The discovery of the mobius strip in 1858 by two German Mathematicians, August Ferdinand Möbius and Johann Benedict Listing gave rise to a new field of mathematics called topology, which is the study of the shape objects assume in space and how these shapes can interconvert into one another. Topology has not only generated useful applications, but it has allowed scientists to make some fundamental discoveries in physics such as new states of matter and properties of materials. In my previous video, I talked about the most known property of mobius strips, which is the punchline of a version of a classic joke. In the video below, I demonstrate more remarkable but lesserknown properties of mobius strips which arise when you cut them in different ways. The video also features an unexpected cameo by science cat! If you want to gain an intuitive understanding of how the above properties are possible, I encourage you to view the excellent video below by the folks from the YouTube channel Think Twice.
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A Mobius Strip is a unique topological object with fascinating properties. It was discovered independently in 1858 by two German Mathematicians, August Ferdinand Möbius and Johann Benedict Listing. Mobius strips are actively studied in several fields of science and have been used in many applications from continuousloop recording tapes and typewriter ribbons to computer print cartridges, electronic resistors, and conveyor belts. The Mobius strip has also been used in art including many science fiction stories. This is the first part of a twopart post about mobius strips. In the video below, I demonstrate their most known property which is part of the punchline of a version of a classic joke. Topology is a branch of mathematics that is concerned with the study of how shapes or objects are arranged in space and whether they can be converted into each other. Objects that can be converted into each other are said to be topologically equivalent. In the video below I provide an example of how two circular strips of paper are equivalent to a square. Far from being an abstract branch of mathematics, topology has many practical applications. For example, in the field of biology a branch of topology called “knot theory” is used to describe the many spatial configurations that the molecule of life, DNA, can adopt and how it interacts with other molecules. Other large biological molecules that can fold in many ways such as proteins are also studied with tools from the field of topology. Another example is physics where the application of topological principles to the area of quantum physics has ushered a revolution in the understanding of the properties of matter that may lead to many applications. 
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May 2022
