 # by Jongsuk Keum

Goal
We already know that what circles are in Cartesian Geometry. But circles in Minkowski geometry are remarkably different. Therefore, it's interesting for students to explore the d istance in Minkowski and Cartesian Geometry using GSP.

1. Distance in Cartesian Geometry

If point A has coordinates (x1,y1) and
point B has coordinates (x2,y2), the distance from A to B is

d(A,B) = sqrt[(x1-x2)2 + (y1-y2)2].

Hence, the distance in Cartesian geometry means the length of the hypotenuse of a right triangle. 2. Distance in Minkowski geometry.

If point A has coordinates (x1,y1)
and point B has coordinates (x2,y2), the distance from A to B is

d(A,B) = |x1-x2| + |y1-y2|.

Hence the distance in Cartesian geometry means the sum of the length of base and height of a right triangle. 3. What are the circles in Cartesian geometry and Minkowski geometry?

a. Circle in Cartesian geometry with center A with a radius r b. Circle in Cartesian geometry with center A with a radius r 4. Equal distance set of A and B

: the set of all points such that d(C,A) = d(C,B).    