The mystery of the Mobius strip
The Mobius strip, also known as Mobius band, is a one sided surface with only one boundary component. It has the mathematical property of being impossible to orient. Also, it has a ruled surface. The Mobius strip was discovered in 1858 by two German mathematicians independently: August Ferdinand Mobius and Johann Benedict Listing.
A model of a this strip can be easily created by giving a half-twist to a strip of paper and then reconnecting the ends of the strip together to form a single strip. Two types of Mobius strips are found in Euclidean space clockwise and counter-clockwise depending of the direction of the half-twist.
No matter the direction of the half-twist, Mobius strips have several rather curious properties. If you take a pen and draw a line down the middle of a Mobius strip made of paper until you reach the starting point, you will end up with a line double the length of the original strip of paper on the whole surface of it. If you were to cut the strip along the line you have drawn, there won’t be two strips obtained, as one would expect, but a longer strip with two half-twists that is not considered to be a Mobius strip. This amazing thing happens due to the fact that the original strip has only one edge that is twice as long as the strip of paper originally used.
Another combination can result from cutting such a strip about a third of the way in from the edge. This creates a thinner sample of the strip and another strip with two half-twists. Other combinations can be obtained when using two or more half-twists. If you divide lengthwise a strip that has three half-twists instead of one you obtain a strip that is tied in a trefoil knot. Cutting Mobius strips and giving them extra half-twists are operations that generate a lot of unexpected figures that are called paradromic rings.
There are closely related objects to the Mobius strip. One of them is the Klein bottle that can be produced by gluing two Mobius strips together along their edges, something that cannot be done in ordinary three-dimensional Euclidian space without creating intersections. A Klein bottle has only one surface, even though it looks like it has inside and outside surfaces. The real projective plane is also a related object to Mobius strips, due to the fact that, if you cut a circular disk out of the real projective plane, what you are left with is a Mobius strip. These two related objects are obtained by gluing together Mobius strips on different sides.
Mobius strips have been an inspiration for a lot of sculptures and graphical art. An example of this is M. C. Escher’s representation of such a strip with ants crawling around its surface. Science fiction stories have been written using the Mobius strip as a recurrent feature like “The wall of darkness” by Arthur C. Clarke and “A subway named Mobius” by A. J. Deutsch. Also, there have been many devices designed on this pattern. Reaching recent days, movies have also a link with Mobius strips, such as some episodes from Stargate and also the Playstation 2 game Ace Combat 04: Shattered Skies has a fictional platoon named like that. To get a clear view of the popularity of Mobius strips, a lot of companies used this pattern to create their logos; the most important of them is the international symbol for recycling that is represented by a Mobius loop.
