Taxicab geometry

Taxicab geometry is a form of geometry consisting of a vector space in which the distance between two points is calculated by summing the distances between them, along each of the dimensions of the vector space.

That is, in n-dimensional taxicab geometry, the distance [math]\displaystyle{ d }[/math] between two points at position vectors [math]\displaystyle{ \mathbf a = (a_1, a_2, ..., a_n) }[/math] and [math]\displaystyle{ \mathbf b = (b_1, b_2, ..., b_n) }[/math] is as follows,

[math]\displaystyle{ d = \sum_ {i=1}^n{|b_i - a_i|} }[/math]

In taxicab geometry, squaring the circle is possible, as [math]\displaystyle{ \pi }[/math] is equal to [math]\displaystyle{ 4 }[/math].