What is a "mobius tape"?

In 1858, August Ferdinand Möbius, to prove his theory about orientability, created an object that to this day still generates some discussion among specialists: this object is the Mobius tape.

 

This item was originally introduced in 1865, it highlighted the importance of geometric illusions from a topological point of view. 

The ribbon came about as a result of studies on the geometric theory of the polyhedron, carried out by Möbius while serving as a professor of astronomy and higher mechanics at the University of Leipzig, Germany. The object consists of an item with "only one side" in a loop format, where if the manipulator placed a finger on the material and followed the path without escaping the face, it would return to the starting point after two complete turns.

The invention, which is nothing more than the joining of two ends of a strip of paper after undergoing a rotation, is a unilateral product that is impossible to determine which is the top and bottom, the inside and out. According to mathematicians, these are the foundations of a "non-orientable object" that may well draw parallels with concepts of time and alternative realities.

The Möbius strip is the clearest representation of infinity, both because of the traditional format as we know it, and because of the property of not having a path with a beginning or an end, but infinite, where one has the impression of running eternally along a two-sided strip. .

Apart from its importance in the studies of orientation and geometric positioning, the Möbius

strip

also makes great contributions to topology, an extension of geometry that serves to designate a family of sets, giving the first airs to the concept of continuity. Scientists in the field study properties of objects that are preserved when moved, bent, stretched or twisted, without cutting or gluing the parts.

This proposal comes with important implications and brings new ways of studying the natural world, helping to develop number theory.

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Sangram Sagar

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