Many twentyfirst century people consider logarithms to be esoteric, both in the dictionary sense of being only accessible to the initiated, and in the pejorative colloquial sense of being pedantic. Presented as though they have always existed in their present form— x = logb n when nx = b (for n 0)—the history of logarithms is often a literal footnote, if it is mentioned at all. However, far from simply existing since time immemorial—just waiting for someone to discover them—the early modern Scottish polymath John Napier invented logarithms as a means of simplifying astronomical calculations involving spherical geometry. They have subsequently evolved, due to the efforts of a variety of mathematicians, scientists, and didactic literature authors, to have a broad range of applications. Although their primary twentyfirstcentury uses are measuring and modeling natural phenomena, for more than three and a half centuries, prior to the widescale availability of electronic computers, logarithmic tables and slide rules were imperative calculation devices, utilized to build Buckingham Palace, Rockefeller Center—and put a man on the moon. By considering not just that logarithms work, but also why they were invented and how they evolved can help us—and our students—to understand that mathematics is not just an abstract construct, but rather a fundamentally human pursuit.
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