Mathematics Problem Of the Week

Spring 2005

POW 1: Running in Circles

A circle is defined to be the set of all points that are a fixed distance (the radius) from a fixed point (the center). If we define the distance between points (a,b) and (c,d) to be the maximum of |a-c| and |b-d|, what does a “circle” look like? (Assume the “circle” is centered at (0,0) and the radius is 1).

A parabola is defined to be the set of points equidistant from a point (focus) and a line (directrix). Using the distance measure defined above, what does a “parabola” look like? (Assume the directrix y=0 and the focus is (0,2).)

Due Friday, January 28^th , at Noon.

Solutions should be submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via e-mail to mbos@stlawu.edu

Presentation counts! The prize-winning entry will be selected from all correct submissions, based on the clarity, creativity and elegance of the solution.

Look for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/