# Slide rule

Tom Reilly

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posted 6 years ago

When I was in high school, we were taught how to use a slide rule. We were required to buy a calculator but the teacher said it was still important to know how to use a slide rule. He was wrong. Does anyone know if they still teach "slide rule"? Does anyone not know what a slide rule is? Does anyone still know how to use a slide rule?

pete stein

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posted 6 years ago

I think everyone over a certain age (myself included) who had any hard science course work will remember using slide rules, and will also wager that most of these folks who come to this forum, by virtue of their loving programming and thus logical thinking, will remember how it works -- and the mathematical basis for it.

Tom Reilly

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pete stein

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posted 6 years ago

Ah, but don't forget the age criteria. How old are you? Myself, I'm 52.

Tom Reilly wrote:I will accept your wager. I say that most people that come to this forum have heard the term but do not know what it is and that most people, including myself, couldn't tell you how to use it nor understand its fundamentals.

Ah, but don't forget the age criteria. How old are you? Myself, I'm 52.

posted 6 years ago

I never learned to use one, but I do own a 4-foot instructional slide rule. (The kind that hung in front of a class for demos.)

*~Joe Strummer*

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pete stein

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posted 6 years ago

I never learned to use one in school. I did have a Trig/Calc teacher who taught us how to interpolate off a log or trig table.

My dad was a EE professor, and he had 3-4 slide rules, including a circular one (a disc on top of a disc, the advantage being you never run off the end). I taught myself how to do basic stuff (multiplication and division) but nothing more complicated than that. A guy in my office has a few that he refers to as his "solar powered calculators", as they don't work in the dark.

My dad was a EE professor, and he had 3-4 slide rules, including a circular one (a disc on top of a disc, the advantage being you never run off the end). I taught myself how to do basic stuff (multiplication and division) but nothing more complicated than that. A guy in my office has a few that he refers to as his "solar powered calculators", as they don't work in the dark.

There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors

posted 6 years ago

I expect that they are not taught. I know my daughter never used one in her schooling, she is not 25+.

I, of course, not only used one, I have a webpage on my website about them. Wrote it in 1995 or so. Pat's sliderule page as it says:

"Pat had, of course, a very serious sliderule in 1969. And of course, serious geeks never get rid of sacred artifacts."

I did teach my kid how to use one, just because I'm a geek.

When I was working in a real Engineering firm in the early 70s, electronic calculators were just becoming available, trying to replace the Frieden mechanical calculator (which were slow, expensive, noisy, complex, and hard to maintain.). We had an Engineer from Korea who used an abacus. So naturally, being guys, we had a race, sliderule vs abacus vs calculator. The winner was the abacus, then sliderule, with the calculator last.

I, of course, not only used one, I have a webpage on my website about them. Wrote it in 1995 or so. Pat's sliderule page as it says:

"Pat had, of course, a very serious sliderule in 1969. And of course, serious geeks never get rid of sacred artifacts."

I did teach my kid how to use one, just because I'm a geek.

When I was working in a real Engineering firm in the early 70s, electronic calculators were just becoming available, trying to replace the Frieden mechanical calculator (which were slow, expensive, noisy, complex, and hard to maintain.). We had an Engineer from Korea who used an abacus. So naturally, being guys, we had a race, sliderule vs abacus vs calculator. The winner was the abacus, then sliderule, with the calculator last.

posted 6 years ago

I owned multiple slide rules -- including a circular one, which i really liked.

The basis of how it works is that with logs -- additions of logarithms is the same as multiplication. So, you can do complex operations that requires multiplication by simply setting one number and adding the distant of the other. Since the measurements are logs, it is the same as multiplying the two numbers.

Henry

I owned multiple slide rules -- including a circular one, which i really liked.

The basis of how it works is that with logs -- additions of logarithms is the same as multiplication. So, you can do complex operations that requires multiplication by simply setting one number and adding the distant of the other. Since the measurements are logs, it is the same as multiplying the two numbers.

Henry

posted 6 years ago

I wonder if that was a fair test. I mean, the abacus and slide rule users probably had years of practice, whereas the calculator user was probably using a new tool he was unfamiliar with.