Moreover, theological meaning has been attributed to the Mobius strip. Due to the fact that there is no difference between the inside and the outside surfaces, it is considered to be an example of the creator which created everything that surrounds us from himself. The universe is also considered to be some kind of such a generalized strip.Even though theMobius stripis a mathematical pattern, it is surrounded by mystery. But everybody knows that mathematics is the universal language and that it stands as the basis for the universe. It has theological meaning attributed to it and it has been a source of inspiration for art and technology.
Article Source: http://www.simplysearch4it.com/article/51478.html
|
|
1840 2d Blue (LH/LL) STRIP of FIVE with wmk INVERTED $19,602.50 |
|
|
1840 2d Blue (DA/DF) Plate 1 Strip of SIX (vertical crease) with Red Crosses $11,291.04 |
|
|
HONG KONG 1862 12c Blue Specimen Strip – RARITY! $5,700.00 |
|
|
CAPTAIN AMERICA 1940′S HEATER SHIELD W/ BLUE STRIPS-LE $1,799.99 |
|
|
US #274 15¢ dark blue, Plate No. Imprint Strip of 3 $1,750.00 |
|
|
U.S. #24 var SCARCE Strip of 3 – 1c Blue, Type Va $1,750.00 |
|
|
1841 2d Blue (JA/JD) Ornament Strip of 4 $1,693.66 |
|
|
Blue Long Dress by Michal Negrin with Flower Print, Lace Strips & Long Sleeves $1,621.00 |
|
|
Blue Long Dress by Michal Negrin with Flower Print, Lace Strips and Long Sleeves $1,621.00 |
|
|
Blue Long Dress by Michal Negrin with Flower Print, Lace Strips and Long Sleeves $1,621.00 |
|
|
Blue Long Dress by Michal Negrin with Flower Print, Lace Strips and Long Sleeves $1,621.00 |
|
|
Blue Long Dress by Michal Negrin with Flower Print, Lace Strips and Long Sleeves $1,621.00 |
|
|
2100 ONE TOUCH ULTRA BLUE TEST STRIPS & 2900 ONE TOUCH DELICA LANCETS & TESTER $1,550.00 |
|
|
1841 2d Blue (KJ/KL) Plate 3 Inscriptional Strip $1,499.20 |
|
|
ADORABLE NEW ENGLISH KHAKI LINEN BLUE STRIP CLUB CHAIR,28”WIDE,SO CHIC! $1,285.00 |
|
|
Michal Negrin Blue Dress with Short Sleeves, Flower Print, Lace & Velvet Strips $1,231.00 |
|
|
Michal Negrin Blue Dress w Short Sleeves, Flower Print, Lace and Velvet Strips $1,231.00 |
|
|
Michal Negrin Blue Dress w Short Sleeves, Flower Print, Lace and Velvet Strips $1,231.00 |
|
|
Michal Negrin Blue Dress w Short Sleeves, Flower Print, Lace and Velvet Strips $1,231.00 |
|
|
Michal Negrin Blue Dress w Short Sleeves, Flower Print, Lace and Velvet Strips $1,231.00 |
|
|
SG4 1840 2d Blue Plate 2 (SA-SD) *Strip of Four* $1,215.36 |
|
|
Vintage Style Blue Long Dress by Michal Negrin w Lace Strips and Spaghetti Strap $1,128.00 |
|
|
Vintage Style Blue Long Dress by Michal Negrin w Lace Strips & Spaghetti Strap $1,128.00 |
|
|
Vintage Style Blue Long Dress by Michal Negrin w Lace Strips & Spaghetti Strap $1,128.00 |
|
|
Vintage Style Blue Long Dress by Michal Negrin w Lace Strips & Spaghetti Strap $1,128.00 |
|
|
Vintage Style Blue Long Dress by Michal Negrin w Lace Strips & Spaghetti Strap $1,128.00 |
|
|
24bxs One Touch Ultra Blue Diabetic Test Strips – 50ct (24bxs) $1,070.76 |
|
|
12bxs One Touch Ultra Blue Diabetic Test Strips – 100ct RETAIL (case of 12) $999.00 |
|
|
NEW ZEALAND 1931 HEALTH BLUE BOY STRIP OF 4 $980.00 |
|
|
1,200 OneTouch Ultra Blue DME Test Strips 01/2013 $960.00 |
|
|
1841 SG14 2d BLUE SCOTTISH CROSSES ON LARGE STRIP OF 4 @ CERT $901.72 |
|
|
330 Feet Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof $779.99 |
|
|
Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof -Custom Cut $779.99 |
|
|
SG 14f 2d blue (OE-OH), VFU strip of 4 $746.46 |
|
|
Michal Negrin Blue Wrap Vest w Lace Strips & Velvet Belt – All Sizes Available $779.00 |
|
|
John Boos Kindred QCL Work Table with Electric Outlet Strip $759.00 |
|
|
1476 Var, MNH – TRANSITIONAL STRIP – BLUE COLOR MISSING $750.00 |
|
|
1841 2d Blue plate 4 a VFU and full margined strip of 7 KE – KK Crisp 124 $705.69 |
|
|
GB, 1841, 2-Blue Pl.3, Superb 4-marg. strip with MC. $705.69 |
|
|
Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof -Custom Cut $701.99 |
