Möbius

Möbius is a term that originates from the name of a German mathematician, August Ferdinand Möbius. It is most commonly associated with the Möbius strip, a surface with only one side and one boundary curve. However, the term "Möbius" is also used in various other mathematical and scientific contexts.

Möbius strip

The Möbius strip is a two-dimensional compact manifold (i.e., a surface) with the interesting property that it has only one side. This is achieved by taking a strip of paper, giving it a half-twist, and then joining the ends of the strip together to form a loop. Despite its simple construction, the Möbius strip has been a source of fascination for both mathematicians and the general public due to its counter-intuitive properties.

Möbius function

In number theory, the Möbius function is an arithmetic function that plays a crucial role in the study of prime numbers. It is defined as follows: for a given natural number n, the Möbius function μ(n) is (-1) raised to the power of the number of distinct prime factors of n, if n has no squared prime factors; otherwise, it is zero.

Möbius transformation

A Möbius transformation, also known as a linear fractional transformation, is a function of the form f(z) = (az + b) / (cz + d), where a, b, c, and d are complex numbers and ad - bc ≠ 0. These transformations are named after Möbius because they can be represented using the Möbius strip.

Möbius syndrome

Möbius syndrome is a rare neurological disorder that is present at birth (congenital). The disorder is characterized by weakness or paralysis of multiple cranial nerves, most often the 6th (abducens) and 7th (facial) nerves.

See also

• Möbius band
• Möbius inversion formula
• Möbius–Kantor graph
• Möbius–Kantor configuration

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