The Past Asks You: An Enchanted Ecosystem, 1494

illustration of cat gamboling on vines and pole in margin Universitätsbibliothek Graz MS 1, f. 409v (1481)

It’s time for another installment of The Past Asks You. Post your answer in the comments!

A mouse is at the top of a tree 60 braccia1 high, and a cat is on the ground at its foot. The mouse descends 1/2 of a braccio a day and at night it turns back 1/6 of a braccio. The cat climbs one braccio a day and goes back 1/4 of a braccio each night. The tree grows 1/4 of a braccio between the cat and the mouse each day and it shrinks 1/8 of a braccio every night. In how many days will the cat reach the mouse?

Luca Pacioli, Summa de arithmetica geometria proportioni et proportionalita (1494)

Do you ever feel like this cat? All you want is to catch the mouse, but for some reason you always seem to take four steps forward and one step back, and the mouse keeps scurrying around incoherently, and maybe you’re crazy but you’re starting to think that even the height of the tree is inconsistent?

  1. The Early Modern Italian braccio is the length of an arm, roughly 23 inches. Unless you have weird arms that grow during the day and shrink at night.