I bet if you had the abacus user use the slide rule, the slide rule user use the calculator, and the calculator user use the abacus, the results would have been VERY different.
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors

Pat Farrell wrote:we had a race, sliderule vs abacus vs calculator. The winner was the abacus, then sliderule, with the calculator last.

I wonder if that was a fair test. I mean, the abacus and slide rule users probably had years of practice, whereas the calculator user was probably using a new tool he was unfamiliar with.

I bet if you had the abacus user use the slide rule, the slide rule user use the calculator, and the calculator user use the abacus, the results would have been VERY different.

posted 6 years ago

What do you mean, fair? Yes, the Korean engineer had been using his abacus since he was 5, and all the sliderule using engineers had been using them daily since they were 20. These guys were in their late 30s on up.

I expect that there was an exponential decay curve on the ability of the abacus/sliderule guys to beat the nubie calculator folks. But I"m sure that it was several years before it came close. Whether the crossover was 5 or 10 years is not important, I think it has happened by now. But maybe not, the abacus guy was very fast.

BTW: there was a huge war in the Engineering College over whether or not to allow programmable calculators in tests/exams. No one cared about the four function cheapies, but a good programmable calculator cost about $500, which was more than a term of tuition. A few years after I graduated, the war was over, and slide rules were obsolete.

fred rosenberger wrote:I wonder if that was a fair test. I mean, the abacus and slide rule users probably had years of practice, whereas the calculator user was probably using a new tool he was unfamiliar with.

What do you mean, fair? Yes, the Korean engineer had been using his abacus since he was 5, and all the sliderule using engineers had been using them daily since they were 20. These guys were in their late 30s on up.

I expect that there was an exponential decay curve on the ability of the abacus/sliderule guys to beat the nubie calculator folks. But I"m sure that it was several years before it came close. Whether the crossover was 5 or 10 years is not important, I think it has happened by now. But maybe not, the abacus guy was very fast.

BTW: there was a huge war in the Engineering College over whether or not to allow programmable calculators in tests/exams. No one cared about the four function cheapies, but a good programmable calculator cost about $500, which was more than a term of tuition. A few years after I graduated, the war was over, and slide rules were obsolete.

pete stein

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Mike Simmons

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posted 6 years ago

I would think that the speed of these devices also depends a lot on what type of operations you're doing. Addition and subtraction are probably where the abacus has the biggest advantage. I think it would be slower at multiplication, but I'm not sure. Certainly if you do square roots or trig functions, the calculator and slide rule will do much better than an abacus.

I'm 42 and never ever learned to use a slide rule in any class. Or even saw one (in class). Naturally they were mentioned when learning about logarithms in Calculus class, but only in passing. A few years later I got hold of an actual slide rule at a yard sale or something and had a lot of fun figuring out how to use it. Sure, the basics of how to multiply two numbers, that's easy. But a good slide rule has a bunch of different scales on it, including trig functions and more. Figuring out how to use them all together efficiently was fun. Of course I never practiced enough to get

I'm 42 and never ever learned to use a slide rule in any class. Or even saw one (in class). Naturally they were mentioned when learning about logarithms in Calculus class, but only in passing. A few years later I got hold of an actual slide rule at a yard sale or something and had a lot of fun figuring out how to use it. Sure, the basics of how to multiply two numbers, that's easy. But a good slide rule has a bunch of different scales on it, including trig functions and more. Figuring out how to use them all together efficiently was fun. Of course I never practiced enough to get

*good*at it, but at least I enjoyed figuring out the principles.
posted 6 years ago

It was a long time ago, I'm not sure what we tested. But multiplication is just lots of additions. You can do it long hand on paper, and the exact same process works in an abacus.

Square roots on a slide rule are instant, there is a scale that does it, just line up the number on one scale, read the square root on another. Same with trig functions on the fancier versions. The number of scales is what made it a "pro" slide rule. Mine had ten scales, it was a Log Log Decilog scale, with orange leather case for your belt.

At my university in the late 60s up until the end of the slide rule, there was a required class named Engineering Economics that everyone took their first term as a sophomore. By the catalog, it taught how to do present worth calculations to see if a particular engineering solution was cost effective. In practice, it was a speed test of the non-trivial use of the slide rule. You simply could not pass that class unless you could really use a serious slide rule. It was a weed course for folks who survived Calculus but still were not engineering material.

