Using a slide rule to solve a 19th century exam
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- čas přidán 19. 06. 2024
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i finally get why these exams are so easy. The real challenge is using this apparatus to calculate!
Makes you really appreciate our multiplication algorithms
The multiplication algorithms are even older than slide rules.
@@dannygjk How old are they?
@@nicolaebacrau355 Hundreds of years old at least. Even calculus is hundreds of years old.
My AG mechanics professor gave us extra credit if we used a slide rule instead of a digital calculator on our tests. I was the high individual at the state AG mechanics competition so it must have done something for me.
....Dear God man, is there anything u didnt do. UK farming, mechanics , geology, chemistry, mining , physics etc
Huge Fan btw
I guess cutting your reliance on calculators really forces you to understand what you’re doing 😂
Fancy seeing you here
Even further credit if you had built your own slide rule?
My dad is a car mechanic. When I showed up with my TI-85 in the early 90s, he laughed at me. He could do most calculations requiring three significant digits almost as easily on the slide rule as I did on the calculator.
Back in the late 1960's when I was in my early 20's I purchased a cylindrical slide rule which gave more accurate results than a straight ruler sized slide rule. Was also very handy as it could easily fit into one of my jacket pockets. Used it frequently until 1974 when I was able to buy my first pocket calculator. Sadly, my cylindrical slide rule got lost over the years. Wish that I still had it to show my ever curious grandaughter.
I found 2 on eBay.
@@johnstonewall917 Thanks. Have also seen some on eBay and elsewhere, but none as high quality as the one I owned. It had a light brown real leather case in which to keep it. Looked really great and used to impress people hugely whenever I produced it from my pocket to tackle a difficult calculation.
@@leonardharris9930 Was yours an Otis King? I have one with the 414 and 423 scales (I think this is the model K) and the other has the 429 and 430 scales, perhaps the model L.
I used a straight side rule in highschool. We were able to get 3 digits accuracy. I didn't know there was a cylindrical side rule. Thanks for bringing that up.
The beauty of using a slide rule is that it forces you to keep numbers and significant digits in your head, fostering your ability to process math quickly in your head. I learned how to use slide rules in High School and my Dad gave me his old Dietzgen which I kept until recently. What I liked about slide rules during exams is that you never had to worry about your batteries draining! Also, back then, if your answer was generally within 5% of the expected answer, it was good to go.
Thanks for the video as it brought back memories. Wish there were pretty mathematicians like you when I was in college. Cheers!
That's what I don't get about slide rules...an acceptable margin of error in your answer. I thought math was either right or wrong. 1 + 0.999 = 1.999, not "oh, let's just call it 2". Perhaps I'm just not understanding something.
dave29123 it was used primarily for science and engineering where measurements and significant digits are more practical. Just because you have a calculator that can give you the answer to the billionth of a mm it doesn’t matter because you don’t need that level of precision
@@JeffreyBue_imtxsmoke or that you could even manufacture or measure something to that precision
@@dave29123 You can see in the slide rule in the video that there are markings. We cannot have an infinite amount of markings, so there is a point at which we need to round.
Think of a ruler, you might measure something that is 12 cm and between the .5 and .6 mark to 13. So it's around 12.55 cm. The actual value might be 12.5398 cm but we can't measure to that accuracy with a ruler.
It's the same with a slide rule, while a slide rule is more accurate than most rulers are, you cannot give an exact, and some students might say 12.55cm and some might say 12.57 cm. It doesn't make your answer wrong, because that's just the degree of technology.
Nowadays, schools are more critical about your precision in the answer, because digital calculators allow for it.
choosing why i am watching your videos :
(A) i love math
(B) i love her
(c) cannot choose
B
I love her math.
Damn, I wish I could understand what she talks about...
(D) A and B
I dont know yours but i am watching due to option A and B 😙😙😙
My high school physics class had one inside a fire extinguisher box with a sign beneath it that read, "In case of battery failure, break glass." Our desks also had log rules laminated into the desks. :P
And I'm not _that_ old, either. That was back in 1996 or so. Also, my dad still has his from his CalTech days though he hardly used it because it was quickly replaced by a calculator. And he also had this really cool (and loud) wooden crank calculator for doing differentials.
