Problem of the Week

Please bring your solutions to my office, or mail them electronically to delgado@hilltop.bradley.edu or by surface mail to the address on the Problem of the Week webpage.

Take a 3 x 5 index card and place one corner at the origin of a coordinate system as shown in yellow on the sketch below.

(a) First, rotate the card about the point B until it reaches the position shown in blue, continue rotating about the point C until it reaches the position shown in green, then about the point D until it finally reaches the position shown in red.  The point A will trace out a curve in the plane.  What is the area enclosed by this curve and the x-axis?

(b) Do the same thing, but this time start with the card rotated 90 degrees as shown below.

(c)  Which area is the largest?   (Is this what you would have guessed?)

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ã2003 Alberto L. Delgado