Mathematics
Problem Of the Week
Fall
2002
POW #12
Where's the Square(s)?
Start
with a rectangle with corners set at the points (0,0), (1,0), (0,b) and (1,b)
for any b>0.
Draw
four lines - one through each corner - that intersect to outline a square.
Your solution should include a diagram, equations for
the lines and justification that they form a square.
Very
easy case: If b=1, you can use the sides of the rectangle itself to form
the four lines.
The
real challenge: Find two solutions that give squares with different
areas.