a glass Klein Bottle? Click here to see the wide selection of=20
Klein Bottles in our finite but unbounded warehouse.

ACME KLEIN BOTTLE is a division of Nocturnal Aviation. This page and=20
others are Copyright =A91999 by ACME Klein Bottle
6270 Colby Street, Oakland, California USA 94618 fax +1 510 654 4265=20
email to

ACME - Where yesterday's future is here today!