In the first question, when you multiplied 32/9 by 31/24, you know that 32 x 31 ends in a 2 because 2 x 1 is 2, and that 9 x 24 ends in a 6 because 9 x 4 is 36. I imagine that the people who sat this exam did those multiplications in their heads......"32 x 30 is 960, plus 32 is 992" and "9 x 24 is 240 minus 24 which is 216".
I did my engineering degree with a slide rule and log tables....loved it as it kept my brain sharp! That was exactly 43 years ago!!
Best ASMR channel on you tube !
Steady, now.
And is not even an ASMR channel 😂
Xdxdd
Did my degree with slide rule and log tables. If all you need to do is multiply and divide, you don't need to write down intermediate steps. The first sum would be multiply 32 by 31 then divide by 24 and divide by 9. By inspecting the numbers the answer should be between 4 and 5 so no need to worry about where the intermediate decimals go. I dug out my old slide rule and got an answer of 4.59. The calculator gets 4.5925.
But why not simplify first? That way, it would only be 4*31/(9*3), so one would actually only need the slide rule for dividing 124 by 27
(Also the third question can be solved by simplification if one can "see" that 288 is actually a multiple of 36)
@@ElchiKing Yes I noticed by inspection that 32 and 24 are multiples of 8 so it simplifies to 124/27 as you pointed out.
@@ElchiKing _"But why not simplify first?"_
Because it doesn't really save any time.
I'm with Elchi King - 4·31/(9·3) = 124/27 = (108+16)/27 = 4 + 16·.[037] = 4.[592] (where numbers in brackets repeat infinitely)
And 288 = 2·144 = 4·72 = 8·36, so 2880/.0036 = 28,800,000/36 = 288·100,000/36 = 8·100,000 = 800,000
Fred
you can solve the last significant figure just by multiplying out the last 2 digits of each numerator and denominator, e.g. 2*1 = 2... so should be 992 .... 4*9 = 36, so should be 216
yes!!
It’s also worth noticing when you can reduce fractions. 32 and 24 can be exchanged for 4 and 3 without losing precision. That makes even more potential for error go away!
“Exercise for the viewer” HAHAHAHA. It sounded just like math books when they tell you to demonstrate an equation.
Wouldn't that involve getting some sticks & cardboard & marker pens, and making protest signs?
Fred
This brings back some interesting memories when I used slide rules (sometimes called "slipsticks") back in the early 70's. It is really amazing how accurately you can do calculations with them. Thank you, Toby!
Slide rules can be still bought on ebay for reasonable prices. Notable brands include Keuffel & Esser, Post, Hemmi, Pickett, Dietzgen, Nestler, Faber-Castell, Aristo, Concise, Flying Fish, and Staedtler-Mars. For those people who are proficient with mathematics & physics, then get a log-log type slide rule capable of involution & evolution of numbers using common & natural logarithms rather than getting a basic slide rule. Look for undamaged slide rules that are still complete with their original parts and storage cases. Some even come with their original instruction manual. Don’t buy a slide rule that has been damaged, warped or has missing parts because it will not work properly.
I just got mine today, a Dietzgen from 1958 with training manuals! I received a larger one and a smaller one.
This is exactly why engineers (the older ones...) are still very good at doing calculations without any tools.
Thanks for the interesting video. I still have my school slide rule, and can still use it. It's often quicker than a digital calculator, if you are practised at using it, and it never needs a battery. Regular use teaches you mental arithmetic, too. To the point that you might not even need a calculator for many figures. For many things in engineering and the sciences, a slide rule is more than accurate enough for practical use, and is actually better than what can be made or constructed in practise.
Contrary to the popular myth, NASA did not use slide rules to get into space; initial calculations were often made by human computers, at least one of whom (a lady called Johnstone) received an award this year, and she's in her 90's. Slide rules were used for rough calculations to 2 or 3 decimal places, and as a means of checking for gross errors. But they're not accurate enough for things like plotting accurate trajectories for going to the Moon and back. Digital computers were used more frequently, a few years later later.
