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Slide Rule

Explore connections in mathematics and science with this article on the Slide Rule.
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Slide Rule

A slide rule is a mechanical device that uses the alignment of numeric values marked on sliding scales to perform mathematical calculations. For the past 400 years, the calculations performed on slide rules have made possible such feats as designing the first skyscraper and putting a man on the moon. You may wonder how such a small, mechanical device is able to perform the sophisticated math calculations necessary to make these accomplishments possible. To answer this question, you'll need to look closer at its history, how its sliding scales work, and the logarithms behind the scales.

Depending on how it is used, the slide rule can have a number of scales inscribed upon it. Simpler slide rules have two duplicate scales that can be manipulated to multiply and divide, while more complex models have additional scales that allow for finding reciprocals, square and cube roots, and trigonometric ratios.

In the image below, you can see how the slide rule uses two identical scales, one above the other, to perform the multiplication of 2 times 3. To find the product, you slide the top scale to the right until the "1" on the top scale is aligned with the "2" (or first factor of your multiplication) on the bottom scale. Next, locate the "3" (or second factor) on the top scale; the number directly below it, "6", is your answer. In fact, once the slide rule has been moved into the "multiply by 2" position, you can see that all numbers on the bottom scale are exactly twice the number directly above them.

You may have noticed that the scale seems a bit skewed from one number to the next; this is because it is a logarithmic scale. The history of the slide rule is closely linked to the development of logarithms, discovered in 1614 by John Napier, a Scottish mathematician. Simply stated, the logarithm Napier is credited with discovering made it possible to translate multiplication and division problems into ones of addition and subtraction, respectively.

This discovery led to the publication of logarithmic tables, which were used to aid in mathematical calculation. In 1620, the English mathematician, Edmund Gunter, took Napier's logarithmic values and drew a number line in which the positions of numbers were proportional to their logs. You can see this number line in the scales shown above. The idea of putting two of these scales together to perform calculations came from another English mathematician, William Oughtred, in 1632. This design soon evolved into the slide rule known today, with additional variations of style into cylindrical, spiral, and circular slide rules.

Despite its many benefits, the slide rule had some disadvantages. Since estimation is involved in reading the tick marks of the scale, math calculations made on the tool were only as accurate as the precision of its marks; to increase its precision, one had to increase its length. In addition, the slide rule does not account for decimal points, so those using this tool had to perform additional operations to adjust their results accordingly. Compared with present-day calculating devices, the slide rule seems limiting, but it is important to remember that this tool was the main method of math calculation for almost 400 years, and a successful one at that. For evidence of this, look at some of the buildings in your community; if their cornerstones reveal a date earlier than the 1970s, chances are that the slide rule was key to their construction.

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