It finds the derivative: The Ott Derivimeter (1930s)

[@peterclancy3653]

I worked in an instrument workshop (hydrography) and serviced Ott chart recorders, beautiful accurate machines

[@Tletna]

I never knew until today that I'd watch a video that included math, antiques, precision measuring equipment, and "Lady, I think you better come back to my place" all in the same video. That's range. Definitely subbed. I didn't even know they were called derivimeters.

[@RichardBuckman]

Drawing the perpendcular with a T square after the mirror would introduce error. It'd be better to just use the fact that the perpendicular will have the negative inverse slope. So if the mirror/normal line has slope -5/4, then the tangent will have slope 4/5. But it makes sense that you didn't use that in the video, because it would have been a ..... tangent

[@ChrisStaecker]

Yes- totally right. The indicator on the Gerber actually points perpendicular to the tangent line, but the scale is inverted like you say so it all works out fine.

[@biquinary]

On the topic of Verniers on non-linear scales, there's a really slick trick you can do with a slide rule (source: "Utilizing the Vernier Principle for Precise Readings of Slide Rule Settings" by Roger Wickenden). The trick is that the log scales on the slide rule are locally linear, so if you line up the right index on the C scale with 9 on the D scale, the C scale can act as a Vernier anywhere else on the D scale (you can do the same for subdividing by 5, 10, 100, etc.). Makes me think that good ol' Gerb's Variable Scale would be really useful for adapting Vernier readouts to any graduated markings!

[@ChrisStaecker]

Very interesting- I'll look into this. I recall seeing a patent for a Vernier-like trick for use on log scales- maybe it's a similar idea.

[@FlatEarthMath]

I was going to make a pithy comment about the derivimeter's Vernier scale, but yours is far more informative and elegant. Thank you. 🙂

[@1337treats]

I like your dating investigation. “Found this photo from 1942. So it could be from the 40s, or earlier! Or later too!”

[@KazimierzSurma]

🤣

[@webgpu]

if it's not from the 40s, could be from earlier, later or neither

[@OGMann]

It would be a derivative...

[@dolata000]

0:12 "spinny roundy thing" -- that got a huge smile out of me

[@ChrisStaecker]

wait til the gnomon bros hear it…

[@suttoncoldfield9318]

Clear, concise, accurate

[@echuidor]

"Look the round things!" "I love the round things" "What are the round things...?"

[@webgpu]

i'd smile if it was "thingy" too :)

[@BravoCharleses]

Young man, you do nice work. I hope you and yours have a happy, healthy, and successful New Year.

[@mathmeetsmachines]

Great to see two commercial derivimeters and great to see somebody demonstrating the prism approach. Concerning your question: The prism derivimeter is described in the paper "Der Prismenderivator und der Differentio-Integraph" von E. von Harbou in "Zeitschrift für angewandte Mathematik und Mechanik", volume 10, number 6, december 1930. As far as I see, this is the published version of the author's doctoral thesis at Königsberg. In the paper, the author in particular makes a series of experiments that supposedly shows that the prism derivimeter is superior to the one with mirror. The author employs the derivimeter in a machine that plots the derivative of a function as a whole. He sees the main application in ballistics and refers to Cranz, Lehrbuch der Ballistik, part 3.

[@ChrisStaecker]

Yes I’ve read the paper (some of it at least- I don’t read German). Can you tell if it was ever a commercial product?

[@LeoStaley]

This is why I have notifications turned on for your channel.

[@jitgtij]

This is the first video I got recommended by yt and it is a GEM. Instantly subscribed

[@LeoStaley]

@ oh boy you're in for a treat. This isn't even his best. It's like a B+ for him. Go through his catalogue of these videos, there's a playlist. And the freaking documentary he did on the Curta. Bro is a Nerd's Nerd.

[@Lucky9_9]

@@LeoStaleyMy first time too! Aaaand your comment made me sub lol thanks 😅

[@maxinehardy9411]

i love how this works. using the mirror is something i never would have thought of but once it was explained it seems so obvious!

[@YZoxK52m]

Rivals in their youth but now they're side by side as friends in my basement Nice. Thanks for doing what you're doing.

