August Ferdinand Möbius. 17 November 1790 – 26 September 1868.
German mathematician, mechanic, and theoretical astronomer. The author of the most famous strip.
Life and Work:
1. Once, a student at a certain school started acting up. To calm down the rowdy, the teacher glued a strip of paper together and told the student to paint one side blue and the other red. The student, probably, has been doing it ever since. You can make this figure as well: take a strip of paper and glue its ends, having previously turned one of them over. The resulting strip is called the Möbius strip.
2. There are plenty of funny coincidences in life: the creator of the “dancing” strip, August Ferdinand Möbius, was born into the family of a dance teacher of the famous Schulpforta school in Saxony at the end of the 18th century.
3. Being descended on his mother’s side from religious reformer Martin Luther, Mobius showed an early interest in mathematics. He studied at the same Schulpforta school, on the territory of which he was born, and then entered the University of Leipzig.
4. Möbius did not study law, as his family wanted, but focused entirely on mathematics and astronomy. Biographers believe that the choice was strongly influenced by his teachers — in Leipzig, Möbius was taught by famous astronomer and mathematician K. B. Mollweide, later in Göttingen, he attended astronomy lectures by C. F. Gauss, and, in Halle, attended a course of lectures by the mathematician I. F. Pfaff, Gauss’ teacher.
5. It was astronomy where August Möbius achieved serious career success: he became a professor at the University of Leipzig and director of an observatory near Leipzig.
6. However, an asteroid was named after Möbius much later, due to his success as a mathematician. Möbius outlined a number of original mathematical ideas in his main work Barycentric Calculus. The remarkable mathematician was the first to introduce a coordinate system and analytical research methods into projective geometry; he developed a new classification of curves and surfaces. Mathematicians also know about the Möbius function and the Möbius transformation, and literally everyone knows the fantastic Möbius strip.
7. Möbius’ contribution to mechanics is also considered significant. In 1837, he published a two-volume Textbook on Statics, one of the most important monographs of the first half of the 19th century on this scientific discipline. Among other important things, in this work, Möbius established a number of theorems of fundamental importance in the truss theory.
8. In scientific terms, the Möbius strip is the simplest non-orientable surface with an edge that is one-sided in ordinary three-dimensional space. You can get from one point of this surface to another without crossing the edges.
9. Do you think this is difficult? But it is not. Möbius saw this shape on the maid’s neck: the famous mathematician watched the girl tie a kerchief.
10. At one of his lectures, Möbius told his students a parable about an eastern ruler who wanted to divide his state among five sons so that in case of trouble, each could come to the aid of the other. It turned out that it was impossible to divide the country into five parts so that each part had a border with the others. Möbius proved this as well.
11. Can the Möbuis strip be used in practice or is it just a mathematical oddity? Yes, it can: the conveyor belt, for example, is shaped like the Möbius strip. This way the entire surface wears out evenly, and the conveyor works longer. Möbius loop-like tapes are used in continuous film recording systems to double the recording time. The ink ribbon in many dot-matrix printers is also glued into the Mobius strip, which increases its resource.
12. It is sometimes claimed that the Möbius strip is the progenitor of the infinity symbol. This is not true: the infinity symbol first appeared in the works of the English mathematician John Wallis two hundred years before the Möbius strip was invented. The Möbius strip actually gave rise to another international sign — the recycling symbol.
13. Among the descendants of Möbius, there are scientists as well: his son August-Theodor is a famous Scandinavian philologist, his grandson Martin is a botanist, his grandson Paul Julius Möbius is one of the fathers of psychotherapy.