In Euclidean algebra, all distance is measured in a "birds-eye view" way, and the euclidean distance formula, [math]d_e=\sqrt{\left(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2\right)}[/math] is used to calculate the distance between two points. However, in taxicab geometry, there is only a grid-pattern, so the birds-eye view distance isn't valid. The distance formula in taxicab becomes [math]d_t=\mid x_2-x_1\mid+\mid y_2-y_1\mid[/math], which is just a sum of the coordinates. We can see the differences in the applet above.[br][br]