|
|
SG14 2d BLUE STRIP OF 4 MALTESE CROSSES RPS CERT NA/ND $666.49 |
|
|
1841 2d blues x 20 in strips etc,inc 2 x strips of 4 $625.71 |
|
|
17″ Kr648 kyowa 17×7 42 5×100 5×114.3 Silver Blue Strip $520.00 |
|
|
Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof -Custom Cut $624.99 |
|
|
Waterproof 7 Color SMD3528 Flexible LED Strip Light 5Meters 600LED Xmas Decor $625.00 |
|
|
US #1895 Slate Blue 20¢ Flag color variety strip of 5, XF OG NH **, APS (1999) $595.00 |
|
|
BLUE 30′s Strip Stars Antique Quilt ~GREAT COLORS! $575.00 |
|
|
Vintage MARNI Blue Strips Drawstring Lounge Pants!I40/M $586.00 |
|
|
US #179 5¢ blue, Strip of 3, unused no gum scarce $580.00 |
|
|
Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof -Custom Cut $545.99 |
|
|
12bxs One Touch Ultra Blue Diabetic Test Strips – 50ct (case of 12) $535.38 |
|
|
6″ Marine Boat Waterproof Underwater 10 LED Light strip BLUE 6 inch scp 03041 $519.95 |
|
|
Aftermarket Fairing Blue For 98-99 9R ZX9R 1998 1999 ABS Strip K9827 $525.00 |
|
|
10 PCs 5m Blue SMD LED 5050 Waterproof 300 LEDs Strip B $524.88 |
|
|
4″ Marine Boat Waterproof Underwater 6 LED Light strip BLUE 4 inch scp 03031 $515.95 |
|
|
1841 SG14 2d BLUE PLATE 3 FINE & RARE STRIP OF 7 (MA/MG) $509.67 |
|
|
Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof -Custom Cut $506.99 |
|
|
Seneca Council New York blue on white strip b&w c20 $499.95 |
|
|
1977 Topps 3-Card Uncut Strip Cardenal Simmons Blue $500.00 |
|
|
1854 BRASIL T)STRIP OF 5 #20,MINT PAPER FOLD,30R BLUE,C $499.99 |
|
|
7 Color SMD3528 Flexible LED Strip Light 5Meters 600LED 120LED/M Xmas Home Decor $499.00 |
|
|
HOLLEY 650 CFM ULTRA DOUBLE PUMPER STREET /STRIP CARBURETOR CARB BLUE SAVE 5 LBS $498.95 |
|
|
10x 5M 300 LED Strip Light 5050 SMD DC12V Blue WPF $496.59 |
|
|
10x 5M 300 LED Strip Light 5050 SMD DC12V Blue WPF $496.59 |
|
|
Vintage Style Michal Negrin Sleeveless Tank Top w Lace Strips and Floral Print $492.00 |
|
|
Vintage Style Michal Negrin Sleeveless Tank Top w Lace Strips and Floral Print $492.00 |
|
|
Vintage Style Michal Negrin Sleeveless Tank Top w Lace Strips and Floral Print $492.00 |
|
|
Vintage Style Michal Negrin Sleeveless Tank Top w Lace Strips and Floral Print $492.00 |
|
|
1840 2d BLUE (HJ-HL) DEEP FULL VERY SCARCE STRIP OF 3 CAT £3300+ $470.44 |
|
|
10 PCs 5m 500cm Blue SMD 5050 Flexible 300 LED Strip B $484.88 |
|
|
GB,1841 2d Violet-Blue, Pl.4, ES17, VFU strip of 3. $468.89 |
|
|
COGH CAPE OF GOOD HOPE Triangle 4d Blue Strip of 4 Used $480.00 |
|
|
GB 1867 TO HONG KONG 2d BLUE + STRIP OF 5 x 6d! RARE $462.62 |
|
|
800 OneTouch Ultra Blue Test Strips 09/2013 *NEW SEALED* NIB $480.00 |
|
|
SMD3528 Flexible LED Strip Light 5Meters 600LED 120LED/M Xmas Home Decor 7 Color $480.00 |
|
|
Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof -Custom Cut $469.99 |
|
|
SG 14wi var. 2d Blue (FH-FJ), strip of 3 $451.64 |
|
|
For 00-01 YAMAHA R1 YZFR1 ABS Fairing Blue Strip Y1013 $473.80 |
|
|
Aftermarket Fairing For 00-01 R1 YZFR1 ABS 2000 2001 Blue Strip Y1013 $473.80 |
|
|
GB 1841 2d blue LOVELY horizontal strip of four v.f.use $456.00 |
|
|
FIRADO ITALY ROME MENS SUITS $1999 DARK NAVY STRIP 46R SUPER FINE 140s HAND MADE $399.99 |
|
|
10x 5M 300 LED Strip Light 5050 SMD DC12V Blue $462.39 |
|
|
10x 5M 300 LED Strip Light 5050 SMD DC12V Blue $462.39 |
|
|
Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof -Custom Cut $453.99 |
|
|
Sg 19 2d Deep Blue Plate 14 EH-EL. A very fine used strip of 5. $431.26 |
|
|
#9 STR/3 POS 1-3L1L TOP ROW STRIP – RARE – W/ BLUE DATE CANCEL CV $415++ BN9014 $450.00 |
|
|
Onetouch Ultra Blue Test Strips 700 lot ~ 7 NIB 100 per Box ~ Exp OCT 2013!!! $450.00 |
