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# Mathematics-Mobius Strip

Mobius Strip / Mobius Band is a surface with only one side and only one boundary region. It is also known as Mobius or Moebius. It satisfies the non-orientable mathematical property.

It was discovered by German mathematicians

*in 1858.*

**August Ferdinand Mobius and Johann Benedict Listing**It can be created by taking a paper strip & giving one of two ends of the strips a half twist and then joining the both ends of the strip together to form a loop.

Based on the way it is twisted, classified as two

**1 ) clockwise**

2 ) Counter - clockwise

Mobius band's Euler Characteristics is Zero.

[

**Note ::****Euler Characteristics -The algebraic topology in mathematics, Euler characteristics is a topological invariant. It is denoted by using the symbol χ. It denotes a number that describes a topological space's shape regardless of the way it is bent. It is calculated using the formula, χ = V - E + F**

=> V = number of vertices

=> E = number of edges

=> F = number of faces ]

Using parametrization,

**x (r,s) = [ 1 + (s/2)cosr/2] cos r**

y (r,s) = [ 1 + (s/2)cosr/2] sin r

z (r,s) = s/2 sin r/2

Where

**0 ≤ r ≤ 2∏ & -1 ≤ s ≤ 1. It creates a mobius band of width 1 & whose center circle radius 1, lies in xy plane and is centerd at (0, 0, 0)**