A poem in response to Paul Lockhart’s “A Mathematician’s Lament”, inspired by the mathematical doodles of Vi Hart.

Inside a box a triangle sits, Somewhere, perhaps in your mind’s eye, Wide as the box, and just as high. In short, the triangle barely fits. | |

What will the triangle’s area be? A quarter of the box? Or maybe a third? More than the box? No, that’s absurd. Hmm, there’s a game here, you can see. | |

A curious game — but how to play? Maybe you should draw a line. To split the triangle, that looks fine, From top to bottom, all the way. | |

Now two boxes sit astride Where there had only been just one. Twice the shapes means twice the fun! And each contains more shapes inside. | |

The leftmost box is cut in half – A line is slicing it in two. Now equal shapes jump out at you. It’s enough to make you laugh. | |

For on the right it’s just the same. Your triangle, you can say with pride, Takes half the box’s space inside. It seems that you have won the game! |