|
|
38″ French Ornate Strip Mirror 30 Old World Finishes $449.79 |
|
|
PKG50,30cm Red/Blue/Green Flash Strip Led Waterproof,FW $449.00 |
|
|
PKG50,30cm Red/Blue/Green Flash Strip Led Waterproof,FW $449.00 |
|
|
PKG50,30cm Red/Blue/Green Flash Strip Led Waterproof,FW $449.00 |
|
|
Striking, very visual red, white, and blue strip quilt. $445.00 |
|
|
Michal Negrin Multi-Color Wrap with Lace, Velvet Strips and Merrow Edge Finish $438.00 |
|
|
Michal Negrin Multi-Color Wrap with Lace, Velvet Strips and Merrow Edge Finish $438.00 |
|
|
Michal Negrin Multi-Color Wrap with Lace, Velvet Strips and Merrow Edge Finish $438.00 |
|
|
Michal Negrin Multi-Color Wrap with Lace, Velvet Strips and Merrow Edge Finish $438.00 |
|
|
Blue 120 Volt LED SMD3528 Strip Rope Light- Waterproof -Custom Cut $429.99 |
|
|
NATAZZI 160S SUIT $2598 CASHMERE 21588_5 NAVY STRIP 46R $424.58 |
|
|
NATAZZI 160S SUIT $2598 CASHMERE 21588_5 NAVY STRIP 46S $424.58 |
|
|
NATAZZI 160S SUIT $2598 CASHMERE 21588_5 NAVY STRIP 42S $424.58 |
|
|
Chef Works CSBA-BCS Chalk Stripe Bib Apron with Pockets, 34-1/4-Inch Length by 27-Inch Width, Black/White $12.60 The Chef Works Chalk Stripe Bib Apron is an understated and stylish cooking garment. With its dark color and white strip accents, this apron is appropriate for dinner parties, or while cooking on any night of the week. The durable poly/cotton blend stands up to harsh cooking conditions, but will not shrink in the wash…. |
|
|
Black Zebra Cupcake Liners Baking Cups Standard Size 50 Count $1.95 Make your cupcakes extra special with a printed baking cup. Also, these work great for party nuts, mints and candies!… |
|
|
Wilton Sugar Sheet The quick and easy way to add colorful details to cakes and dessertseven if youve never decorated before. Use an edible, flexible Sugar Sheet to cut or punch virtually any shape or border design. Theres no preparation, no mess. Just peel, punch or cut and place your decorations in minutes. Sugar Sheets have a light, sweet flavor that works with buttercream or fondant-covered treats. One 8-Inch by … |
|
|
Elephant $7.76 No Description Available.Genre: Popular MusicMedia Format: Compact DiskRating: Release Date: 1-JUL-2008… |
|
|
Icky Thump $7.24 No Description AvailableNo Track Information AvailableMedia Type: CDArtist: WHITE STRIPESTitle: ICKY THUMPStreet Release Date: 06/19/2007… |
|
|
Strip [Explicit] $1.29 … |
|
|
Varsity Blues $1.10 This MTV-produced drama only looks like an adaptation of H.G. Bissinger’s expert dissertation of the church of high school football, Friday Night Lights. The energetic, breezy movie has none of the seriousness of Bissinger’s book except on its basic level: in West Texas, high school football is life. Into this world comes Jonathan “Mox” Moxon (James Van Der Beek), a brainy, uncharacteristic jock … |
|
|
Velcro Reusable Self-Gripping Cable Ties, 0.5 Inches x 8 Inches Long, Black, 100 Ties per Pack (91140) $3.79 Ties, Reusable, Adustable, Pre-cut, 8, 100 Count, Black Velcro 91140 Reusable Self-Gripping Cable Ties 1/2 x 8 Long Black 100 Ties per Pack… |
|
|
Fulcrum 30010-301 LED Battery-Operated Stick-On Tap Light, 3 Pack $5.99 Sold as each. 3 pack. Ultra bright energy efficient LED stick-on lights. Provides reliable lighting solution for just about anywhere. Mounts with supplied adhesive tape. Tap on/off fixture. Uses (3) AAA batteries not included. Silver. Clamshell. Manufacturer number: 30010-301. Country of origin: China…. |
|
|
Velcro Cable Tie Roll, 3/4 x 5 yards $1.66 Cable Management is much easier with this Velcro tie roll. Double-sided Velcro allows you to cut custom-length Velcro rings to wrap unsightly cables together…. |
