Klein Bottle Cartoons, Limericks, Rhymes, and Haiku
This is from Jean~Pierre Petit's le Topologicon -- a delightful book of adventures in topology. Alas, it's only in French. Jean Petit has worked extensively on Boy's Surface, and his series of books, Les aventures d'Anselme Lanturlu, tickle the mind and bring smiles to the eye. See http://www.jp-petit.com for more!
One sided verses:
I like to live in my little Klein bottle.
Imagine a cylinder, stretched up'l and out'l.
Push in the bottom to link with the throttle.
You need 4 dimensions to bring this about'l.
A home that's ingenious, clever, and crafty.
I find it delightful, but a little bit drafty.
(apologies to Katharine O'Brien)
A mathematician named Klein
Thought the Möbius Loop was divineSaid he, "If you glue
The edges of two
You get a weird bottle like mine."
This ray of from Edith Emeritz's brillaince:
I can tell by my friends' wondrous gazes
That my Klein Bottle truly amazes.Some find my new phial
It not only amuses, it crazes.
Deena Skolnick, Stanford University's Class of 2003 is happy with her Acme Klein Bottle:
One day as I was sitting, merely resting at my work
There approached a friend of mine who first stared, then went berserk.
But since I'd learned in infancy that attention follows gaze,
I watched his eyes and saw they fell on a bottle to amaze.
It was, of course, none other than my Baby Classic Klein
A bottle without volume and with one side by design.
Quoth he, "Might I inquire, if I could be so bold,
As to where you have acquired this no-boundary manifold?"
"Why sure," said I, "it's no surprise, just look where you would think:
Who else could be behind this glass but Acme Bottles, Inc.?"
"Aha!" he cried and jumped for joy and rushed out and was gone
Leaving me to ponder my 3D phenomenon.
My friends, I have no moral with which to end this tale
Except to let you take a look at where they are on sale!
Here's an unsolicited endorsement from Adrian Anderson who bought an Acme Klein Bottle in the summer of 2000:
Having received a bottle by Klein
An Acme product quite fineIf dimensionally able
I shall place on a table
And admire for a mighty long time
Andrea Blumberg tells us that::
A bottle, created by Klein,
Caused a fuss on both banks of the Rhine.This miraculous flask
Spurred the people to ask,
"Can you do the same thing with a stein?"
Michele Denber writes::
I'm very happy to say
My Klein bottle got here today.It's really quite fine,
This bottle by Klein
In an odd topological way.
Thinking in 4-D is hip,
But it gives my poor braincells a trip.So I think that I ought'l
Leave Klein to his bottle;
I'll just stick with Moebius' strip.
To add to dimensions one more,
You just square what you had before.So if I've got it straight
That the strip's figure-eight,
Is Klein's figure then sixty-four?
Alex Rennet (of McMaster Univ) has a poetic father:
There once was a physicist who made bottles topological,
whose surfaces defied all the senses logical;
One day in pursuit of dimensions unattainable,
using all the strength of which he was capable,
he blew so hard, one turned insideoutical.
Chris Innanen (aka Nonsanity) writes:
"This fleaker's no leaker," Roy fessed
"But all thickened solutions congest.
But decanting is quick
With no 'insides' to stick
So an Erlenmeyer Klein bottle's best!"
This one by Peter Beuret:
There once was a bottle called Klein
That had such a clever design
It would turn inside out,
Which created some doubt
When it came to decanting the wine.
Bill Kilner's contribution to nonorientable poetry::
When a Klein Bottle's blown out of glass
(Like a flat drawing of Mobus class)
Since the object's 4-DThen the cross-overs pierce where they pass.
If you crush it to 3
A Haiku by Jacob and Shari Bandes:
In 4 dimensions
there is no intersection
but in 3 there is.
Ode on a Klein Bottle
by Edith Emeritz, With sincere apologies to Keats
Thou perfect unspoiled borosilicate manifold,
Thou alien sojourner from dimension four,
Crystal visitor, who canst thou behold
A transparent image more puzzling than before:
What Mobius loops haunt about thy fringe
Of self-intersection, or of neck,
Twisted in nonorientability?
What curves or bends are these? What aura check?
What mad pursuit? What effort to unhinge?
What zero volume vial? What wild ecstasy?
Arrival of My Klein Bottleby RAD Donato
I thought that I might haversine,
but then I figured, nope,
since she was neither in nor out,
immersed in visions of
R four projections of
spirals of Cote
I thought then I might sine myself,
when Ida surfaced later,
she wanted one too, in just four hues,
and one like an overfed
eyes of pink
We then went out to celebrate
the film "Paradromic" was playing,
reviewers had written that "so many twists,
left the viewers in knots
and ringing in ears
and chair surfaces
The theater first showed us Mobius shorts,
but this held no interest for I,
the movies were all simple one-sided plots,
full of holes
she made me watch twice
'cause she likes some n 2-tori.
I somehow was able to watch the hole movie,
though many times made sounds quite glottal,
needless to say I hurried right home
so I could go hit the Klein Bottle.
The following by Cliff Stoll:
Acme's Klein Bottl
Looks a lotl
Like a big ol'
The space it takes'll
Needs a tunnel
With a hole
Like a funnel.
Make a circl
In it's space'l
Its sides be singl
Like its handl.
This twisty thing'l
An Acme Manifold'l
Keep you out of troubl
This boundless bottl
Spheres with crosscaps
...Cliff Stoll 10/2000 (with apologies to David McCord)
Mathematicians try hard to floor us
With a non-orientable torusThe bottle of Klein
They say is divine
But it is so exceedingly porus.
from the Space Child's Mother Goose by Winsor & Parry (a whimsical 1950's book, recently republished by Purple House Press) :
Three jolly sailors from Blaydon-on-Tyne
They went to sea in a bottle by Klein.
Since the sea was entirely inside the hull
The scenery seen was exceedingly dull.
Oliver Humpage of Bristol, England wrote these two haiku after receiving an Acme Klein Bottle:
bottle of one side
holds nothing and ev'rything;
no one understands
when filled with water,
this four-dimensioned vessel
would leak in odd ways
"THE BOTTLE WITH NO INSIDE This model of a Klein bottle, which has "no inside" belongs to topologist Albert W. Tucker of Princeton University. Nobody will ever see an actual Klein bottle because it exists only in the topologist's imagination. A true Klein bottle passes through itself without the existence of a hole, which is of course a physical impossibility."
I (Cliff Stoll) have written to Albert Tucker's sons, Alan and Tom. Both are also mathematicians (!). Alan, who now teaches statistics at SUNY/Stonybrook, remembers seeing this Klein Bottle in his father's office. Tom, who teaches math at Colgate University, now has this Klein Bottleat his home. One of the oldest glass Klein Bottles.
Jean-Pierre Petit has designed some wonderful new Klein Bottle derivatives, seen in his paper, TOPOLOGIE- Le retournement non trivial du tore. (C.R. Acad. Sc. Paris t. 287, 20 November 1978). Here are a few figures from this brilliant mind. Note that these are not Klein bottles - as far as I can tell, each is homeomorphic to a torus. Figure 4 is very much like the Acme double "Klein bottle" (which is really a torus, not a Kleinbot).
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Acme Klein Bottles - Exclusive Purveyors of the Non-Orientable
Cliff last updated this page on October 30, 2015