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Draw a perfect triangle on a piece of paper, and then draw around the triangle free-hand. Try to make each new shape closely match the previous one, including its imperfections. You’ll find wavy patterns developing (just like doing the same with straight lines) which makes a nice picture.  But can you manage to do all this, with the ultimate goal that after 50 lines you will reach a perfect square?  This animation shows a computer program having a go. [code]

Draw a perfect triangle on a piece of paper, and then draw around the triangle free-hand. Try to make each new shape closely match the previous one, including its imperfections. You’ll find wavy patterns developing (just like doing the same with straight lines) which makes a nice picture.  But can you manage to do all this, with the ultimate goal that after 50 lines you will reach a perfect square?  This animation shows a computer program having a go. [code]

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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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