Thursday, May 10, 2007 05/10/07-Slide Rules and Logarithms

In today's encore excerpt--the invention of logarithms is followed almost immediately by the invention of the slide rule:

"John Napier, a Scottish mathematician, physicist and astronomer, invented logarithms in 1614. ... Logarithms--that horror of high school algebra--were actually created to make our lives easier. So how did Napier's logarithms work? ...

"[U]sing logs, multiplication simplifies into sums, division becomes subtraction, finding a square root turns into dividing by two, and figuring out a cube root becomes dividing by three. For example, to multiply 3.8 by 6.61, you look up the logarithms of those numbers in a table. There you will find 0.58 and 0.82. Add these together to get 1.4. Now go back to the table and find the number whose log is 1.4 to get a close approximation of the answer: 25.12. Begone ye slippery errors!

"Napier's invention revolutionized mathematics--mathematicians adopted it immediately to speed their calculations. German astronomer Johannes Kepler used these modern logarithms to calculate the orbit of Mars at the start of the 17th century. ... [B]ut ready access to books of log tables was crucial to the procedure. So in 1620 mathematician Edmund Gunter of London marked a ruler with logarithms ... [and] around 1622 William Oughtred, an Anglican minister in England, placed two sliding wooden logarithmic scales next to each other and created the first slide rule. ...

"Napier went on to invent the decimal point ... and to lay the groundwork for Isaac Newton's calculus."

Cliff Stoll, "When Slide Rules Ruled," Scientific American, May 2006, pp. 81-84.


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