[a "weed" course is designed to weed out the folks who don't belong in the program. Its required, and hard. Separates the wheat from the chaff.]

Mike Simmons wrote: I think it would be slower at multiplication, but I'm not sure. Certainly if you do square roots or trig functions, the calculator and slide rule will do much better than an abacus.

It was a long time ago, I'm not sure what we tested. But multiplication is just lots of additions. You can do it long hand on paper, and the exact same process works in an abacus.

Square roots on a slide rule are instant, there is a scale that does it, just line up the number on one scale, read the square root on another. Same with trig functions on the fancier versions. The number of scales is what made it a "pro" slide rule. Mine had ten scales, it was a Log Log Decilog scale, with orange leather case for your belt.

Mike Simmons wrote: I'm 42 and never ever learned to use a slide rule in any class. Or even saw one (in class). Naturally they were mentioned when learning about logarithms in Calculus class, but only in passing. A few years later I got hold of an actual slide rule at a yard sale or something and had a lot of fun figuring out how to use it. Sure, the basics of how to multiply two numbers, that's easy. But a good slide rule has a bunch of different scales on it, including trig functions and more. Figuring out how to use them all together efficiently was fun. Of course I never practiced enough to getgoodat it, but at least I enjoyed figuring out the principles.

At my university in the late 60s up until the end of the slide rule, there was a required class named Engineering Economics that everyone took their first term as a sophomore. By the catalog, it taught how to do present worth calculations to see if a particular engineering solution was cost effective. In practice, it was a speed test of the non-trivial use of the slide rule. You simply could not pass that class unless you could really use a serious slide rule. It was a weed course for folks who survived Calculus but still were not engineering material.

[a "weed" course is designed to weed out the folks who don't belong in the program. Its required, and hard. Separates the wheat from the chaff.]

Mike Simmons

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posted 6 years ago

Sure. Of course the most naive interpretation of "lots of additions" is hopelessly inefficient for many applications. But:

Sure. It's obvious that it's

Which is why I didn't bother differentiating between slide rules and calculators here. They're both fairly comparable, I suspect. At least for the first two or three significant digits.

Which, BTW, is a major benefit of slide rules that I omitted earlier: people who used slide rules were much less inclined to give an answer as 1.23456789 when 1.23 would do. Or to believe that those later digits matter at all. Because usually, they don't.

Hmmm, "log log decilog" sounds familiar. I think that was written on the slide rule I studied. I think it indicated that the first and second horizontal regions of the rule were calibrated in terms of natural logs, while the third region was calibrated in terms of log base ten. Does that sound right?

Ah, cool. I remember reading (in the course catalog) about an Engineering Economics course that sounded cool. It wasn't required at that point, and I knew no one who took it. From your comments, I suspect it was a leftover from an earlier course. Seems like the original course required two important skills, mastery of the slide rule, and hard-nosed cost-benefit analysis. That course was later viewed as unimportant because the former skill became irrelevant. Yet the latter skill remains important in many, many contexts. I hope they found a way to bring that back in some class somewhere.

Or, the wheat from the weeds.

Pat Farrell wrote:Mike Simmons wrote: I think it would be slower at multiplication, but I'm not sure. Certainly if you do square roots or trig functions, the calculator and slide rule will do much better than an abacus.

It was a long time ago, I'm not sure what we tested. But multiplication is just lots of additions.

Sure. Of course the most naive interpretation of "lots of additions" is hopelessly inefficient for many applications. But:

Pat Farrell wrote:You can do it long hand on paper, and the exact same process works in an abacus.

Sure. It's obvious that it's

*possible*to do this. It's less clear how fast it is compared to the alternatives.

Pat Farrell wrote:Square roots on a slide rule are instant, there is a scale that does it, just line up the number on one scale, read the square root on another. Same with trig functions on the fancier versions.

Which is why I didn't bother differentiating between slide rules and calculators here. They're both fairly comparable, I suspect. At least for the first two or three significant digits.

