1. Moebius & Plank Rastakraut Pasta Machine
2. Moebius & Plank Rastakraut Pasta Maker
3. Moebius & Plank Rastakraut Pasta Sauce
4. Moebius & Plank Rastakraut Pasta Salad

Moebius syndrome is a rare neurological condition that primarily affects the muscles that control facial expression and eye movement. The signs and symptoms of this condition are present from birth. Weakness or paralysis of the facial muscles is one of the most common features of Moebius syndrome.

• Moebius Models is a manufacturer of sci-fi and and horror model kits. Their model subjects include superheros (Batman, Wonder Woman, Superman), science fiction (Battlestar Galactica, Lost in Space, Voyage to the Bottom of the Sea), and vintage horror (Dracula, Grim Reaper, Frankenstein, etc), and more.
• Check out Rastakraut Pasta by Moebius & Plank on Amazon Music. Stream ad-free or purchase CD's and MP3s now on Amazon.co.uk.
• The real Moebius is a supercomputer that hypnotized its creators; ie. The people of Labyrinth. He tries to kill the Cures by self-destructing himself, but the Cures manage to escape at the last possible second.

Less...

The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving one of the two ends thus produced a half twist, and then reattaching the two ends (right figure; Gray 1997, pp. 322-323). The strip bearing his name was invented by Möbius in 1858, although it was independently discovered by Listing, who published it, while Möbius did not (Derbyshire 2004, p. 381). Like the cylinder, it is not a true surface, but rather a surface with boundary (Henle 1994, p. 110).

The Möbius strip has Euler characteristic (Dodson and Parker 1997, p. 125).

According to Madachy (1979), the B. F. Goodrich Company patented a conveyor belt in the form of a Möbius strip which lasts twice as long as conventional belts. M. C. Escher was fond of portraying Möbius strips, and they appear in his woodcuts 'Möbius Strip I' and 'Möbius Strip II (Red Ants)' (Bool et al. 1982, p. 324; Forty 2003, Plate 70).

A Möbius strip of half-width with midcircle of radius and at height can be represented parametrically by

(2)

for and . In this parametrization, the Möbius strip is therefore a cubic surface with equation

The illustration above shows interlocked turning gears along the length of a Möbius strip (M. Trott, pers. comm., 2001).

The coefficients of the first fundamental formfor this surface are

(5)

(7)

the second fundamental form coefficientsare

(9)

the area element is

and the Gaussian and meancurvatures are

(12)

The perimeter of the Möbius strip is given by integrating the complicated function

from 0 to , which can unfortunately not be done in closed form. Note that although the surface closes at , this corresponds to the bottom edge connecting with the top edge, as illustrated above, so an additional must be traversed to comprise the entire arc length of the bounding edge.

Cutting a Möbius strip, giving it extra twists, and reconnecting the ends produces unexpected figures called paradromic rings (Listing and Tait 1847, Ball and Coxeter 1987) which are summarized in the table below.

half-twists	cuts	divs.	result
1	1	2	1 band, length 2
1	1	3	1 band, length 2
1 Möbius strip, length 1
1	2	4	2 bands, length 2
1	2	5	2 bands, length 2
1 Möbius strip, length 1
1	3	6	3 bands, length 2
1	3	7	3 bands, length 2
1 Möbius strip, length 1
2	1	2	2 bands, length 1
2	2	3	3 bands, length 1
2	3	4	4 bands, length 1

A torus can be cut into a Möbius strip with an even number of half-twists, and a Klein bottle can be cut in half along its length to make two Möbius strips. In addition, two strips on top of each other, each with a half-twist, give a single strip with four twists when disentangled.

The topological result of attaching a Möbius strip to a disk along its boundary is a real projective plane, which cannot be embedded in . However, there are three surfaces that are representations of the projective plane in with self-intersections, namely the Boy surface, cross-cap, and Roman surface.

Any set of regions on the Möbius strip can be colored using only six colors,as illustrated in Tietze's graph above.