[@AlRoderick]

Well, it's a German instrument from the '30s, so more than likely at least a few calculations related to the angle of London from mainland Europe or perhaps the slope of someone's forehead were made with an instrument like this.

[@ChrisStaecker]

yeah I decided not to get into it, but well said

[@sergioperez2594]

Your explanation of the derivative: "it's a specific way of measuring how fast something is changing" You can read completely all popular 1000 pages Calculus books and you will never find a better explanation of the derivative. Your explanation is GENERAL, accurate, intuitive and beautiful. Most Calculus books tend to explain the derivative by one of its infinite interpretations.

[@TarenNauxen]

I love nerdy gadgets almost as much as I love your delivery when explaining said gadgets. Keep up the ORIGINAL work!

[@Blingsss]

This is such a cool piece of history! Never thought I’d see a device like the Ott Derivimeter. It’s crazy to think about how far technology has come. Sometimes, I wonder what it’d be like to have something like this back when I was struggling with derivatives. Thankfully, tools like SolutionInn have made learning math so much easier!

[@Joe_VanCleave]

Chris, your Ott has a serial number, perhaps the company has production records that can more accurately date its manufacture.

[@GimpGladly]

I think the rough engraved number I believe you are referring to would have been added and used by the university it came from for inventory and loan tracking purposes.

[@HaileISela]

there's a finely done Number next to the maker's name...

[@sprky777]

It's German, of course there are records. The Ott company probably knows when it was made and by who.

[@drfoop]

In some German and East German camera equipment of that era the year of manufacture is the first two digits of the serial number.

[@SummerCrowfpv]

It occurred to me while you showed me more about math in 8 min than I learned in my first calculus class, that my teachers in high school were idiots THANK YOU SIR ❤

[@laurencefinston7036]

For anyone whose memory of differential calculus is a little rusty, the tangent to a curve 'C' at a point 'p' can be approximated by taking two points on 'C', 'a' and 'b' (with 'p' between them), and drawing a line 'L' through them. Let 'd' be the distance between 'a' and 'b'. The true tangent to the curve is the limit of 'L' as 'd' goes to 0. That is, as 'd' decreases, the approximation to the tangent becomes more and more accurate. Using mirrors to reflect the curve is a clever way of getting around the unsolvable technical problem of finding and fixing points that are ever closer together. From a drafting point of view, this is a very difficult problem to solve and I'm not sure how much a Derivometer would help. I learned to do technical drawing by hand and I'm glad I did, but I say thank goodness for computer graphics and there are many things that I hope I never have to do by hand again.

[@t850]

...ingenious simplicity of mechanical tools like this one never fails to impress me...:D

[@BillRicker]

Love a Vernier. Free extra resolution. (Which is accurate because of the mirrors.)

[@ChrisStaecker]

One of my all-time favorite simple ideas.

[@BillRicker]

@@ChrisStaecker same. Key as always is knowing when the extra precision is meaningful. The mirror on the present device I'm guessing is what makes the Vernier worthwhile? How obvious is the kink in the reflection if you intentionally misalign the vernier by just one division?

[@michaelbauers8800]

Guy was great. 10,000 leagues under the sea, Around the World in 80 days... ;)

[@AndyZhang-vu5ey]

Another banger mathematical device. I try to make alot of the Mathematical devices on this channel. You got me excited for greens theorm I might 3d print a polar planimeter and attempt to combine it with a 3d printed derivameter and have the full range to do calculus on paper!!!!

[@ChrisStaecker]

A 3d-printed polar planimeter sounds amazing, and probably pretty doable.

[@markloubser2433]

These old precision instruments are outstanding. Wonderful craftmanship. Thanks.

[@RichWoods23]

With luck some of them will survive the inevitable demise of humanity and be helpful to whatever species takes over after us. We just have to store them well away from any subduction zones...

[@brendawilliams8062]

You could hand that over to quantum computing and they could build pyramids.

[@N.A._McBee]

A joyful beginning of 2025 with Chris' presentation of the Ott derivimeter! Never saw this one before, really neat and elegant, indeed!

[@LordMarcus]

Man, I fucking love metrology.

