81. Play With A Moebius Strip! Play with a moebius strip! A few playing instructions Below is a moebius strip(aa one sided surface in 3space) that exists in virtual reality (vrml). http://www.angelfire.com/hi/funline/moebius.html

Play with a Moebius Strip! A few playing instructions... Below is a Moebius Strip (a a one sided surface in 3-space) that exists in virtual reality (vrml). Click at any point in the vrml window on your left mouse button to change your viewpoint. Click on the right mousebutton for a menu that allows many options such as changing the colors and spining the strip around. I particularly recommend the "navigation" submenu that allows switching between spinning motion, walking motion, fixed point motion, and sliding motion. I'll let you figure out the rest on your own... Don't try to cross an edge, because it won't get ya anywhere. Play with a Moebius Strip! / mariojm@hotmail.com / © Mario Johannes Meissl / revised April 1998

82. Vitanuova.loyalty.org: July 3, 2002 I've been having a debate with a friend about how to calculate the area of a moebiusstrip, where the moebius strip is constructed by taking a 1 by 10 area http://vitanuova.loyalty.org/2002-07-03.html

Wednesday, July 3, 2002 Jonathan Walther I've been having a debate with a friend about how to calculate the area of a moebius strip, where the moebius strip is constructed by taking a 1" by 10" area, twisting it, and joining the ends. I have been maintaining that the area remains the same; that is, 10 square inches. My friend insists it is 20 square inches. After discussion with my friend it became apparent that our different calculations came from our having different concepts of "area". He used a strip of paper to "illustrate" the moebius strip, and I feel this gave him erroneous intuition in this case. My observation was that if you did make the strip from paper, you would need 20 sq. in. of paint in order to paint the whole thing. If you used 10 sq. in. of paint, you would have 10 sq. in. of surface unpainted. (Normally you deal with areas in a plane, and the definition is easier. Is there something handy from multivariate calculus here?) Microsoft meeting Five people came from Microsoft to meet with us on Tuesday about Palladium. It was very interesting. "Sealed storage" is a very technically clever idea. Some of the subtleties hit me only after the meeting. Basically, you have a hardware co-processor within a machine which contains some unique secret symmetric key (not known to anybody other than the co-processor). Call this s. Also assume that the co-processor is also to take a hash h of whatever kernel k is running on the ordinary CPU. (In Palladium this is actually something called a "nub" in their marketing materials a "Trusted Operating Root" or "TOR" but we can pretend it's the OS kernel instead.)

83. Moebius Card card only has one side, officially. Look up moebius strip in theencyclopedia and you'll find out. The real trick to this project http://www.ee0r.com/proj/moebiuscard.html

Moebius Card A single sided business card August 2001 As I mention in the text for another project most business cards are boring. I'm always on the lookout for ways to make my business card, which is basically my representation in information space, stand out from those of the crowd. Most people have business cards that are single sided, but the card actually has two sides, it's just that only one of them is printed upon. These business cards only have one side. If you put your finger on them and trace it around, you'll wind up right back where you started. Even though I had to take two pictures to show the whole card, and the card is flattened out so it will fit in my wallet, the card only has one side, officially. Look up "Moebius Strip" in the encyclopedia and you'll find out. The real trick to this project wasn't figuring out how to print onto paper in a way that I could make a moebius strip out of the results, but figuring out how to print onto paper so that the resulting moebius strip would be the same size as a standard business card once it was flattened. I'm no math genius, so the geometry was a hit or miss proposition. I have a stack of five prototypes that get incrementally closer to the final product. These are kind of a pain to make, so I really haven't gotten around to using them as actual business cards. I need to update the design for my new email address and URL, though. I also should figure out something keener for the third panel of each view than the boring rainbow gradients I have there now.

84. Moebius Strip II moebius strip II, Sciart Home Page. moebius strip II $47.00 Poster Size21 x25 Frame Color Gold Code LES002 Order Checkout. UNIQUE ART. http://www.shop.sciart.com/les-002.html

Moebius Strip II Sciart Home Page Artist: M.C. Escher All posters come pre-framed in a color coordindated metal frame that compliments the art. Moebius Strip II Poster Size: 21"x25" Frame Color: Gold Code: LES-002 [Order] [Checkout] UNIQUE ART Please contact us with any questions at: webmaster@qoro.com

85. Knot Theory Online - The Web Site For Learning More About Mathematical Knot Theo 1) Cut that out! Fun activity with a moebius strip that becomesone of our knot friends. Let the moebius strip do it for you! http://www.freelearning.com/knots/fun.htm