I used slide rules in high school and college, switching from straight rules to circular ones to eliminate running off the end of the scales. The HP35 calculator came out as I was finishing college. In your first problem, the results on a typical 10 inch (25 cm) scale rule would give 32 x 31 as a little over 990, which a student would take as 992 because the product of the units digits is 2. Similarly, 9 x 24 would be 216. Use of a slide rule entails also using some math for reasonableness checks. I have an 8 inch (20 cm) diameter circular rule that gives 992 and 216 directly and gives an approximate answer of 4.5925 for the division.
I was going to post the same thing.
That's the thing that's often missed: the tool didn't do all the work for you; you the user were expected to apply mathematical common sense (which, as I remember, was actually a statement in slide rule manuals). I will say that keeping track of the decimal when you were doing running calculations could get to be mind-numbing (as were the three or four times you re-ran the calculations to make sure you didn't screw the pooch).
@@terpcj It's interesting that in the U.S. "screw the pooch" means make a mistake/screw up in some way but where I live in Canada screw the pooch, (except people normally say it as "f**k the dog"), means to do nothing or next to nothing when you are supposed to be working.
Up until I did Year 10 in 1979 we used log tables to do multiplication and division. We also used them for trig functions. For years 11 and 12 (1980 and 1981 for me) we were able to use a pocket calculator. However my parents could not afford to buy me one, so I was the only student in my year 12 at school who did their maths exam using log and trig tables. It did affect my result somewhat because it was a lot slower and I ran out of time!
We weren't allowed to use calculators until year 11 (Australia). In the first semester of year 11 we weren't allowed to use calculators in the maths exams because we were learning to use log tables.
I was in a similar position to you: my parents couldn't afford to buy me a calculator until halfway through year 11, and until then in the other subjects where we could use calculators (physics, chemistry, applied mathematics) I used a slide rule. Also like you, my results in those subjects in that semester were adversely affected because it took me longer to do calculations.
I never sat an exam where we were allowed to use a digital calculator until at tertiary education. But even then, the rules stipulated that we were not allowed to connect them to an AC supply. Used a slide rule and trig tables right through to my 4th year at uni (an extra year for a second, higher qualification). I was the only one not using an electronic device. Then for the final year, 1977/8, I had a TI-28 scientific calculator for the final exams (they were very expensive, so mine was bought, second user, for more than 5 weeks' rent). Never had a problem with running out of time, because tables and slide rules are just as quick, maybe quicker, for most of the time.
Ahh, the mythical 'good old days'!
@@vk2ig g0mrb here.
@@RWBHere Hi G0MRB :)
Unfortunately, I was always quicker on a calculator than a slide rule or log tables. And I think the tests were timed on the basis of everyone having calculators. My biggest bugbear was that I had difficulty demonstrating my knowledge of the physics concepts due to the time it took to do calculations in the exams - evidence of this was in year 12 I blitzed the electronics unit (with a calculator in the exam), and some four years later when I went to university and studied effectively the same material in the first year of my engineering degree course, I got very high marks in the physic subject ... but I had a calculator in the exams. :-)
Up to 2005 I believe the exam provided a table for the normal distribution in the year 12 Maths methods exam in Victoria.
Hi Toby! If the product goes off the end of the scale, just divide using the reciprocal (Cl scale) instead, it saves writing down numbers and all intermediate results are "saved" under the cursor. I used one in school back in the 60s (not 1860s) instead of log tables and nobody knew what I was doing. I still have my Faber-Castell 10 inch rule and when I was proficient with it, I graduated to a 7 inch double-sided one and use them to keep my mental arithmetic skills good. Then I was spoiled by HP calculators with Reverse Polish Notation, the HP41CV was the best ever!
I graduated from engineering school in 1973 and used a slide rule throughout my entire undergrad years. I knew how to use each of the 12 scales. We put men on the moon with slide rules.....and mainframe computers.
Hey tibees, I'm from Brazil and want to go into ITA (AERONAUTICS INSTITUTE OF TECNOLOGY) so I think It would be nice if you showed their entrance exam just for your Brazilian audience to see how it would look like from a foreigner's perspective. Thanks for the channel! You are awesome!
up prova do Ita é hard
@@brenofilho3320 Queria saber oq ela vai achar, acho q pra ela vai ser bem tranquilo
UPPPP segunda fase do IME é hard tbm
Por fin un hermano latinoamericano, pense que era el único, saludos desde Chile :D
Question 10 from the sample phase 2 math test appears to be impossible.
