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I just inherited two slide rules from my grandfather-in-law, one wood with smooth action despite nearly a century without use.1 (I used a K+E slide rule myself as an undergraduate in the 1970's.) It struck me that the conversion of multiplication/division to addition/subtraction via the logarithmically ruled markings might serve as a memorable physical instantiation of $\log ab = \log a + \log b$, or $x^a x^b = x^{a+b}$, etc. One of the slide rules came with instructions on how to take the $n$-th root of a number!

I've never taught logarithms, but I wonder if those who have, ever bring in to the classroom slide rules as "props"?


1Lawrence Engineering Service, Peru, Indiana.

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    $\begingroup$ I carry a pocket slide rule in the backpack that I bring to class. When there's a reason to multiply and divide numbers, I'll use it. Sometimes students ask what it is and I'll show them a simple example. Sometimes if they check me on a calculator and we disagree in the third significant figure, I'll tell them that their calculator is probably a little off and needs to have its calibration adjusted using a little screw underneath the back cover plate. $\endgroup$ – Ben Crowell Jan 2 at 23:58
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    $\begingroup$ @BenCrowell: "I'll tell them that their calculator is probably a little off"--Ha! $\endgroup$ – Joseph O'Rourke Jan 3 at 0:09
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    $\begingroup$ Related: matheducators.stackexchange.com/q/10571/77 $\endgroup$ – Joel Reyes Noche Jan 3 at 10:12
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    $\begingroup$ When I was studying for my Private Pilot License in the early 90s, we had to use an E6B Flight Computer (here is a nice metal one) for some of the questions on the written Knowledge Exam. I think electronic units were also available then, but they could give an answer that was too precise, leaving one between the 2 of the choices given on the multiple choice exam. However, if worked out using circular slide rule (which is the heart of the E6B) the correct answer could be found. I think I also had to use it for some of the questions when I get my IFR rating a couple years later. $\endgroup$ – CrossRoads Jan 3 at 18:01
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    $\begingroup$ Here's a nice metal one, I picked it up at an aviation swap meet. aircraftspruce.com/catalog/pspages/… The less expensive cardboard units that students start with also work, I still have mine from my student days. $\endgroup$ – CrossRoads Jan 3 at 18:03
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A few thoughts:

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but I wonder if those who have, ever bring in to the classroom slide rules as "props"?

In the Olden Days (before hand-held calculators) I remember that we had (at Ohio State) a big demonstration slide rule. It was maybe 6 feet long, on a stand with wheels. So the instructor would wheel it in to the front of the classroom, and demonstrate calculations on it. The students, in their seats, would try to replicate what was done on their own slide rules.

So this was not for teaching logarithms, but for teaching the use of the slide rule.

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    $\begingroup$ Those things are gorgeous! They used to be giveaways for pretty minimal classroom purchases of handheld slide rules. The last time I searched eBay for one, they were running like 500 dollars! :( $\endgroup$ – Matthew Daly Jan 3 at 14:57
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(too-long comment) I think it's a nice adjunct, but I would not introduce the topic that way. Introduce it after teaching of rational (math meaning) exponents and roots in a rational (well thought out meaning) progression. I.e. on the board, with some discussion of concepts they learned in exponents that are also used in logarithms. In addition to the slide rules, it is nice to hand out a sheet to each student of log-log and semi-log graph paper.

Furthermore, a cheap handout of log TABLES is nice. And not because we are going to force them to use tables (scientific calculators have been cheap and ubiquitous since late 70s). But because it is easy to see, right in front of your face, how logarithms work and some useful ideas like mantissa and characteristic. From a table (which is essentially a printed out Excel spreadsheet!), you can see at a glance, many different values. Not possible with calculator. I also think it's an easier step to understand (a table) than the sliding nomograph like properties of a slipstick. A nice set of tables to print and distribute is the ones that were handed out for AP chemistry through the mid-90s.

All of this is not to say don't show the slide-rule. Sure, do it. But don't make it central to the teaching. More of a little enrichment exposure that perhaps clicks with some minority of the monsters.

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I have my college algebra students create slide rules each semester.

Key pedagogical question:

  • What is the point of having an algebra student construct a slide rule?

Possible answers:

  • The goal is to convince the students that things like $\log 5$ are real numbers. If you ask a student what $\log 5$ is, you often get the answer that it is a function, or a procedure, or even a question. Having students physically work with expressions like $\log 5$ could help them better conceptualize what the data type of $\log 5$ is [citation needed; and I have none].

  • It's neat. Show students neat things.

Materials:

  • Yardsticks (here yardsticks are actually better than metersticks)
  • Tape that is dry-erase
  • Dry erase markers

Prep:

  • Put tape on the yardsticks so that half the yardstick is covered but not the other half. The tape needs to wrap around covering both sides.

enter image description here

Outline:

  • Split the class into groups and give each group one prepared yardstick.

  • Ask half the class (the weaker groups) to put the yardstick so that "1" is on the left. They will make a mark on their yardstick labeled $x$ at the position $\log x$ feet for $x = 1, 10, 100, 2, 20, 200, 3, 30, 300, \ldots, 1000$.

enter image description here

  • Ask the other half of the class (the stronger half -- this is tricky) to flip the yardstick over so the "1" is on the right. They will make a mark on their yardstick labeled $x$ at the position $3 - \log x$ feet for the same values of $x$.

enter image description here

  • Then if you combine two of these sticks, you have a slide rule.

Key question to ask students:

  • How far is it from the end of the stick to the mark labeled "5"?
  • How far is it from the end of the stick to the mark labeled "4"?
  • How far is it from the end of the stick to the mark labeled "20"?

Key thing to emphasize from student answers:

  • $\log 5$, $\log 4$, and $\log 20$ are numbers.

Then of course show them that you can now physically see $\log 4 + \log 5 = \log 20$.

Then pull out the actual slide rule you brought in.

Then show them the clip from the movie Apollo 13 where the engineers frantically calculate with a slide rule.

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