Which, BTW, is a major benefit of slide rules that I omitted earlier: people who used slide rules were much less inclined to give an answer as 1.23456789 when 1.23 would do. Or to believe that those later digits matter at all. Because usually, they don't.

Pat Farrell wrote: The number of scales is what made it a "pro" slide rule. Mine had ten scales, it was a Log Log Decilog scale, with orange leather case for your belt.

Hmmm, "log log decilog" sounds familiar. I think that was written on the slide rule I studied. I think it indicated that the first and second horizontal regions of the rule were calibrated in terms of natural logs, while the third region was calibrated in terms of log base ten. Does that sound right?

Pat Farrell wrote:At my university in the late 60s up until the end of the slide rule, there was a required class named Engineering Economics that everyone took their first term as a sophomore. By the catalog, it taught how to do present worth calculations to see if a particular engineering solution was cost effective. In practice, it was a speed test of the non-trivial use of the slide rule. You simply could not pass that class unless you could really use a serious slide rule. It was a weed course for folks who survived Calculus but still were not engineering material.

Ah, cool. I remember reading (in the course catalog) about an Engineering Economics course that sounded cool. It wasn't required at that point, and I knew no one who took it. From your comments, I suspect it was a leftover from an earlier course. Seems like the original course required two important skills, mastery of the slide rule, and hard-nosed cost-benefit analysis. That course was later viewed as unimportant because the former skill became irrelevant. Yet the latter skill remains important in many, many contexts. I hope they found a way to bring that back in some class somewhere.

Pat Farrell wrote:[a "weed" course is designed to weed out the folks who don't belong in the program. Its required, and hard. Separates the wheat from the chaff.]

Or, the wheat from the weeds.

posted 6 years ago

Remember how they taught you do do multi-digit multiplication in grade school. Write the two numbers down, one over the other with a line under the bottom one.

what you did was multiple 7 times 123 and write it down. Then multiply 6 times 123 and write it under the first answer, moved over one digit. Then multiply by 5, write it down, then by 4 and write it down then add up the four numbers under the ----- line.

You do the by-digit multiplication in your head, as you learned in earlier grades. The abacus was great at addition. And keeping partial totals is why there are so many columns on the abacus.

No!, its not that 1.23 "will do" its that 1.23 is correct, and 1.23456789 is fiction. When you do many typical calculations, you start with measurements, and the measurements have only a few digits of precision, in your 1.23, there are two digits of precision. All that the "3" does is tell you reliably that the real measurement is somewhere between 1.20 and 1.26, and it most likely is near 1.23, but 1.24 or 1.22 is equally likely. It is both pointless and wrong to pretend that you have ten digits of precision just because the computer calculated it.

Plus, in nearly all real engineering, you either buy parts that come in only a few fixed sizes (bolts are 5mm, 7mm, 10mm, never 5.4mm) or you have to throw in a safety factor of 3 to cover slop in the construction (concrete workers love to have lunch on the forms and throw their lunch bags into the form where they will be pouring concrete in a few minutes). Its simply wrong to think you can buy say a 4.789 horsepower motor. You buy a 5 HP motor, because that is what the make and sell.

Mike Simmons wrote:It's obvious that it'spossibleto do this. It's less clear how fast it is compared to the alternatives.

Remember how they taught you do do multi-digit multiplication in grade school. Write the two numbers down, one over the other with a line under the bottom one.

`123`

4567

-------

4567

-------

what you did was multiple 7 times 123 and write it down. Then multiply 6 times 123 and write it under the first answer, moved over one digit. Then multiply by 5, write it down, then by 4 and write it down then add up the four numbers under the ----- line.

You do the by-digit multiplication in your head, as you learned in earlier grades. The abacus was great at addition. And keeping partial totals is why there are so many columns on the abacus.

Mike Simmons wrote: people who used slide rules were much less inclined to give an answer as 1.23456789 when 1.23 would do.

No!, its not that 1.23 "will do" its that 1.23 is correct, and 1.23456789 is fiction. When you do many typical calculations, you start with measurements, and the measurements have only a few digits of precision, in your 1.23, there are two digits of precision. All that the "3" does is tell you reliably that the real measurement is somewhere between 1.20 and 1.26, and it most likely is near 1.23, but 1.24 or 1.22 is equally likely. It is both pointless and wrong to pretend that you have ten digits of precision just because the computer calculated it.