"Escolhem-se aleatoriamente três números distintos no conjunto 11,2,3,...,29,301. Determine a probabilidade da soma desses três números ser divisível por 3"
I loved my slide rule! I used both slide rule and calculator for a while. Early calculators were not much more than add, subtract, multiply, divide and square root. And in college, I had a small pocket slide rule, the center stick doubled as a drink stirrer. The great thing about a slide rule was that it didn't mess with your idea of accuracy. Calculators with their 6 or 7 decimal points make you think that you have accuracy to that level, and most times you don't. As for calculators, the only one I liked were the HP reverse polish notation machines. I could stack the constants of a formula and get the result faster than any algebraic notation machine. Still have one on my phone. Still love it. Oh, a slide rule app, that sounds like something fun to write.
My dad used a slide rule to design the landing gear for the space shuttle . They were widely used in engineering throughout the 70s.
I really appreciate the work u do.. plzzz never stop!!! just started loving u..
When multiplying the fractions, if you had cancelled out the common multiples first, the slide rule calculation would have been easier, and more importantly, more precise, as you would not have run into the low precision end of either scale. Enjoyed the presentation anyway. BTW when I qualified, the slide-rule was a state-of-the-art device and its use was likened almost to cheating. 😂
I love the homemade slide - very creative! :D
This was a suggested video when I was watching LMES, an excellent engineering channel in tamil about the calculations in 1800's using Genaille-Lucas ruler. I love this way of computing, but honesty, I didn't get a chance to use it till now.
I just dug around and found my Pickett from high school. It was in my old drafting table box. Hadn't even thought about it in years. Precision tool. Your video takes me back to the 60's.
You could always tell the engineer/scientist in the 60’s - we had slide rules and pocket protectors! Big step up was the Friden electromechanical calculator - dividing by zero caused it to go nuts! Then the 4 function Nixie tube gadgets - ah, the good olde days!
It's worse when the divide-by-zero error occurs on an abacus - the beads end up all over the floor ...
Hahaha "olde".
Really cool this video about the slide rule and then using your own home-made paper slide :-)
I really really like your videos, think you're amazing and I appreciate a lot that you are making this kind of videos showing us new interesting things, but I think you should rest you deserve one, or at least try to take some breaks because you look tired and thats something that might affect your health. Cheers 😊 have a nice week
I actually have two slide rules (one with the vinyl case it came in), one is metal, and the other is plastic. My dad was big into calculating machines, and this was essentially the first pocket calculator.
Isaac Asimov has a great book on using slide rules (An Easy Introduction to the Slide Rule) that you can still find on Amazon.
I really love watching your channel. I find your voice very soothing.
I'm glad that we have an alternative algorithms in division and multiplication! It would take me forever to use that slide ruler :
Tibees I love your videos, I'm hoping you're not losing sleep to them though.
I'm a math teacher, and I became a mild slide rule enthusiast about 10 years ago. There's a really good paper one that was featured in Scientific American. I recently took it and added my own modifications and enhancements (LL scales for raising to powers, finding roots, and logs of different bases).
My father was one of the engineers at KSC during the Gemini and Apollo programs..still amazing to me what they accomplished using slide rules !
Slide rule was faster than a calculator once you got used to it, but like others have said, it wasn't super accurate like modern calculators
In high school chemistry and physics in the 80's, I didn't find the tests challenging enough. So instead of a calculator I used a slide rule. It annoyed my classmates.
Another great video! There's plenty of used slide rules on eBay these days as they are quite collectable. The tables brought back memories from the 70's when I was in high school.
Happy New Year 2019 @Tibees !!! 😍🍾🎉 🎆
Anyone who is interested check out how much time it took people to calculate the log tables.
It's not for the faint of heart. lol
For example:
"... a great collection, called Tables du Cadastre, was constructed under the direction of Gaspard de Prony, by an original computation, under the auspices of the French republican government of the 1790s. This work, which contained the logarithms of all numbers up to 100,000 to nineteen places, and of the numbers between 100,000 and 200,000 to twenty-four places, exists only in manuscript, "in seventeen enormous folios," at the Observatory of Paris. It was begun in 1792, and "the whole of the calculations, which to secure greater accuracy were performed in duplicate, and the two manuscripts subsequently collated with care, were completed in the short space of two years."
