Nicolas Chuquet first noticed in 1484 that to multiply any two members of the geometric series 1, r, r2, r3, r4, …, we only need to add their exponents, r a ×r b = r a+b . Similarly, Chuquet found that division among terms corresponds to subtraction of exponents: r a ÷r a-b = r a-b . More than 100 years later John Napier made this idea useful by calculating “logarithms” for all 8-digit decimal fractions. It is difficult to overestimate the value of Napier’s log tables. They have been used billions of times each year to do accurate multiplications of every conceivable sort in navigation, engineering, science, and business.
KeywordsInterest Rate Annual Rate Geometric Series Fiddler Crab Continue Fraction Expansion
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