Nonlinear Web Quest

I was somewhat familiar with the mathematicians, Leonardo Pisano (a.k.a. Fibonacci) and Pierre de Fermat.  Fibonacci was familiar for obvious reasons, his sequence, but I was amazed by the amount of study done on just this one sequence.  I was really, really surprised to see that a journal is devoted to Fibonacci, The Fibonacci Quarterly.  As my students would ask, “Don’t these people have anything better to do?”  I learned a few things about the sequence that I didn’t know before: 1.) the ratio of consecutive numbers approaches the golden ratio (http://www.lifeinitaly.com/heroes-villains/fibonacci.asp); and 2.) you can use this application of the golden ratio to convert from miles to kilometers because in 1 mile there are about 1.6 kilometers. For example, look at the 5.  The next number is 8.  In 8 miles, there are about 8 kilometers.   (http://www.daviddarling.info/encyclopedia/F/Fibonacci_sequence.html) 

 

I was also familiar with Fermat, though it was in name only.  To introduce probability I always give the activity, “The Problem of Points.”  (http://mathforum.org/isaac/problems/prob1.html)

Years ago I had heard of Fermat’s Theorem, so this was a nice reminder of that. (http://en.wikipedia.org/wiki/Fermats_Last_Theorem) I was also familiar with the golden ratio, even though I had not seen some of the applications with pentagons and pentagrams.

 

I found the images in nature particularly interesting and also those that were created by computers using fractals.  What I found most interesting was the theory of chaos.  I remember that theory from Jurassic Park, but had never really put much though into it because it is Hollywood.  Just the fact that chaos is not really chaos, but does follow some type of small “generalizable” pattern is interesting to try to wrap your mind around.  The fact that so many things in nature follow these patterns is astonishing.  Nature picks the easiest path; that must mean that math is the easiest path one can take to making sense of the world around us.  (http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html)

 

I cannot honestly say that I was able to identify any applications of nonlinear patterns in my home or school.  I’ve looked, but maybe my mind just isn’t trained quite well enough to notice nonlinear patterns.

 

I certainly would like to adapt this type of web quest for the classroom.  I think I would just webquest mathematicians to begin with and see where this takes us.  It opens up so many doors into math for the children to dive into.  I did this many years ago within a data unit that incorporated technology and was amazed at the results and at how much the students learned.  They were excited, really excited that these “old Greek guys” I told them about were actually people and did a lot more than just what they are remembered for.  Of course, the web quest will only work if our computers do (about a 50-50 proposition these days).  Another application of this that would tie in well with the gender issues in math is web questing for female mathematicians and their accomplishments in the field.  We all could stand to learn more in this area of math.