Long before cell phones with their calculator apps and long before laptops and desktops and long before handheld calculators, but centuries after abaci, there was the slide rule. What a device! A device that was required where I attended college.
I went to the college bookstore before freshman classes began and bought mine—for $30! In 1952, $30 was a LOT of money. I really had little choice because I was told I needed the features on the one I bought. And those features were many. I recently took mine out of the storage where it has reposed for several years. Yes, I still have it. One can use it to find, among other things, the square, square root, sine, cosine, tangent, logarithm and exponential of a number.
I imagine many of you will remember from the distant past, perhaps not with deep pleasure, some of the terms in the preceding paragraph. Because I can’t help it, I’m going to talk about the most basic function of a slide rule: multiplication. If you wish to skip the next four paragraphs, I will understand.
The slide rule uses an elementary property of logarithms. Sorry for mentioning them again. The property is the following. If x is a number, there is an associated number called the logarithm of x and it is written log(x). Suppose y is another number. Then a third number is the product xy. These numbers also have logarithms, log(y) and log(xy), respectively. Here’s the exciting thing. Try to restrain your enthusiasm. It turns out that log(xy) = log(x) + log(y). Now, you might be tempted to say, “So what?” Well, thanks for asking.
A slide rule has a scale that is fixed, and another scale that is on a part that slides; hence the name of the device. Suppose I wanted to figure out the product of 2 and 3. Now I know you know the answer, but all numbers aren’t as nice. How would you use the slide rule? On the fixed scale find the number 2. You’re not told this, but where 2 is located on the scale is actually a distance from the leftmost end of the scale. But it isn’t a distance of 2 units. Instead it’s a distance that is proportional to the number log(2).
The sliding scale’s left end is positioned on top of the 2 (really a distance log(2) from the left end of the fixed scale). Now look at 3 on the sliding scale. Of course, it’s not a distance of 3 from the left end of the sliding scale, but rather a distance of log(3). If you add the two distances, you get log(2) + log (3). And what is log(2) + log(3)? By the above property, it should be log(2x3) or log(6). And what is written below that distance of log(6) on the fixed scale? Not log(6) (which is really the distance from the left end of the fixed scale), of course, but just the number 6 which we take to be the answer! And that’s how slide rules do multiplication. I’m sure you agree that’s beautiful.
The Wikipedia page on slide rules is https://en.wikipedia.org/wiki/Slide_rule#:~:text=In%20its%20most%20basic%20form,multiplication%20and%20division%20of%20numbers. Please don’t overload the Wikipedia site as you rush to it.
I have a collection of slide rules in addition to my original, nine in all. The smallest is about five and a half inches and the largest, my father’s, is approximately two feet. I’ve seen ones displayed in high school classrooms that are at least eight feet in length. The math department of my university has a donated collection displayed in a glass case.
The accuracy of a slide rule is low, maybe two to three correct digits, significantly less than any calculator you have used. The accuracy increases as the length of the rule does, assuming the manufacturer did a precise job of marking it.
I took an undergraduate course called Statics and I think the professor was named Dr. Stone. He was a tough old guy and was angered by our inability to provide accurate answers. He took one day to “teach” us how to use a slide rule and said that from then on errors would not be tolerated. And they weren’t.
When I was in college, you could tell the nerds by the fact they wore a slide rule clipped to their belt.
I wore mine with pride. After all, it cost $30.
I went to the college bookstore before freshman classes began and bought mine—for $30! In 1952, $30 was a LOT of money. I really had little choice because I was told I needed the features on the one I bought. And those features were many. I recently took mine out of the storage where it has reposed for several years. Yes, I still have it. One can use it to find, among other things, the square, square root, sine, cosine, tangent, logarithm and exponential of a number.
I imagine many of you will remember from the distant past, perhaps not with deep pleasure, some of the terms in the preceding paragraph. Because I can’t help it, I’m going to talk about the most basic function of a slide rule: multiplication. If you wish to skip the next four paragraphs, I will understand.
The slide rule uses an elementary property of logarithms. Sorry for mentioning them again. The property is the following. If x is a number, there is an associated number called the logarithm of x and it is written log(x). Suppose y is another number. Then a third number is the product xy. These numbers also have logarithms, log(y) and log(xy), respectively. Here’s the exciting thing. Try to restrain your enthusiasm. It turns out that log(xy) = log(x) + log(y). Now, you might be tempted to say, “So what?” Well, thanks for asking.
A slide rule has a scale that is fixed, and another scale that is on a part that slides; hence the name of the device. Suppose I wanted to figure out the product of 2 and 3. Now I know you know the answer, but all numbers aren’t as nice. How would you use the slide rule? On the fixed scale find the number 2. You’re not told this, but where 2 is located on the scale is actually a distance from the leftmost end of the scale. But it isn’t a distance of 2 units. Instead it’s a distance that is proportional to the number log(2).
The sliding scale’s left end is positioned on top of the 2 (really a distance log(2) from the left end of the fixed scale). Now look at 3 on the sliding scale. Of course, it’s not a distance of 3 from the left end of the sliding scale, but rather a distance of log(3). If you add the two distances, you get log(2) + log (3). And what is log(2) + log(3)? By the above property, it should be log(2x3) or log(6). And what is written below that distance of log(6) on the fixed scale? Not log(6) (which is really the distance from the left end of the fixed scale), of course, but just the number 6 which we take to be the answer! And that’s how slide rules do multiplication. I’m sure you agree that’s beautiful.
The Wikipedia page on slide rules is https://en.wikipedia.org/wiki/Slide_rule#:~:text=In%20its%20most%20basic%20form,multiplication%20and%20division%20of%20numbers. Please don’t overload the Wikipedia site as you rush to it.
I have a collection of slide rules in addition to my original, nine in all. The smallest is about five and a half inches and the largest, my father’s, is approximately two feet. I’ve seen ones displayed in high school classrooms that are at least eight feet in length. The math department of my university has a donated collection displayed in a glass case.
The accuracy of a slide rule is low, maybe two to three correct digits, significantly less than any calculator you have used. The accuracy increases as the length of the rule does, assuming the manufacturer did a precise job of marking it.
I took an undergraduate course called Statics and I think the professor was named Dr. Stone. He was a tough old guy and was angered by our inability to provide accurate answers. He took one day to “teach” us how to use a slide rule and said that from then on errors would not be tolerated. And they weren’t.
When I was in college, you could tell the nerds by the fact they wore a slide rule clipped to their belt.
I wore mine with pride. After all, it cost $30.
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