Monday, April 16, 2018

What is a slide rule for?

I was listening to Sam Cooke's classic song "Wonderful World" and thought of the line: "Don't know what the slide rule is for". When the song was released in 1960, the line was describing how disinterested the protagonist was about math and algebra, as the slide rule was a common tool for doing calculations. Today, that line would probably describe most young adults or younger, as the slide rule has not been used for calculations for many years with the rise of the calculator. When I was in high school, we used electronic calculators in our tests and exams, but out of curiosity my brother and I bought a slide rule anyway (they were still being sold in bookstores at the time, but disappeared soon after from the shelves). I was fascinated by how you can multiply two numbers merely by aligning the start of one ruler with the first number and reading off the result off the second number.  This is due a property of logarithm: log(ab) = log(a) + log(b). Thus multiplication is reduced to addition. By printing the numbers in logarithmic scale and lining up segment end-to-end (corresponding to addition), we achieve the operation of multiplication using a slide rule. Similarly, division can be done with a slide rule as it corresponds to subtraction. And it can do a lot more, such as trigonometry and taking square and cube roots. Accuracy was a problem, and they were soon supplanted by calculators which can compute to many digits of precision. As the song is continuously being covered by many artists, I wonder if the current audience would find the lyrics strange?

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