SEE ALSO:Boy Surface, Cross-Cap, Map Coloring, Möbius Strip Dissection, Nonorientable Surface, Paradromic Rings, Prismatic Ring, Roman Surface, Tietze's GraphREFERENCES:

Ball, W. W. R. and Coxeter, H. S. M. MathematicalRecreations and Essays, 13th ed. New York: Dover, pp. 127-128, 1987.

Bogomolny, A. 'Möbius Strip.' https://www.cut-the-knot.org/do_you_know/moebius.shtml.

Bondy, J. A. and Murty, U. S. R. GraphTheory with Applications. New York: North Holland, p. 243, 1976.

Bool, F. H.; Kist, J. R.; Locher, J. L.; and Wierda, F. M. C. Escher:His Life and Complete Graphic Work. New York: Abrams, 1982.

Derbyshire, J. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. New York: Penguin, 2004.

Dickau, R. 'Spinning Möbius Strip Movie.' https://mathforum.org/advanced/robertd/moebius.html

Dodson, C. T. J. and Parker, P. E. A User's Guide to Algebraic Topology. Dordrecht, Netherlands: Kluwer, pp. 121 and 284, 1997.

Escher, M. C. 'Moebius Strip I.' Wood engraving and woodcut in red,green, gold and black, printed from 4 blocks. 1961. https://www.mcescher.com/Gallery/recogn-bmp/LW437.jpg.

Escher, M. C. 'Moebius Strip II (Red Ants).' Woodcut in red, blackand grey-green, printed from 3 blocks. 1963. https://www.mcescher.com/Gallery/recogn-bmp/LW441.jpg.

Forty, S. M.C. Escher.Cobham, England: TAJ Books, 2003.

Gardner, M. 'Möbius Bands.' Ch. 9 in Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, pp. 123-136, 1978.

Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, p. 10, 1984.

Geometry Center. 'The Möbius Band.' https://www.geom.umn.edu/zoo/features/mobius/.

Gray, A. 'The Möbius Strip.' §14.3 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 325-326, 1997.

Henle, M. ACombinatorial Introduction to Topology. New York: Dover, p. 110, 1994.

Hunter, J. A. H. and Madachy, J. S. MathematicalDiversions. New York: Dover, pp. 41-45, 1975.

JavaView. 'Classic Surfaces from Differential Geometry: Moebius Strip.'https://www-sfb288.math.tu-berlin.de/vgp/javaview/demo/surface/common/PaSurface_MoebiusStrip.html.

Kraitchik, M. §8.4.3 in MathematicalRecreations. New York: W. W. Norton, pp. 212-213, 1942.

Listing and Tait. Vorstudien zur Topologie, Göttinger Studien, Pt. 10,1847.

Madachy, J. S. Madachy'sMathematical Recreations. New York: Dover, p. 7, 1979.

Möbius, A. F. Werke, Vol. 2. p. 519, 1858.

Nordstrand, T. 'Moebiusband.' https://jalape.no/math/moebtxt.

Pappas, T. 'The Moebius Strip & the Klein Bottle,' 'A Twist to the Moebius Strip,' 'The 'Double' Moebius Strip.' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 207, 1989.

Pickover, C. A. The Möbius Strip: Dr. August Mobius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology. New York: Thunder's Mouth Press, 2006.

Steinhaus, H. MathematicalSnapshots, 3rd ed. New York: Dover, pp. 269-274, 1999.

Trott, M. 'The Mathematica Guidebooks Additional Material: Rotating MöbiusBands.' https://www.mathematicaguidebooks.org/additions.shtml#G_2_01.

Underwood, M. 'Mobius Scarf, Klein Bottle, Klein Bottle 'Hat'.' https://www.woolworks.org/patterns/klein.txt.

Wagon, S. 'Rotating Circles to Produce a Torus or Möbius Strip.' §7.4 in Mathematica in Action. New York: W. H. Freeman, pp. 229-232, 1991.

Wang, P. 'Renderings.' https://www.ugcs.caltech.edu/~peterw/portfolio/renderings/

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 152-153 and 164, 1991.

CITE THIS AS:

Weisstein, Eric W. 'Möbius Strip.'From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MoebiusStrip.html

updated 11/18/2020

There is still a steady stream of kits coming out. 2020 has been a busy year. We don’t have a lot of news about what is coming in 2021, but that should change soon. Atlantis promises to announce 40 kits later this month. Stay tuned.

