In my last post, I showed the powers of 3 as a series of fractal drawings. I had lots of other doodles in my math notebook, so I spent the morning dotting little pieces of paper to share them with you.
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These could serve as exercises for a student wanting to practice using exponent notation, but they could also serve as decent stand alone problems. Something as simple as “How many dots?” maybe. Perhaps I’ll post some on 101qs.com and see what kind of questions they get. (I did.)
Problems and exercises can both be valuable, but they aren’t the same thing. Math students should know the difference between doing math in its most free and open form, and completing exercises to build familiarity, skill, and speed. I need to do a better job of including this in my teaching.
What do you make of these?
Perhaps you’re wondering “How much time did he spend drawing all those dots?
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Through school and work, I’ve been able to download two copies of Mathematica, and I LOVE it! It’s especially good for all of my mathematical art and imaging needs. It also has an exceptional documentation system with hyperlinks and examples that make it very easy to teach yourself and play. I’m amazed how much I’ve learned in two weeks.
Mathematica also handles recursive programming nicely, which is perfect for fractals. I wrote some code this afternoon and generated these images. Enjoy.
Now how long would THAT have taken me to draw?