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The Beginnings and End of the Slide Rule Kendyl Kennard

Imagine you’re a mathematician working for NASA in the year 1953, armed with the task of calculating the trajectories for space shots which determined the timing for launches.

You’re sitting at your desk armed with the latest technology at your disposal. What kind of tools are your imagining? After all you’re trying to put a man on the moon. Are you imagining a ? Wrong. were introduced in the 1940’s, and didn’t become common place until around the 1980’s. Even then, the computers at this time could only add, subtract, and maybe perform basic . So what about a ? Nope. The pocket calculator was invented even later in the 1970’s. So how, you may ask, are you supposed to compute such complicated without the modern conveniences we take advantage of today? Just ask

Katherine G. Johnson, the mathematician who completed the daunting task at question. Dr.

Johnson calculated the trajectory for the mission to the moon with the help of a simple slide rule. A tool that is foreign to the engineers and scientists of the modern world, yet was vital to the engineers and scientists of the early 20th century and beyond. You may be thinking, what is a slide rule? How does it work? Or even, why have I never heard of it? The rest of this paper aims to answer these questions.

In order to understand the invention of the slide rule, we must venture back to the early

1600’s to the works of . In 1614, Napier published a book titled Mirifici

Logarithmorum Canonis Descriptio. This book contained detailed explanations of , and pages of tables of numbers related to natural logarithms. Napier’s discovery made it possible to perform multiplication and by simple and subtraction. For instance, a*b = 10log(a+b) . Using logs to multiply a and b, one would look up the logs of a and b, add them together, then find the number whose log was the sum. Shortly after the invention of logarithms, a mathematician named Edmund Gunter of Oxford, made the process of multiplication and division even simpler by creating a device using a . Simply stated, the logarithmic scale is a number line in which the positions of the numbers are proportional to their logs. Instead of having to go through the entire process Napier invented to find the product of two numbers, the user just simply measured the distance from the beginning of the scale to one factor with a pair of dividers, then moved them to start at the other factor and read the number at the combined distance all on the same scale. Let’s take a look at Edmunds scale

below6 and perform the simple

multiplication problem 2x3.

First we start by using the

divider to measure the distance

from the beginning of the scale,

1 to the first factor, 2. Then, without altering the span of the divider, you add this length to the second factor of 3 to find that the span of the dividers lands on 6, the product of 2 and 3. Division can be performed using the same method, except by subtracting the lengths instead of adding them.

Finally, in 1622, , an Anglican minister and mathematician, placed two of these Gunter scales side by side, eliminating the dividers and creating the very first modern

slide rule. Let’s take a

look at a simplified

sketch of Oughtred’s slide rule above2 and perform the same calculation of 2x3 to understand the simplification that brought us the modern day slide rule. First, we start by sliding the top scale to match one of the factors, which in this case is 2. The answer to 2X3 is given by the number on the bottom scale the corresponds to the other factor,3, on the top scale which we see is 6.

The slide rule went through a series of manipulations and after it’s initial conception, until 1859 when the modern slide rule that we know today was created by French artillery lieutenant Amédée Mannheim. The rapidly evolving world at this time evoked the beginnings of the profession, which in turn spurred a demand for Mannheim’s slide rule. Finally, in 1881 the slide rule became a staple computational tool in the United States. The slide rule was used by various professions’ ranging from bombardiers and navigators in World

War II, to rocket scientists and engineers working for NASA. The slide rule slowly became an iconic symbol of the engineering profession in the 1950’s. In fact, if you were an engineering student in the 50’s, chances are, you would be sporting a 10 inch slide rule in your belt holster.

This trend carried on for years until the slide rule started its gradual demise in 1960.

In 1960, IBM introduced some of the first affordable computers geared specifically for the engineering profession. The computer made even easier than the slide rule. The user could simply type in a formula and receive an answer without the reformulation needed when using a slide rule. However, the slide rule was still convenient at this point because they were accessible on the go and computers weren’t yet common in the home. The real demise of the slide rule came in 1972 when Hewlett Packard introduced the first pocket which combined the convenience of the slide rule and the ease of the computer. In 1976 the pocket scientific calculator could be purchased for less than $25 and the slide rule became nonexistent. In my opinion, the demise of the slide rule and rise of the calculator impacted more than just the science and engineering professions. The education system in America was forever changed with the invention of the calculator and not necessarily in a good way. This past week I asked my Calculus 1 students if they knew what a was, and I was met with blank stares and confusion. The power of the calculator allowed my college students to perform advanced mathematical computations for years without even second guessing or questioning exactly what they were doing. Unlike the calculator, the slide rule actually provoked thought and understanding when performing complex computations. Sadly, this deeper level of mathematical understanding in most American students met its demise along with the slide rule in the 1970’s.

Works Cited

1. Blakemore, E. (2015, February 20). Before , This Tool Helped Put a Man on the Moon. Retrieved November 1, 2016, from http://modernnotion.com/slide-rules-helped-put-man- moon/ 2. Slide Rule. (n.d.). Retrieved November 1, 2016, from https://en.wikipedia.org/wiki/Slide_rule#History 3. Slide Rule History. (2013, December 13). Retrieved November 1, 2016, from http://www.oughtred.org/history.shtml 4. Kuhman, H. J. (n.d.). Slide Rule. Retrieved November 1, 2016, from http://www.encyclopedia.com/science-and-technology/mathematics/mathematics/slide-rule 5. John Napier. (n.d.). Retrieved November 1, 2016, from https://en.wikipedia.org/wiki/John_Napier 6. Gunter's Rule. (n.d.). Retrieved November 1, 2016, from http://www.nzeldes.com/HOC/Gunter.htm