This page tracks of upcoming releases from Moebius, Round 2, Pegasus, Bandai, Atlantis, Revell, Dragon and others. All dates are tentative and may change. If you don’t see it listed here, I just don’t have any new info. Links provided to the CultTVman shop when available. Some products that have been released may be out of stock. Some products are not available to preorder (especially imports!). All kits are plastic unless otherwise indicated.

Bits of news… Snoopy’s Sopwith Camel has slipped to early 2021.. Batgirl has slipped to 2021 at Moebius. Round 2 has been releasing news monthly without any big announcements.. Nothing new on the Star Wars front from Bandai.

Available Now!

For these kits and more, please see the What’s New page in the CultTVman Hobbyshop

• Speed Racer Mach 5 SNAP KIT from Polar Lights reissue (this week)

• Earth Vs The Flying Saucers – Silver 3rd Edition from Atlantis reissue

• The Forgotten Prisoner of Castel Mare – Glow Square Box – Aurora reissue from Atlantis

Coming Late 2020

• NEW Halloween Michael Myers from Moebius Models restock

Coming Late 2020/early 2021

We don’t really know when the Dragon kits will arrive….

• Apollo 11 CSM 1:48 model kit from Dragon Models (this seems to be perpetually delayed)
• Saturn 1B 1:72 scale model kit from Dragon Models new kit
• Apollo Recovery – SH-3D “Helo 66” & Apollo Command Module – 1:72 from Dragon new kit

• Wacky Races – Penelope Pitstop’s Compact Pussycat from MPC
• Wacky Races – Dick Dastardly’s Mean Machine from MPC

Early 2021

• Snoopy & his Sopwith Camel reissue from Atlantis (delayed)
• NEW The Red Baron and his Fokker Triplane reissue from Atlantis (delayed)
• Classic Enterprise Display Model – 1:350 scale from Polar Lights prebuilt

• NEW: Land of the Giants Spindrift – 1:64 scale from Doll and Hobby GA
• NEWHaunted Manor: Play It Again Tom from Polar Lights –
• NEWArea 51 UFO reissue 1:48 from Polar Lights
• NEWUSS Excelsior reissue 1:1000 from AMT/Round 2
• NEWWacky Races – Creepy Coupe from MPC/Round 2

Moebius & Plank Rastakraut Pasta Machine

Way out in 2021

• Batgirl 1966 – 1:8 scale from Moebius Models (2021)
• 2001 Aries 1B – large kit from Moebius Models (early 2021)
• 2001 Astronaut – 1:8 scale from Moebius Models (likely 2021)
• NEW Vampirella from X-Plus in Japan

Moebius & Plank Rastakraut Pasta Maker

Release date pending

• NEW 40 kit announcements from Atlantis
• Even more 2001 kits from Moebius?
• More ’66 Batman kits from Moebius? (status unknown)
• New 1:1000 Trek ship from Round 2 (teased for the future)
• New Star Trek kits from Round 2 (status unknown)
• Shuttlecraft with interior from Round 2 (they want to do this in the future)
• more classic Revell, Aurora, Monogram, Renwall reissues from Atlantis (TBD)
• The Moon Suit from Monarch – this is hinted to be coming sometime
• The Fly figure kit from Monarch – this is hinted at coming in the future
• New kit reissue from Doll and Hobby GA
• More Snoopy reissues from Atlantis

Moebius & Plank Rastakraut Pasta Sauce

Likely not happening/Cancelled

Moebius & Plank Rastakraut Pasta Salad

• Lon Chaney Phantom of the Opera from Pegasus – details unknown
• The Fly 1:6 resin kit from Moebius (status unknown)
• The Fly 1:8 styrene kit from Moebius (status unknown)
• Kaiyodo Godzilla reissues.
• more Star Trek Movie kits from Moebius? (status unknown)
• The Space Pod and Chariot 1:35 scale from Moebius (appears to be indefinitely delayed)
• 2001 Discovery – 1:96 scale from Kaiyodo (status now unknown) No updates in over a year.