A Framework for Technology-Rich Explorations - Extensions and Other Optimization Problems

Antonio Quesada and Michael Todd Edwards

The Two Towers Problem is easily generalized in several ways beyond the version found in Stewart.  For example:

  • If the ratio of the taller tower to the smaller tower is m, then how does the location of the critical point change as a function of m?
  • If the restriction between the poles' heights is removed entirely, show that the critical point is still determined by similarity of the two triangles.

Clearly, all the solutions presented in this article will still apply.

In addition, you or your students may suggest other problem solving avenues, such as equating the slopes of the segments PR and RT'.

Here again is the link from page 2 to other familiar optimization problems that would serve to illustrate various solution techniques that are accessible at each of the four levels of the framework.

Some examples of other easily accessible optimization problems

You may know these problems as

  1. the riverbank fence problem,
  2. the kite design problem,
  3. the isosceles triangle inscribed in circle problem,
  4. the ladder over the fence problem.