[@michaelbauers8800]

Right thinking people do. You can tell they are right thinking, because they love metrology. Which is an acceptable definition, because eventually all dictionaries will result in circular definitions.

[@halfasleeptypist]

8:09 Didn't expect trying to woo Elsa with your TWO ~ORIGINAL~ derivimeters 🤣

[@ChrisStaecker]

gotta do somethin with all this game

[@torfley]

game is game

[@BrianTRice77]

Hey, math teachers go clubbing, too. 😎 (I actually gifted a goth math teacher some slide rules she wanted for her students to learn recently.)

[@halfasleeptypist]

@@BrianTRice77 AWWWW that's so sweet of you!!!!!!!!! 😭❤️ Also, I didn't think a goth math teacher would actually exist, I thought I'd be the only person in the world to dare to like both fashion AND math, HAHA

[@toddyampol1088]

The slope never bothered her anyway. 😂

[@jitgtij]

I was blown away. You taught me something and also made me laugh with your humor, loved it. Happy New Year

[@nickjohnson410]

You gave me a better understanding of geometry in 10 minutes than my 10th grade teacher was able to do in a year.

[@horacerumpole6912]

Cool instrument! I have an OTT pantograph. These guys were serious instrument makers-

[@ChrisStaecker]

Nice! Somebody (I think Ott?) actually made a "differentiograph", which was a pantograph-like thing that traces a curve but draws the derivative curve. Very fancy- I've never actually seen one.

[@GimpGladly]

​@@ChrisStaecker for the sake of all things good in this world, please find such a device. I can barely begin to imagine how that would work and now that the idea is in my mind, I must see it!

[@Pallethands]

I would love to see a video about the von Harbou device but with two videos on slope calculating devices already, I am afraid it could be a bit derivative

[@richardthunderbay8364]

Another great video. I just love all the mathematical devices that you present.

[@karl-heinzbirkenbeil1331]

Nice device and video and explanation. My chemistry teacher showed us how to use small (capillary) glass tubes intead of the prism to read the reaction speed out of a hand-recorded concentration plot.

[@michaelbauers8800]

This is great. youtube has done a great thing by giving people like you, really into cook, geeky stuff, a platform to educate and entertain. You ott to get more views :)

Thanks, mate. Your channel is a boon to this site.

[@BabyHoolighan]

When I asked my calculus teacher what the derivative is, he said it's a function. If I had had an Ott derivameter I would have discovered the first day what it took me a quarter to understand. The tangent line is so tangible with this device.

[@boriscat1999]

This would have been really useful for scientists that collected data from chart plotting machines.

[@ChrisStaecker]

Yes- I think this is the typical way it was used.

[@antiphlex]

You, sir, are awesome. Math comedy done right.

[@Aldo.flores]

I love this kind of mechanical instruments made for measuring complex functions by its geometric properties, I think there so clever and reminiscent of an era were people use their imagination to do productive things. And now the planimeter could have good and trusted friends

[@cdorcey1735]

I demonstrated the prism trick with an prism (as used to fold the optical path in binoculars). Unfortunately, the vertex of the right angle planes was not sharp, so there was always a gap between the lines that limited the accuracy and the localization of the x-coordinate.

[@cheeseparis1]

I value extra accurate time measurement. Loved your video, didn't know about these tools.

[@txkflier]

Pretty cool video. I worked in metrology for 37 years and also have tuned PID controllers..

[@Muck-qy2oo]

Mechanical differentiators are really fascinating.

[@haraldmittbacher6937]

Minute 7:30: Try this source: Author: Eberhard von Harbou from the district town of Kętrzyn (German: Rastenburg) in the now Polish Warmian-Masurian Voivodeship (former German Königsberg administrative district in the province of East Prussia of the German Empire). Title of the doctoral thesis: The "Prism Derivator" and the Differentio-Integraph". Inaugural dissertation for the award of the doctorate. Approved by the Faculty of Philosophy of the Albertus University of Königsberg Special print from: Journal of Applied Mathematics and Mechanics, Vol. 10 (1930) No. 6 *** German version *** Autor: Eberhard von Harbou aus der Kreisstadt Kętrzyn (deutsch Rastenburg) in der polnischen Woiwodschaft Ermland-Masuren. Titel der Doktorarbeit: Der "Prismenderivator" und der Differentio-Integraph". Inaugural-Disseratation zur Erlangung der Doktor-Würde. Genehmigt von der philosophischen Fakultät der Albertus Universität zu Königsberg Sonderdruck aus: Zeitschrift für angewandte Mathematik und Mechanik, Bd. 10 (1930) Nr. 6

[@ChrisStaecker]

Yes I've read it! Or some version of it at least.

