If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of
these numbers must be 1. Now for the complexity! When are the other
numbers real and when are they complex?
Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
Solve quadratic equations and use continued fractions to find
rational approximations to irrational numbers.