A Miraculous Mistake
In the cloister of Basel's Peterskirche (St. Peter's Church), an epitaph commemorates the life of Jacob Bernoulli, who died on August 16, 1705. Bernoulli, a towering figure in the history of mathematics, liked the properties of the logarithmic spiral. He dubbed it the Spira mirabilis—the "miraculous spiral"—due to its unique characteristic of self-similarity. As the spiral grows, its shape remains unchanged with each turn. This mathematical constancy fascinated Bernoulli so much that he requested it be carved on his tombstone.
He paired the spiral with the Latin motto Eadem mutata resurgo, which translates to "Though changed, I rise again the same". The phrase was a double-entendre, referring both to the spiral's ability to retain its form as it expands and to his own hope for the resurrection of the body. However, a stonemason, unfamiliar with the subtleties of geometry, made a significant error. Instead of the requested logarithmic spiral, an Archimedean spiral was carved into the stone. The two are visually distinct: the turnings of an Archimedean spiral have a constant separation, whereas the distance between the turns of a logarithmic spiral increases in a geometric progression. The very symbol of mathematical constancy was rendered incorrectly for eternity.