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6 articles on this topic.
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Fold a square of paper four times, make three straight snips, and unfold a six-pointed star. Every fold is a mirror, so every snip gets copied once for each layer, and a kid can watch exactly how that happens one unfold at a time.
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Drop charged vertices into a 3D workspace, join them, and let them settle. Every Platonic solid comes out with its edges equal to within a thousandth, from an energy that has no notion of an angle and no rest length. The Archimedean solids come out wrong, and the reason why turns out to be the interesting part.
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Two rules, a handful of coloured dots, and a longest game so vast that with three colours nobody can write the answer down. Build sequences here and let the computer tell you the moment you break the rules.
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In a magic square of order n, every row, column and diagonal add up to the same number while using each of 1 through n squared exactly once. Here is how to build them, and why the odd, even and doubly even cases each need a trick of their own.
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Dig a straight tunnel between any two points on Earth, pump out the air, and let gravity supply the propulsion. The trip takes 42 minutes, and the remarkable part is that it takes 42 minutes no matter which two cities you pick.
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The Earth stays in orbit because of its angular momentum. Take that away, stopping the planet dead in its tracks, and how long until it reaches the Sun? Working out the answer turns up an unexpected appearance by pi.