Plus, in nearly all real engineering, you either buy parts that come in only a few fixed sizes (bolts are 5mm, 7mm, 10mm, never 5.4mm) or you have to throw in a safety factor of 3 to cover slop in the construction (concrete workers love to have lunch on the forms and throw their lunch bags into the form where they will be pouring concrete in a few minutes). Its simply wrong to think you can buy say a 4.789 horsepower motor. You buy a 5 HP motor, because that is what the make and sell.

Mike Simmons

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posted 6 years ago

Um, OK. If you want to spell out this stuff slowly for others, fine - but please don't do it for my benefit. My comment was that it's not immediately clear which technique is faster. That still isn't clear. Please don't assume that means I have no idea how to do multiplication on an abacus.

This, I agree with, actually. I was being overly tolerant of stupidity when wrote that. People who quote (or believe) excessive sig figs are simply wrong, and shouldn't be coddled.

[quotes fixed after edit]

Pat Farrell wrote:Remember how they taught you do do multi-digit multiplication in grade school...

Um, OK. If you want to spell out this stuff slowly for others, fine - but please don't do it for my benefit. My comment was that it's not immediately clear which technique is faster. That still isn't clear. Please don't assume that means I have no idea how to do multiplication on an abacus.

Pat Farrell wrote:Mike Simmons wrote:people who used slide rules were much less inclined to give an answer as 1.23456789 when 1.23 would do.

No!, its not that 1.23 "will do" its that 1.23 is correct, and 1.23456789 is fiction.

This, I agree with, actually. I was being overly tolerant of stupidity when wrote that. People who quote (or believe) excessive sig figs are simply wrong, and shouldn't be coddled.

[quotes fixed after edit]

posted 6 years ago

Very little in life is faster than simply multiplying two numbers with a slide rule. That what it is designed to do. But adding two numbers with a slide rule is not fun, since it doesn't help there.

What most folks don't grok is how fast an experienced abacus user can sling the beads. Its comparable to a professional typist on a keyboard. My Korean friend was tons faster with his fingers than we were on the ten-key pad of the calculator. Its a motor skill question. Similar to watching a good CPA or bookkeeper doing taxes on an adding machine, the keys are flying and the paper jumps up out of the machine. Or watching an experienced gamer blow away bad guys in a first person shooter.

What most folks don't grok is how fast an experienced abacus user can sling the beads. Its comparable to a professional typist on a keyboard. My Korean friend was tons faster with his fingers than we were on the ten-key pad of the calculator. Its a motor skill question. Similar to watching a good CPA or bookkeeper doing taxes on an adding machine, the keys are flying and the paper jumps up out of the machine. Or watching an experienced gamer blow away bad guys in a first person shooter.

posted 6 years ago

An ancient 17th century instrument for doing calculations, which people used before electronic calculators were invented in the 1970's.

Bert Bates

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Sheriff

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posted 6 years ago

I still have mine - my Dad gave it to me when I was in high school - just before calculators were affordable. It's beautiful; wonderful craftsmanship and materials (bamboo and so on).

I haven't used it in years, but as I recall, the other benefit to slide rules is that the pilot has to be able to estimate the order of magnitude of the answer. IMHO, the ability to estimate is an important, and increasingly lost art.

I haven't used it in years, but as I recall, the other benefit to slide rules is that the pilot has to be able to estimate the order of magnitude of the answer. IMHO, the ability to estimate is an important, and increasingly lost art.

Spot false dilemmas now, ask me how!

(If you're not on the edge, you're taking up too much room.)

pete stein

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Posts: 1561

posted 6 years ago

And my dad gave me his as well. It felt almost that it was made from ivory and was a thing of beauty.

Heck, the ability to do simple algebra is becoming a lost art. I was doing simple high school geometry review with my daughter two nights ago, and she felt lost because she couldn't find her calculator and had to stumble through some very basic multiplication. Sad.

Bert Bates wrote:I still have mine - my Dad gave it to me when I was in high school - just before calculators were affordable. It's beautiful; wonderful craftsmanship and materials (bamboo and so on).

