Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

Marcus Vitruvius Pollio was a contemporary of Julius Caesar, and we know of him largely through his extensive writing about architecture and science. Vitruvius’s works were very influential in the Renaissance, and Leonardo da Vinci’s Vitruvian Man is named after him. In the third book of his De architectura, he talks about good temple building (including always using an odd number of steps, so when someone places their dominant foot on the first step, they will use the same foot when they reach the top). He also talks about an easy mistake to make when positioning your columns. For a temple twice as long as it is wide, “those who built twice the number of columns for the temple’s length seem to have made a mistake because the temple would then have one more intercolumniation than it should.” In the original Latin, as well as having the columns as columnae, Vitruvius talks about the intercolumnia, or the spaces between the columns. Doubling the length of the temple does not need twice as many columns but, rather, twice as many between-column spaces. Vitruvius is warning those building a temple not to make a fence-post mistake and end up with one column too many. If anyone can find an older example of a fence-post mistake, or any off-by-one error, I’d love to hear about it.