Knot Funny Have a little bit of "knotty" fun along your journey to becoming a better mathematician. Links on this site: [HOME] [HISTORY] [INTRO] [ADVANCED] ... KT HOME Main Page KT HISTORY History of Knot Theory INTRO TO KNOTS What are knots? ADVANCED KT Knot Theory in the Real World KT ACTIVITIES Online activities with knots for you to try KNOT FUNNY Interesting facts, knot-knot jokes, and knotty pictures... "Knotty" Fun for All This page is packed with fun and interesting diversions for you to enjoy as you learn more about the world of Knot Theory: 1) "Cut that out!" - Fun activity with a Moebius strip that becomes one of our knot friends. 2) The Dancing Knot - Test your knot-making skill with this activity. 3) Tangled Hands - Can you make a knot without letting go of the ends of the string? 4) Human Knots - A fun group activity to try with your friends. 5) Knot-knot Joke - A little clean knot humor. "Three strings walk into a bar..." 6) "Links" to Other Great Knot Sites

86. Construcao-Moebius As illustration of what has been said, links to animations, which correspond to cutting(and separating) a moebius strip longitudinally, respectivaly along the http://www.atractor.pt/mat/Moebius/Construcao-Moebius-e.html

mathematica and translated to Java using applets from Live Graphics3D . If you have never used these applets , start by looking at the corresponding help . Keep in mind in particular that: a double click of the mouse interrupts or restarts the animation; on the first line is the number of twists before glueing; on the fourth line, the sizes of the files are links to the final figures obtained, with the border marked; on the fifth line, the small figures are links to animations which suggest the longitudinal cut of each strip along the central circle; on the seventh line, the small figures are links to animations which suggest the longitudinal cut of each strip starting from a point on the strip which is at a distance of 1/3 of the width of the strip from the border; on the eighth line the question of the non-orientability of some surfaces is raised. n: Animations: Figures: Animations (central cut) Animations (non-centered cut) Orientability Paint the surfaces obtained, to conceal the glueing area. Take two of the paper models and try to find what there is in common between them and what is different. Do that for each couple. The ideal would be to identify a

87. | Strip Poker | Free Strip Poker | Comic Strips | Strip Clubs | Strip Blackjack moebius strip Find out how to make a moebius strip or view images of models createdby Mathcad. obtain a moebius strip, start with a strip of paper. http://www.e-loans.com/chnl0.asp?keywords=Mobius Strip

88. Tricks Of Topology Now a moebius strip a loop with a twist. If you were to cut it in half as you justdid the loop, what would you expect? Why? Cut your moebius strip in half. http://www.eecs.berkeley.edu/Programs/doublex/amazingpaper.html

The Amazing One-Sided Piece of Paper One-Sided Web Sites Topology Worksheets The Amazing One-Sided Piece of Paper What is math in college? A generalization of the math we already know each type of number has different rules associated with it – adding fractions is different from adding integers What about telling time – how do we add numbers on a clock? We’d also like to do this with geometry. So how do we generalize geometry? The geometry you already know: called EUCLIDEAN R = the line = rays, line segments R = the plane = circles, squares, triangles, R = 3 dimensional Euclidean space cubes, spheres, cylinders, R : What might a four-dimensional square look like? What space is the floor of this room? So, we would like to do math (add vectors, do calculus, ) on any space, not just Euclidean. Generalized geometry is called TOPOLOGY. The sphere (earth) looks like R locally (in small regions, really close up) – since we know how geometry works in R , this is good. A mathematical object that looks like R n locally is called a MANIFOLD.

89. Shortcut To Resources Creation of a moebius strip (267264 bytes); A twisting moebius strip (155648 bytes)An animated gif file (295853 bytes) is also available Steven Tan from the http://www.cut-the-knot.org/shortcut.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Resources The only way to create a movie I know of is with the help of the Mathcad software package. Thus a few movies (avi files) I created owe their existence to this superb software tool and an excellent organization and maintenance of the MathSoft Web site where one can find dozens of good examples. Every single movie below is described by a set of equations of varying degree of difficulty. Naturally, all have to do with a little of Trigonometry, equations of curves and 2D and 3D transformations. All of them appear in one context or another elsewhere on these pages. Creation of a Moebius strip (267264 bytes) A twisting Moebius strip (155648 bytes) An animated gif file (295853 bytes) is also available Steven Tan from the Netherlands sent me a smallish twisting Moebius strip. It's also an animated gif that takes all of 8084 bytes. Creation of a Moebius strip, front view (303104 bytes) Formation of a 3-knot (437248 bytes) Formation of a knot (437760 bytes) Transforming a cube into a sphere (258560 bytes) Creation of a torus (389120 bytes) Creation of the Klein's bottle (389140 bytes) Play with it in slow motion Alexander Bogomolny G o o g l e Web Search Latest on CTK Exchange embedding applets Posted by Stuart Carduner 1 messages 09:05 AM, Feb-19-03

90. Graphics Archive - Flat Moebius Strip By Henry Rowley (Science U) Flat moebius strip by Henry Rowley This moebius strip is isometric to a flat rectangle,which differs from the standard parametrization. Flat moebius strip. http://www.scienceu.com/library/graphics/pix/Special_Topics/Differential_Geometr