And my dad gave me his as well. It felt almost that it was made from ivory and was a thing of beauty.

I haven't used it in years, but as I recall, the other benefit to slide rules is that the pilot has to be able to estimate the order of magnitude of the answer. IMHO, the ability to estimate is an important, and increasingly lost art.

Heck, the ability to do simple algebra is becoming a lost art. I was doing simple high school geometry review with my daughter two nights ago, and she felt lost because she couldn't find her calculator and had to stumble through some very basic multiplication. Sad.

posted 6 years ago

This is a key benefit. With a slide rule, you could not just enter data and get an answer and have zero clue what it meant. You only got 3 or so digits of precision and nothing about the order of magnitude, so you had to know that before hand.

A related good thing is to work out the units when you are multiplying a long string of things. If you start with revolutions per minute and multiply by foot and then by pounds, if you didn't expect to get revolution-feet-pounds per minute, you did something fundamentally wrong. Horsepower times RPM is torque, so it had better work out that way.

Bert Bates wrote:the other benefit to slide rules is that the pilot has to be able to estimate the order of magnitude of the answer. IMHO, the ability to estimate is an important, and increasingly lost art.

This is a key benefit. With a slide rule, you could not just enter data and get an answer and have zero clue what it meant. You only got 3 or so digits of precision and nothing about the order of magnitude, so you had to know that before hand.

A related good thing is to work out the units when you are multiplying a long string of things. If you start with revolutions per minute and multiply by foot and then by pounds, if you didn't expect to get revolution-feet-pounds per minute, you did something fundamentally wrong. Horsepower times RPM is torque, so it had better work out that way.

Bert Bates

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Sheriff

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posted 6 years ago

In high school our chemistry teacher taught us what he called the "factor-label" method... Just exactly what you're talking about. For instance this helps you calculate the speed of light in furlongs per fortnight.

A related good thing is to work out the units when you are multiplying a long string of things. If you start with revolutions per minute and multiply by foot and then by pounds, if you didn't expect to get revolution-feet-pounds per minute, you did something fundamentally wrong. Horsepower times RPM is torque, so it had better work out that way.

In high school our chemistry teacher taught us what he called the "factor-label" method... Just exactly what you're talking about. For instance this helps you calculate the speed of light in furlongs per fortnight.

Spot false dilemmas now, ask me how!

(If you're not on the edge, you're taking up too much room.)

John Eipe

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posted 5 years ago

They had one in the EE department's lab when I was an undergraduate. It was very cool looking. Lots of sliders, patch panels, capacitors and inductors. At least a student could go up and touch it. The university-wide "computer" was a IBM/360 in the usual glass walled facility surrounded by high priests, altar boys, and the othe select few.

But I never has a good excuse to use the analog computer. At the time, my work was all on punch cards.

John Eipe wrote:"analog computer" that's something! I had never used one before.

They had one in the EE department's lab when I was an undergraduate. It was very cool looking. Lots of sliders, patch panels, capacitors and inductors. At least a student could go up and touch it. The university-wide "computer" was a IBM/360 in the usual glass walled facility surrounded by high priests, altar boys, and the othe select few.

But I never has a good excuse to use the analog computer. At the time, my work was all on punch cards.

Frank Silbermann

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posted 5 years ago

Do you remember magazines with ads selling posters by mail? One had this gauzy romantic photo of a woman walking through a wheat field with Hallmark-Card style cursive/italic message along the lines of: "Why do I love him? Is it because of his smile? His wavy hair? The way he looks at me? No, I love him so much because he knows calculus." Then it the bottom in smaller print it said "Brought to you by the American Mathematical Society."Ernest Friedman-Hill wrote:A friend and I taught ourselves to use them in 4th grade (you can imagine how popular that made us with the ladies.) This would have been 1973 or so.

Vikram Shah

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posted 5 years ago

I think that a slide rule is important to understanding logs, and also just history in general. Now everyone at school has a Texas Instruments graphing calculator that can even solve multi variable equations, but people forget that before the calculator, people were able to build the Apollo Rockets and the Golden Gate Bridge...

I'm currently in high school but I can multiply and divide on a slide rule.

I'm currently in high school but I can multiply and divide on a slide rule.