It's a lost art. Working two slide rules together was a very powerful technique to scope and develop concepts on some problems like multi body kinematics. Also, I remember that in some exams you would have to add next to the answer 'by slide rule'. I've still got mine (somewhere!).
We learned to use slide rules, In our 1970 Electronics Technology classes. Texas Instruments LED pocket calculators came out about that same time but they only did basic addition, subtraction, multiplication and division. It was very useful solving formulas with large numbers using scientific notation. For example: Resonant Frequency = 1/ (2 Pi x (Square Root of L*C))
It's good that you showed your audience how to use the slide rule and log tables; I'm sure that some of them may have wondered how complex calculations were done before the days of calculators and computers - those that realize there was a time before processor chips ;) But of course neither slide rule or logs would have actually been needed for the simple questions on this test.
It's interesting to watch someone trying to figure out the kind of math that I grew up with. Well done!
Slide rules only was the rule as a Physics major 1970-1974. The hardest part was keeping track of exponents. If your answer was 10**9 but the correct answer was 10**8, you got zero credit. The prof would say "You might be building a bridge some day."
I did my O levels with a slide rule and log tables. Had forgotten how to use a slide rule so thanks for this.
Chinese abacus [算盤] (2+5), Japanese soroban [そろばん] (1+4), Korean abacus [주판] (1+5), Pickett N-500-ES, and a plethora of Log and Trig tables.
Good video! Thank you.
I have used the log tables as a high school student in asia, we had calculators but they were not allowed in exams. We had a gigantic 20 feet slide rule in our engineering department at my PhD university in the US. My Russian PhD advisor once told me he knows how to use the slide rule as he had to use it when he was a student, a Chinese professor ( graduate of MIT) under whom I was a TA also told me that he knows how to use the slide rule, he used to say it's actually pretty straightforward.
You could explain where the 1 comes from when doing the log base 10 of 73 to reduce the mystery but of course the down side would be a longer video. :)
Slide rule got us to space. Calculator has gotten us twitter. I think we know which is the superior device.
The advantage of a slide rule over a calculator is that the user has to stay engaged in the reality of how big or small makes sense for the answer. The rule gives you nicely the digits.....but it is up to you to understand where the decimal should go. Students plugging something into the calculator will often blindly accept really preposterous results because they completely disengage from the process and just believe whatever number shows up on the little screen.
7:52 if you are confident with the first two digits, you can get the last digit by considering modular arithmetic modulo 10.
31 mod 10 = 1, and 32 mod 10 = 2,
their product will have a last digit of 2*1=2, so we get 992 (which is indeed the correct answer)
Similarly :
9 mod 10 = 9, 24 mod 10 = 4
4*9=36 which gives 6 as the last digit, so we get 216 (which is indeed the correct answer, your guess was an off by 1 error ;)
What's not to like about these videos. Keep it going, Tibees. They're great.
Ur pretty smart actually!! solving varies question papers !! Cool
When I was a young man I used slide rules and at one time I had a pretty good collection of them.
I saw an electronic calculator for the first time in 1972. Not only was the calculator simpler to use but it gave eight or ten significant figures whereas as a slide rule only gave three.
Because a calculator was way more accurate than a slide rule the slide rule got blasted into history.
Good working slide rules can be found in such places as thrift stores.
If you have an Android phone or tablet you can get a calculator emulator for little or nothing. (seven inch or larger tablets are best all sorts of emulators can be had.
One that's really smoking is Emu48. It emulates all sorts of HP calculators. If you emulate an HP48 or hp49 you can save your work to a file(s).
How do you smile While studying?
I cry.
Is everything going alright MSquare? Might be pseudobulbar affect (PBA). Maybe go and see a doctor or therapist. Hope you feel better mate :)
@@animationspace8550 Its because of the camera. Noone Smiles while studying.
MSquare Dance Videos well, call me „Noone“ then, I smile occasionally while studying. Don’t get me wrong, there certainly are times I‘m frustrated but overall, diving deep into a subject I‘m interested in makes me happy, that’s why I study in the first place.
Still have a Keuffel & Esser log log somewhere in the basement. Used circular ones for flying and have one on my watch for conversions if the phone battery is dead.
