Rule of Four

Three Hundred Third Post: Rule of Four

In the book “Calculus: Concepts and Contexts,” by James Stewart he calls attention to the Rule of Four when looking at math problems. That is why there are 4 electric violins on the cover. It is supposed to represent four ways of looking at the same problem. This is a good text to learn from and pertains to the “Arched Doorway” problem on Constructor’s Corner. You may have noticed that there are now four ways to solve for this problem. (One on Calculated-Curves.com)

But you may be asking yourself: Yes that’s very nice, but do I really need all four? And the answer is simply: Of course, we need four. Four is greater than one. More power “awl oh” as Tim Allan would say on “Tool Time.” More power yeah! Not just more power more mathematical power! Geek power!

More seriously, if the same problem can be written more than one way, there may be patterns or similarities that can be applied to other problems that are solved using one of the same methods. So if you are using the Pythagorean Theorem to solve for the segment and that segment and radius can also be described using a parabola, you now have an new way of explaining other circles using a parabola. It can be hard to find useful similarities, but their there. (That is what we need to do on the message board or Math Wiki on Constructor’s Corner.)

There has to be a way to relate an linear equation to the “Arched Doorway” problem. I have some hunches, but really haven’t worked on it yet completely. So if you have any hunches feel free to post them on the message board. But until then... May the Creative Force be with You