Our lives have been greatly affected by mathematical discoveries throughout history. Even such things as basic as the Arabic numeral system (0,1,2,3…9) or more recent inventions and innovations such as deep fractal loops (see figure 1.1). These involved society in many ways; the number system is constantly used in our daily life, since hardly anyone says what a fractal is. Another such discovery is the MÖbius strip discovered by Augustus Ferdinando MÖbius in 1858.
Augustus Ferdinand MÖbius was born on November 17, 1970 in Schulpforta, . His father Johann MÖbius was a dancer who died when MÖbius was three year olds ( (Conner and Robertson). His mother was a descendant of Martin Luther, the man who made one of the creation traditions. religion in the Protestant sect of Christianity. MÖbius schooled at home 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). 1809, where he began a course at the University of Leipzig (led by O’Conner and Robertson). His relatives forced him to study law. He who soon learned to study law was not so much for him as he 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, director of the local observatory (www.mps.k12.nf.ca). Gauss was revered as one of the greatest mathematicians of his time (Robertson and O’conner). Then in 1815 he submitted his doctoral thesis on “the occultation of the fixed stars” (written by Robertson and O’conner). When he wrote these things, he affirmed that he should try to join the Prussian army.
These are the most disgusting things I have heard, and whoever dares, dares, whoever dares, dares, whoever dares to propose, will not be safe from my dagger. Leipzig in the Chapter of astronomy and higher mechanics (Robertson and O’conner). In 1816 he was offered an astrologer’s post in Greifswald and a mathematical post in Dorpat in 1819, but he declined both positions (Robertson and O’conner). MÖbius author of Topology (scidiv.bcc.ctc.edu). He married in 1820 and had two sons and one daughter (Robertson and O’conner).
In 1831 he wrote a paper introducing MÖbii 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 a professor of astronomy (Robertson and O’conner). Although most of Möbius’s reputation was generated from mathematics, he also wrote many notable works on astronomy (Robertson and O’Conner). Most of his works in mathematics were published in Crelle’s Journal, the first journal devoted to mathematical astronomy (Robertson and O’conner). This gave him the means to publish works in the configuration now known as the MÖbius net which plays an important role in the astronomy of projective geometry (Robertson and O’conner). Although Möbius discovered the Mbius strip in 1958, it remained undiscovered until his death on September 26, 1868 in Leipzig, astronomy (Robertson and O’conner). A MÖbius strip is a two-dimensional surface with only one edge and side (mps.k12.nf.ca).
It was verified by John Benedictus Listing and Augustus Ferdinando Möbius, independently. Sensation, although discovered at about the same time, did not collaborate in their research (mps.k12.nf.ca). The two types of straps created one half twist to the left, the other half twist to the right, which gives these two objects the same chirality or characteristics (wikipedia.org). When the MÖbius strip is cut in half, you get one long strip with two twisted halves. And when it is further in the middle, they put two bundles round each other. If you cut through the edge, you get two bands, one is a thinner MÖbius, the other is a long strip with two half-twists that is not considered a MÖbius strip. Since the Möbius strip has three twists, when it is split lengthwise, the strip is tied with a trefoil knot.
The MÖbius strip has many applications outside the mathematical world. MÖbius tape is used in industrial applications with conveyor belts, thus extending its use evenly to the weight of the garment and over all tear surfaces (scidiv.bcc.ctc.edu). These belts can also be found at airports international airports that accommodate idle passengers not 100 yards from the terminal or walking disabled passengers. Also, a MÖbius strip can be applied to what is known as a continuous tape loop, which in turn doubles the amount of playtime on carpets (scidiv.bcc.ctc.edu). Professional skaters have named the difficult acrobatic, death and gravity-defying stunt the “MÖbius flip” (see figure 1.0) (scidiv.bcc.ctc.edu)). MÖbius is also known as the universal symbol for recycling (see Figure 1.2) (mps.k12.nf.ca)). It has been said that inspiration is a symbol of infinity.
However this is often refuted because the infinity symbol is around much longer than the MÖbius strip has been officially discovered (wikipedia.org). The MÖbius strip is also an inspiration for abstract and non-abstract art, the famous work “MÖbius Strip II” or “Red Ants” by M.C. Escher ((See 1.4) (wikipedia.org))
As has been clearly demonstrated, the Möbius strip affects millions of souls in a way that no other mathematical invention can. As it is carried, the belt and tapes loop are continuous. Although he is best known for his mathematical discoveries, the enriched education of Augustus Ferdinando Möbius also allowed him to excel in astronomy. The ribbon itself is considered a curious thing and the greatest thing; although it has the deceptive appearance of a double side, one side and one side.
How Möbius undressed;
1.Gather a rectangle of paper
2.Apply a 180 degree twist to the paper
3 join the opposite edges together
