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 . . . .

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