Our lives have been greatly affected by mathematical discoveries throughout all of history. Even such things as basic as the Arabic numeral system (0,1,2,3…9) or more recent discoveries and innovations such as internet fractal loops (see figure 1.1). These have impacted society in a multitude of ways, respectively; the number system is used constantly in our everyday lives whereas hardly anyone could tell what a fractal is. Another such discovery is the MÖbius strip discovered by August Ferdinand MÖbius in 1858.
August Ferdinand MÖbius was born on November 17th, 1970, in Schulpforta, . His father Johann MÖbius was a dancer who died when MÖbius was three years old (O’Conner and Robertson). His mother was a descendant of Martin Luther, the man who single handedly brought about the creation of the protestant sect of religion in christianity. MÖbius was home schooled by his mother until the age of thirteen (O’Conner and Robertson). In 1803 he attended the local college in Schulpforta(O’Conner and Robertson). He graduated in 1809 where he than began taking a course at the University of Leipzig(O’Conner and Robertson). His relatives pressured him to study law, he obliged. He soon learned studying law wasn’t for him so he than took up the study of mathematics, astronomy, and physics (www.mps.k12.nf.ca). In 1813 MÖbius went to Gottingen where he studied astronomy under Gauss, the director of the local observatory (www.mps.k12.nf.ca). Gauss was venerated as one of the greatest mathematicians of his time (Robertson and O’conner). Then in 1815 he went on to write his doctoral thesis on the “occultation of fixed stars” (Robertson and O’conner). While writing his thesis they attempted to draft him into the Prussian army he stated…
This is the most horrible idea I have heard of, and anyone who shall venture, dare, hazard, make bold and have the audacity to propose it will not be safe from my dagger.-August MÖbiusThe following year he was given the chairmanship position at Leipzig as head of astronomy and higher mechanics (Robertson and O’conner). In 1816 he was offered a post as an astronomer in Greifswald and than a post as a mathematician in Dorpat in 1819, he refused both positions (Robertson and O’conner). MÖbius was a pioneer of Topology (scidiv.bcc.ctc.edu). In 1820 he took a wife and had two sons and one daughter (Robertson and O’conner).
In 1831 he wrote a paper introducing the MÖbius function entitled Uber eine besondere Art von Umkehrung der Reihen (www.mps.k12.nf.ca). In 1844 he was offered a full time job at the University of Jena as an astronomy professor (Robertson and O’conner). Although the majority of MÖbius’ fame was generated from mathematics but he also wrote many significant works on astronomy (Robertson and O’conner). Most of his works in mathematics were published in Crelle’s journal, the first journal devoted entirely to mathematis astronomy (Robertson and O’conner). This gave him a means to publish works on a configuration which is now known as the MÖbius net which plays a crucial role in projective geometry astronomy (Robertson and O’conner). Although MÖbius discovered the MÖbius strip in 1958, it remained undiscovered until his death on September 26, 1868 in Leipzeig, astronomy (Robertson and O’conner).The MÖbius strip is a two dimensional surface with only one edge and side (mps.k12.nf.ca).
It was co-discovered by Johann Benedict Listing and August Ferdinand MÖbius, independently. Meaning, although it was discovered at approximately the same time, they did not collaborate on their research (mps.k12.nf.ca). There are two types of strips one is created by a half twist to the left and the other by a half twist to the right, which gives these two objects chirality or the identical characteristics (wikipedia.org). When the MÖbius strip is cut down the middle you get one long strip with two half twists. When that is further cut down the middle you get two strips wound around each other. If you cut along the edge you get two strips, one is a thinner MÖbius strip, the other is a long strip with two half twists which is not considered a MÖbius strip. When a MÖbius strip has three twists, when it is divided lengthwise it becomes a strip tied in a trefoil knot.
The MÖbius strip has many applications outside the world of mathematics. The MÖbius strip is used in the industrial business when it is applied to conveyer belts, thus extending their use by distributing equal amounts of wear and tear on all surfaces (scidiv.bcc.ctc.edu). Also these belts may be found in international airports for lazy passengers who will not walk 100 yards to the terminal or disabled passengers. Also, a MÖbius strip can be applied to what is known as a continuous loop recording tape, which has in turn doubled the amount of play time on tapes (scidiv.bcc.ctc.edu). Freestyle skiers have named a difficult acrobatic, death and gravity defying stunt known as the “MÖbius flip” ((see figure 1.0) (scidiv.bcc.ctc.edu)). The MÖbius strip is also observed as the universal sign for recycling (see figure 1.2) (mps.k12.nf.ca)). It has been said that it is the inspiration of the infinity symbol.
Although this is often refuted because the infinity symbol has been around much longer than the MÖbius strip has been officially discovered (wikipedia.org). The MÖbius strip has also served as inspiration for both abstract and non-abstract artwork, a famous work is “MÖbius Strip II” or “Red Ants” which were created by M.C. Escher. ((See figure 1.4) (wikipedia.org))
As clearly demonstrated, the MÖbius strip has affected the lives of millions in a way no other mathematical discovery can. Such as the conveyer belt and the continuous loop tapes. Although mostly known for his mathematical discoveries, an enriched education enabled August Ferdinand MÖbius to excel in astronomy as well. The strip itself is considered a very curious object and his greatest achievement; although it has the deceptive appearance of double sidedness it has one side and one edge.
How to make the MÖbius strip:
1.Gather a rectangular piece of paper
2.Apply a 180 degree twist to the paper
3. Join the opposing edges together
