User:ARUN SUBRAMANIAN R/sandbox

EQUATION OF SQUARE: The Chebyshev distance between two vectors or points p and q, with standard coordinates and , respectively, is This equals the limit of the Lp metrics:

The taxicab distance,, between two vectors  in an n-dimensional real vector space with fixed Cartesian coordinate system, is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes. More formally, where are vectors. For example, in the plane, the taxicab distance between and  is

Taxicab circles are squares with sides oriented at a 45° angle to the coordinate axes. The image to the right shows why this is true, by showing in red the set of all points with a fixed distance from a center, shown in blue. As the size of the city blocks diminishes, the points become more numerous and become a rotated square in a continuous taxicab geometry

While each side would have length √2r using a Euclidean metric, where r is the circle's radius, its length in taxicab geometry is 2r. Thus, a circle's circumference is 8r. Thus, the value of a geometric analog to is 4 in this geometry. The formula for the unit circle in taxicab geometry is in Cartesian coordinates and in polar coordinates.

So the general equation of a square of side ‘a’ and point of intersection of its diagonals (h,k)is;


 * x-h|+|y-k|=(a/sqrt(2))

the square is inclined at 45 deg in coordinate axis.

max(|x-h|,|y-k|)=(a/sqrt(2))