That blue pen has some sick tribal tattoos on it, gets a like from me.
Unironischer Antinatalist it's the erasable Frixion pen from Pilot
I have 2 of them, took them from my grandpa's office because they looked interesting. Never knew what to do with them. Stumbled over this video and now i'll try using it.
This dear woman saved me when parachuting in Russia . My chute did not open ,we landed safely laughing.Thank you dear.
I still have an old slide rule in the shed, I never really got much into calculators but jumped straight to computers, ending up using 80bit doubles for sparse matrix solving (for electronics simulators) done in hardware.
The interesting point of our technology - of which the slide rule is a milestone, freeing us from books of tables - is that the world's monolithic structures such as the base stones of Baalbek, the major pyramids etc must have involved a certain amount of maths. The quantity surveyor team for the Great Pyramid couldn't have just used beads or chalk marks.. no one ever found any notes about how much stone to order for the capstone, cladding, edging or granite chambers either yet it must have been calculated. IMO they are too precise to have been made on a 'send me a few more stones' basis. Perhaps theres a binary abacus waiting to be found?
I dont know man, my heart melted!
I have a few slide rules that my grandfather used in the Army. I also have used a type of slide rule called an E6-B for flight planning. I am pretty sure they wouldn't use a slide rule for these. Looking up on the table then adding the logs, then looking up the anti-log takes much longer.
👍👍👍 I just went to find my slide rule, it's a "BEST" brand, model No 102B and I still have the instructions that came with it. I can scan & send them to you if you want. Thanks for the great S-R tutorial.
I have several space age slide rules that I found on EBay. A miniature Pickett model of the type that went to the moon on The Apollo Lunar Excursion Module (LEM), and an antique German Nestler 23 which was the personal slide rule of Wehner von Braun, Albert is Einstein and, (so I’ve heard) Sergei Korolyev-Korolyev’s magic wand”. It’s amazing to think about what they accomplished back when computers were made of vacuum tubes.
The last time I saw one was in school back in 1987. They used them in my math class, drafting class, and in my machine shop, but we weren't required to use them in any of the classes. We didn't get very much training with them. The drafting teacher and the shop teachers carried one with them all the time.
This is awesome!
A little surprised slide rules were used for Moon trajectory calcs. I used a slide rule for a while in high school. The problem is, that even the best are only about 0.1% precise and over use, the accuracy usually decreases as well. They were great for ball park estimates or for double checking that answers were in the ball park, but for high precision tasks, tables were more precise. The first mechanical machines, were used for calculating tables, taking the errors out of the hand made calc method's that had been used in table manufacturing before them.
We spent of lot of time learning the slide rule from Mr. Ganter in 8th grade math class..Just shows how old I am... I don't think I got a Texas Instruments LCD calculator (the red numbers) until I graduated high school in 1974...thanks for the video...
Pilots use circular ones to calculate true airspeed speed, distance, fuel consumption, density altitude, and convert between units. There is also a wind triangle plotter and they don't need batteries. Have a look at /watch?v=uNFNFZq2BFY 1:42 and you will see the pilot use one. Foresters also use them as damp dripping forests are not kind to calculators and smartphones!
I used my slide rule at university (chemistry) during the years 1970-1972. It was a Faber Castell novo-duplex which gave you an accuracy of 4 digits. With it, I was capable of solving all the exercises our professor threw at us... in inorganic and organic chemistry.
In fact, it required a lot of mental arithmetic too because the slide-rule gives you only digits. Therefore, you needed mental math to calculate an approximate result which later on was confirmed by slide rule. Do not worry, after a while you really become an expert in mental arithmetic.
By the way, because of Tibees's commentary, I now looked again at this slide rule and could not understand a jot of it.
That seems way more time consuming than just doing the multiplication by hand. Plus, no tables or tools needed than way.
Good luck reversing a log in your head. :) Also trig functions.
For smallish numbers yes people did it by hand. One thing tho with practice you can do chains of calculations quickly with a slide rule keeping intermediate results in your head. If 4 or more significant digits are required tho you have to do things by hand.
