Mathematics Problem Of the Week

Spring 2005

POW 7: A Tumbling Playing Card

A 3x5 playing card starts (as in the diagram below) with it’s lower left corner at the origin (0,0) and the long side along the y-axis. The card is then rotated (keeping the lower right corner fixed) until the other long side lies along the x-axis. Then rotate again around the new lower right corner so it is upright and upside down (relative to the starting position), then one more rotation to bring the original lower left corner to the bottom right and a final rotation around that corner puts the card to its original orientation.

If we follow the original lower left corner throughout this process it will form a curve, starting at (0,0) and ending at (0,16).

(a) Find the area between that curve and the x-axis.

(b) Find the length of the curve.

Due Friday, March 11^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/