Computer math and the Chaos game

In the last blog post I mentioned the talk that Conrad Wolfram gave at the Computer Based Math Education Summit which you can find here:

I found his thoughts on using computers in math education to be extremely interesting.  As I wrote yesterday, I’m not sure that I’d take things as far as he does, but I think that his arguments have a lot of merit.  My plan is to introduce the boys to more computer based math, and do so as soon as possible.

Following a field trip on Monday, my older son is starting a chapter on graphing quadratic equations on Tuesday, so bringing computers into the fold there should be easy.  I’m currently covering some introductory number theory with my younger son, so the computer side there isn’t quite as obvious.  Guess I’ve got something to think through for tomorrow!

Today I introduced them to the “Chaos Game.”  Seemed like a nice and easy starting point for computer-based math – the math itself is fairly easy and the result is stunning.  The program I wrote to work with them uses the programming section of Khan Academy.  I picked that simply because it is easy to share with others who are interested.  The program is here:

Feel free to play around with it, share it with kids, and make fun spin offs.  The video of the three of us going though the game is here:


If today’s exercise is any indication, the boys are really going to enjoy the computer math.  Can’t wait to do more!

Conrad Wolfram’s Computer-Based Math Education Summit talk and “Perfect” Pentagons

A few weeks ago, while we we were in the middle of studying quadratic equations, I wanted to show my older son a neat example beyond what the book was doing.  The purpose of this topic was just to provide a fun break, so whether or not we’d covered the part of math where the example came from wasn’t a major concern.  I settled on showing him how to make a regular pentagon.  Turned out to be a even more fun than I was expecting because quite a bit of math that we’ve studied during the past few years came into play:

Today I got nice surprise when my younger son was drawing a picture and asked me how to draw a perfect pentagon.    We obviously haven’t covered nearly as much material with him, yet, so I took a slightly different approach.  The approach was influenced a little by Conrad Wolfram’s talk from last week’s Computer-Based Math Education Summit:

He goes a little farther than I probably would go in terms of using computers early on with kids – I won’t be introducing calculus just yet! – but I probably wouldn’t have thought to pull out the scientific calculator and talk about sin() and cos() with my younger son if I hadn’t see this talk.  FWIW, my initial idea after listening to his talk was to show the boys the “chaos game,” but the jet lag from returning from London won out over the motivate to code that up this morning.  Hopefully next week.

So, with that background, here was tonight’s attempt to show my younger son how to make a perfect pentagon:


After we finished, I mentioned to him that one of the numbers that came into play, cos(72), is equal to  ( \sqrt{5} - 1 ) / 4.  That was a fun conversation, too, since he knew that 5 wasn’t a perfect square and was confused how you’d find the square root of a number that wasn’t a square.   That’ll make for a neat follow up topic, or maybe it is time to introduce Newton’s method . . . .