August Ferdinand Mobius Essay, Research Paper
August Ferdinand M?bius was born on November 17, 1790 in Schulpforta, Germany. (Then called Saxony.) He was the only child of Johann Heinrich Mobius, a dancing teacher. She was related to the famous Martin Luther, the man responsible for writing the document known as the 96 Thesis. M?bius himself was home schooled until he was thirteen. Showing an avid interest in mathematics, he went to college in Schulpforta, Germany in 1803.
When M?bius graduated from college in 1809 he became a student at the university of Leipzig. Here he started to study law against the will of his family. However, halfway through his first year he realized that law did not fit his interests. He then switched to the study of mathematics, physics, and astronomy.
During his time in college, some well-known mathematicians and astronomers influenced M?bius. It is said that his greatest influence was that of Karl Mollweide, his astronomy teacher. Mollweide is known for the trigonometric relations he discovered in 1807.
M?bius then went to G?ttingen, Germany in 1813. Here he studied under Carl Friedrich Gauss. Gauss, like Mollweide, was also an astronomer. However, Gauss’ main interests were mathematical. From G?ttingen M?bius went to Halle and studied under Johann Pfaff, Gauss’ teacher. Pfaff taught him mainly mathematics. By the end of his studies, M?bius had established firm roots in both mathematics and astronomy.
In 1816, M?bius was appointed to the chair of astronomy at Leipzig. He hoped to soon become a full professor. However, his hopes were abolished when it became clear that M?bius’ ability to give an interesting lecture was not quite up to par. In fact, he had to advertise his lectures as being free just to get people to come to them. He was, however, offered other jobs as a proffessor in both mathematics and astronomy at other schools. He turned these jobs down due to his loyalty to Leipzig. In 1844, Mobius was offered professorship at the University of Jena. Seeing how they might lose Mobius, Leipzig granted him full professorship.
Mobius was also an observer at the observatory at leipzig. He was also involved in the reconstruction of the observatory. He was supervisor of
M?bius made many contributions to the world of mathematics. The M?bius strip, M?bius net, M?bius function, and Mobius inversion formula. He also wrote a paper entitled Uber eine besondere Art von Umkehrung der Reihen, which introduced the M?bius function. M?bius also focused on analytical geometry and was considered a pioneer in topology. He also wrote important papers contributing to theoretical astronomy. These papers included The Principles of Astronomy and The Elements of Celestrial Mechanics.
M?bius is best known for his work in the area of topology. Topology can be divided into three main areas: point set topology, algebraic topology, and differrential topology. The first studies in the area of topology are acctually credited to Euclid, but M?bius did some major pioneering action also. His most famous topological discovery is the mobius stip.
Have you ever wondered what that odd-looking shape on the bottom of recycleable products is? Probably not, why would you. But in case you have, it is a M?bius strip. The strip is a one sided band and apparently has no beginning or end. Thus it efficiently represents the recycling program.
What is so special about this strip? First, it is one of the few one sided surfaces known to man. One can take a marker, start coloring anywhere on the strip, and color every visible part without lifting the marker. Second, one can make such a fascinating object anytime, anywhere. Simply take a long strip of paper, turn it 180 degrees, and attach the ends. It is that simple.
The M?bius strip is just one of many important contributions made by M?bius to the math world. Without these contributions, we would miss out on important and fascinating information in both the areas of mathematics and astronomy. M?bius was truly one of history’s greatest mathematicians
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mobius.html
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