@@dannygjk Hand multiplication with numbers like 73x19 (Q2) involves only 2 steps really, one multiplication & one addition. Numbers like 22x63 would involve 3 steps, two multiplications & 1 addition. Hand multiplication like this really isn't much work & you can do it very quickly if you have your multiplication tables until 10 memorized.
_"That seems way more time consuming than just doing the multiplication by hand."_
Once you get some experience, using a slide rule is much faster than doing calculations by hand.
@@flowerdolphin5648 Are kids still memorising multiplication tables? Young shop assistants don't seem to any more. My generation learned 1 to 12 times (for shillings and pence) and also 14 and 16 times tables (for pounds and ounces).
Nice, thanks to show this to us !
Btw I hope that one can do faster calculations with such tool, when used to it, because I'm sure I can solve all those problems faster with just a paper and a pencil.
Yep, I was indeed using a slide rule and log tables in school back in the 70's. That's the 1970's not the 1870's ! Back then the slide rule did indeed feel like a bit of wizardry to use..
I'm just old enough to remember there being large demonstration slide rules mounted on the walls of the math classrooms in my high school... but too young to ever see them actually being used. They were basically relics they just hadn't gotten around to removing. Everybody was using calculators by then.
This was in the late '70s, when scientific calculators had become inexpensive enough that it became reasonable to require parents to buy them for their kids.
Calculators became affordable for high school students in 1974. I know that because I was going into Grade 9 that year and had mastered the slide rule on my summer break only to find that everyone else had a calculator. However, it gives you a great visual tool for understanding logarithms since it turns a multiplication problem into an addition problem.
I think you would make an excellent teacher!
When using a slide rule, and are presented with both multiplications and divisions, you do them alternately if possible.
set cursor to 32 of D. x 32
Move 9 of C to cursor. / 9
Move cursor to 31 of C. x 31
Move 24 of C to cursor. / 24
Read answer on D at 1 on C (458)
Estimate answer (~4) Answer is 4.59 (calculator is 4.5925)
Note that in the middle of calculation, only 1 move is required per calculation, alternately the C scale and the cursor. If the calculation "runs off the end of the rule", reset by setting cursor on one 1 of the C and moving C so the other 1 aligns to the cursor. Changing order of calculation can avoid this.
I would have never passed high school physics doing it your way!
I am in love...
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With slide rule,,😍😍😍
with the co- ..... Oh! , ok den
Please make a video of making of slide rule also. Also explaining what each component or scale of it is.
Calculators were first appearing in the early 70s but they were ridiculously expensive. By mid-70s they became less expensive and with more advanced features.Then rapidly reduced in price.and I felt like kicking myself for not waiting a month when they were then half the price.
We still had the giant slide-rule above the blackboard when I graduated in 1974. In college, the giant slide rules were quickly being removed. I remember how all the cool kids at first had the slide rules in a holster on their belts. They were then replaced by electronic calculators.
My father is quite old, he was born in 1950 (52 years before me), and we still have his old slide rules in working condition. And instructions on how to use them!
Oh by the way slide rules are a great way to change say from kilometers to miles and back set 5 on either the C or D scale and 8 next to it and you have the conversions next to each other. This is approximate of course after all you are dealing with a slide rule. You can do this with those types of straight conversions.
I was in a technical program in the early 70's. The first pocket calculators were just coming out. My friend bought a 4 function calculator (+, -, x, /) . It cost $200.00. I kept using my slide rule.
They got cheaper soon. In 1975 a four function calculator was next to nothing.
You focused on multiplying / dividing the numbers --- the mantissa --- but skimmed over the exponents.
2880 / 0.0036
is 2.880 * 10 ^ 3 / 3.6 * 10 ^ -3
is (2.880 / 3.6) * 10 ^ 3 / 10 ^ -3
is ( 0.8) * 10^3 * 10^3
is 0.8 * 10 ^6
And quick mental arithmetic involving first-approximations is important ... 73 * 19 is close to 70 * 20 which is 1400.
You were always looking for ways to check, verify, to determine bounds.
My older brothers got a heavy dose of slide rules in high school. in the late 60; in the early 70s I got a lighter dose and never used them after that.