Browse By: Graphics Archive Up Comments Special Topics ... Differential Geometry Flat Moebius Strip by Henry Rowley This moebius strip is isometric to a flat rectangle, which differs from the standard parametrization. The steps involved in its creation are found in Rowley's Summer Institute 1991 report. How to make it: Mathematica was used to obtain the parametrization, and MinneView (the precursor to Geomview) was used to view it. Image created: summer, 1991 The Geometry Center For permission to use this image, contact permission@geom.umn.edu External viewing: small (100x100 2k gif), medium (500x500 20k gif), or original size (400x400 15k tiff). The Geometry Center Home Page Comments to: webmaster@geom.umn.edu Created: Thu Jun 25 15:09:38 CDT 1998 - Last modified: Thu Jun 25 15:09:38 CDT 1998 Info Center Geometry Center Library Observatory ... Science Me Page last updated Fri Oct 2 15:49:58 CDT 1998 Comments to webmaster@ScienceU.com

91. Möbius (Moebius) Strip Möbius (moebius) strip. Written by Paul Bourke May 1996. The Möbius stip isthe simplest geometric shape which has only one surface and only one edge. http://astronomy.swin.edu.au/~pbourke/surfaces/mobius/

Written by Paul Bourke May 1996 where s ranges from to 2*pi and t ranges typically from -0.4 to 0.4 An example of such a strip is shown below. Featured in "mama 27", November 2000, pp 91, Figure 17. The band for different values of t are illustrated below. Increasing the range of t even further yields interesting folded and increasingly convoluted forms.

92. Möbius Strip OK, so making a Möbius strip is easy, why bother mentioning it? http://web.meson.org/topology/mobius.html

Let's start with something simple. Just about every kid learns about these early on. You take a strip of paper and join the ends in a loop after giving one end a half-twist so it joins up with the other one upside-down. If you've never tried this before, you should immediately (a) feel ashamed, and (b) try it out. The big deal about this is that it has only one side and one edge. The cool trick is that if you cut it in half lengthwise, it doesn't fall into two pieces. Instead, it makes one loop with two Seamless Topology A page on the web mentioned knitting one from the edge . Obviously it's simple enough to knit one: you can knit a strip and graft the edges together. But knitting it from the edge is another matter: You wind up with a strip with no seam! It also rather freaked me out when I realized it was working. I didn't actually understand the description used in the web page, so I did my best to interpret it and basically worked it out myself. The result is pretty cool. Here's what I did: start with a nice big circular needle (29-inch or so). I used one size 9, but it shouldn't matter much. Cast on a mess of stitches, at least enough to cover half the needle. Better to make it close to the whole thing, but make sure to cast on loosely (the success of the whole thing depends on a lot of give everywhere). Also, don't cast on too many stitches. You need them

93. :MöBIUS moebius / NVM. Presentation. Möbius är numera en sektionsförening inom UTN, UppsalaTeknolog och Naturvetarkår. Vår sektionsbokstavskombination är NVM. http://www.student.uu.se/studorg/mobius/

Om Moebius Historik Lokalen Möbius Staff ... Länkar Möbius / NVM Presentation Moebius är numera en sektionsförening inom UTN , Uppsala Teknolog- och Naturvetarkår. Vår sektionsbokstavskombination är NVM Studierådet MN1 kommer att bli en del av Moebius. Moebius har sedan länge varit en intresse- och festförening för matematik- och naturvetarstudenter vid Uppsala Universitet i allmänhet och studenter på NVP ingång 1 i synnerhet. Föreningen huserar för tillfället i källaren till hus 2, Polacksbacken i Uppsala ( karta Nyheter På grund av ombyggnation i hus 2 under våren så kommer Möbiuslokalen att vara tillfälligt flyttad till källaren i hus 1. Då lokalen inte kommer vara lika stor kan vi inte ha samma volym på försäljningen som tidigare, men då färre studenter kommer vara i området så går det säkert ändå. Poincaré, Jules Henri (1854-1912) Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures. In G. Simmons

94. Mobius Strip The Möbius strip. 1. Start with a long rectangle (ABCD) made of paper. But, as aresult of the half twist, the Möbius strip has only one side and one edge! http://scidiv.bcc.ctc.edu/Math/Mobius.html

1. Start with a long rectangle (ABCD) made of paper. 2. Give the rectangle a half twist. 3. Join the ends so that A is matched with D and B is matched with C. This curious surface is called a Math Homepage BCC Homepage

95. Www.math.niu.edu/~rusin/known-math/98/moebius_str From lrudolph@panix.com (Lee Rudolph) Newsgroups sci.math Subject Re Moebiusstrip Date 28 Jun 1998 103117 0400 Allen Adler adler@hera.wku.edu writes http://www.math.niu.edu/~rusin/known-math/98/moebius_str

From: lrudolph@panix.com (Lee Rudolph) Newsgroups: sci.math Subject: Re: Moebius strip Date: 28 Jun 1998 10:31:17 -0400 Allen Adler

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