[@felixbouvet1746]

Alors je connaissais pas du tout cette ustensile c'est plus précis qu'un rapporteur en effet est équipé d'une loupe d'un miroir je vais tester vos méthodes trigonométrique😊😊😊😊 moi je connais déjà le sinus et le cosinus

[@stevepaltzer7605]

The topic covered here is Metrology. The glass dome is an optical center. An optical center punch is used to mark a point.

[@michaelbauers8800]

I thought that was the science of controlling hurricanes ;)

[@stevepaltzer7605]

@michaelbauers8800 The people with too much money from oil production are doing that. I would like to try to make it snow someday. Shoot boiling water into the atmosphere so it instantly evaporated and percipitated down as snow. If would have to be done in a cold climate area at a high elevation.

[@colinslant]

What a fabulous bit of kit.

[@rrangana11]

In the end you put a smile on my face.

[@trdsf]

I love these manual, analog ways of doing things. Absolutely gorgeous. Does it have ten digits of precision? No. Do I care? No. It's a very hand's-on way of doing math, rather than just punching numbers into a calculator.

[@johnnzboy]

That is indeed one comely original box, though there's an unusual reverberation in there... But what's this? A channel renowned for its comprehensive scrutiny of precision instruments, for the correct identification of obscure apparatuses, their functions and related terminology, yet you settle for the vague and, um, fuzzy 'green billiard fabric' rather than the incomparable and mellifluous 'baize'?!

[@moshe778950101]

What a gemm of a video. Brilliant.

[@peteraltavista7508]

Good stuff. Chris Staeker, meet This Old Tony.

[@cdorcey1735]

A treat, as always. I must recommend it to my mathematician friend, Elsa! I'm just slightly disappointed that you didn't use a slide-rule, instead of a digital calculator.

[@ChrisStaecker]

Elsa you say?

[@cdorcey1735]

@@ChrisStaecker Last initial "H", also dances ballet. You know her, too?

[@ChrisStaecker]

@@cdorcey1735 i was thinking of somebody else 8:15

[@zbynekdolejsek8930]

3:55 It is 31,85°, I use the outer scale to measure degrees fractions. On 8 is slightly less an on 9 is slightly over. So my guess is 0.85

[@zbynekdolejsek8930]

OK, I'm wrong, its @erikziak1249 28,175

[@ronstiles2681]

I seen this tool before my science teacher in 7th grade, I don't have any use for it but I want one, I know I'm a tech goof nice video

[@BrennanYoung]

"I don't have a little mirror" [polished butcher's knife appears] "maybe get your Mom to help out with this"

[@ebaab9913]

This was so interesting and informative, I would love to own instruments like that ❤, but being married for nearly 50 years I also know that they would be a bone of contention with my wife.

[@charlesbenca5357]

Please do not auto translate your channel. The experience on youtube is garbage (youtube wont let me see the original title of the video in english, no way to tell what language a video is until i click on it, because youtube gives no indication that the title is translated, auto translated title and description are often bad, cringe, and are always an annoyance when you speak multiple languages because, again, youtube provides no mean to show the original untranslated title and description).

[@ChrisStaecker]

Thanks for letting me know about this- KZbin recently released some new language features which were default opt-in. I didn't know they would translate my titles & descriptions like that. I'll keep this in mind.