And while ordinary calculators went out in the 70s, I learned to fly airplanes about 10 years ago. They had special slide rules for calculating where the center of balance of the plane is, to determine how much gas you need, for dealing with true & magnetic north. Of course any serious pilot quickly switches to a table / iPad, but the training used custom slide rules
A bit of mental arithmetic to trim the ends of multiplication and division plus a gross approximation of whole thing in rounded figures gives you an answer to check on the sliderule.., typical guesstimation techniques that are faster and lighter for a circular type, in repeat calculations such as the old landscape Surveys, than mechanical calculators were then.
When I was at school, we had slide rules along with tables for logs, sine, cosine and tangent. Can't recall whether they were in separate booklets, or together in one.
The use of a slide rule requires the user to remember certain rules and have intuition. Yes, it is hard to see on a slide rule the difference between 215 and 216, but immediately 9 x 24 is an odd number multiplied by even, which is always even. That is a very basic arithmetical property, one of many, that needs to be kept in mind if you want to use the slide rule successfully.
Cool video. I’ve been playing with slide rules for the past six months or so, just for fun. I’ve got a nice collection I purchased over the months on eBay, including 3 of the 20”, 4-digit precision rules. If anyone is interested, there are many available on eBay. My most recent addition is a British made spiral slide rule from 1922. It is capable of 5 to 6 digits of precision and is equivalent to a 41 foot long linear rule. I’m impressed that you were achieving 3 digits of precision with your home made rule. I find the slide rule is much faster than a digital calculator for the math I do in electrical engineering. The 3-digit precision is enough for a lot of measurements. For example, power supply efficiency is output voltage times output current divided by input voltage times input current. That can be completed with four slides, versus about 25 key presses for a calculator, and I generally only record 3 significant figures for efficiency anyway. My only problem is I’m so old I can only read them with a magnifying glass but they are a lot of fun.
You are awesome!
I recently read that Buzz Aldrin used a slide rule on the Apollo mission to the moon to check trajectory calculations.
On the first problem you didn’t need to look up the actual result on a calculator the slide rule got you close enough then just find the last digit by using modular arithmetic (but in practice it’s should be obvious a number ending in 1 multiplied by a number ending in 2 ends in a 2)
Loved the video, but it seems to me that I will be faster by hand, starting by simplifying the fraction.the log table looks great. Of course for more complex problems and bigger numbers the S rule will be great.
In 1977 during the first exam of my Physics finals at the University of Manchester I asked for a set of log tables and caused a panic among the invigilators, who had not been issued with any. They did manage to rustle one up for me, and were better prepared for the rest of my exams. Manchester Physics changed the rules after that to remove the right to use them in exams. Calculators had been allowed for a few years, and most students used them.
So that's how I became the last parson to use a log book in a Manchester Physics finals exam.
Wow, my physics and chemistry classes in 1962-3! The teachers had fancy 12 inch ones. Slide rules saved time over using log books but you had to round off.
Very neatly printed markings and numbers Toby. You do not want auto adjust on if your PRINTING this using a word processor.
You would first approximate 32/9 ≈ 30/10 = 3 and 31/24 ≈ 30/20 = 3/2 yielding 3*3/2 = 4.5 to know your order of magnitude. Then you rearrange calculations to increase economy, i.e. 3.2/2.4 * 3.1 / 9. I can read of 4.59 on the folded scales reading from CF to DF (on Faber Castell 2/83 N). The folded scales are offset from C and D scale exactly by PI, therefore are useful for many calculations involving PI by shifting from C or D to CF or DF but they also can be used to avoid index shifts like I did here. There is a nice short article you could put into your description "When Slide Rules Ruled": www.uvm.edu/pdodds/files/papers/others/2006/stoll2006a.pdf
I used a slide rule while learning chemistry, physics and electrical engineering (Laplace transforms, Fourier transforms, differential equations, Calculus, etc) calculators in that era cost hundreds of dollars, and were limited to addition, subtraction, multiplication and division.
Yay it is a good little innovation that makes the process of higher number calculations simpler
I'm old enough to have been taught how to use a slide rule and I still have 3. My engineer brother gave me 2 of them when I was quite young. With use you can get really quick and as others have pointed out it forces you to pay attention to decimals and sign figs.
But the most impressive thing to me was the precision manufacturing, when properly adjusted they were absolutely silky smooth in use and dead on accurate. That's the reason I've held on to them....