[@halfasleeptypist]

​@@ChrisStaeckerY'know, as a native German speaker, I can say the translation is honestly not that bad. It's not perfect, there are some things that could've been worded better and made it sound less formal for a video like this. The auto-generated German audio track (which i've never used in my life until now) is also not bad at all. It does sound robotic and it speeds up and slows down sometimes to accommodate for the length of the original English sentences, but hey, it could've been worse. What irks me though is that these features are apparently opt-in by default and it seems like they put it in your videos without telling you. Like heck, there's apparently even a thing where you can choose from AI-generated responses to reply to comments instead of writing them yourself. Makes me kinda melancholic thinking about what other generative AI features KZbin will introduce without telling us 🥲

[@ChrisStaecker]

Well they did notify us that it was happening. There was a (one-time) dialog when looking at YT analytics that I had to click on to accept the new defaults. But it was presented only as new features that viewers could use if they wanted- not new features that would become defaults for viewers. And it seems to be all-or nothing: if I disable it, then autotranslations will become unavailable, which seems a shame. Hopefully they’ll change the rules soon-

[@tarbucktransom]

​@@ChrisStaecker"Hopefully they'll change the rules soon." KZbin has long worked by the logic of "better for us beats better for users" so it's fairly unlikely that it will change. We can hope though.

[@BrianTRice77]

Wait, so is the audio in German and then Spanish for everyone? I thought I was losing my mind. I can't seem to get any other language in the audio track. The closed-captioning is helping because my Spanish is quite rusty for technical topics.

[@johnsrabe]

I wish you had told me, I had unopened boxes of all three of those devices in the trunk of my Cord.

[@portblock]

I love this piece of equipment!!!

[@Mural]

"pretty darn good!" is what I say to myself at the end of each of your videos

[@markrix]

That is neat o. Wonder what the actual use was when the department used it, obviously derivatives but maybe just a guess changes in temperature?

[@bnsmith314]

You really want to date the one who says "you had me at derivameter...."

[@creamwobbly]

That quip at the end was a bit protracted and over-the-top

[@creamwobbly]

Oh! I forgot to say it was derivative and UuNnOoRrIiGgIiNnAaLl!

[@michaelbauers8800]

You ott to be ashamed of such attempts at humor

[@copperminekd]

Man, I really love your videos! To bad there is a finite supply for new stuff 😢

[@thinkbolt]

Okay, the Elsa ship was unexpected.

[@AngrocSound]

Thoroughly enjoyed as always! 😁

[@ernestsmith3581]

I remember using a similar (? complimentary?) instrument to integrate areas of ellipses in Celestial Mechanics (Was it called an "ellipsometer"? I can't remember) class way too many years ago. ;-). Ahh, the days of mechanical analog computers! (I don't miss them at all.:)

[@random832]

one thing you didn't explain much was how the vernier scale actually works... the point in the video where you read off the result of 28.2 would have been a good opportunity the prism approach seems like it has an enormous downside: you're actually measuring the slope along a pretty good sized section of the curve rather than at a point, you might as well just mark off two points to draw a "tangent" line [well, a line that will have been parallel to a tangent at *some* point between the two chosen points] by hand (or to use a protractor).

[@happyvirus6590]

0:38 Start the clonk!

[@gabeteuton]

not sure if the ladies will fall for it, but i certainly did, well done!

[@idaho_girl]

I'm swooning over your derivimeters! Be still my beating heart!

[@BaroqueViolin]

Excellent! Thank you!

[@JohnDlugosz]

People back then would just find the tangent using their slide rule, which in this case is exactly a table of tangents, albeit scaled by log. I see you device has a prominent *serial number* . The company may have a date range

[@hamaljay]

Wake up hun the math guy has an original case for his derivometer!

[@luiseduardo586]

AWESOME.... I did not know those things even existed. Damn algorithm did it again!

[@TommyLikeTom]

The reason they rare is the same reason they are simple and elegant: They are almost completely useless. It's so much easier to just measure with other tools instead of buying and keeping around this extremely specific instrument. Measuring the slope of a curve is not a procedure that requires a dedicated instrument.

[@RossMarsden]

I just LOVE your videos, man. Are you from Canada? Or one of the northern plains states, or the northeast.

[@ChrisStaecker]

Boston

[@RossMarsden]

@@ChrisStaecker There you go! Thanks.

[@georgemoore5307]

Looks like it has a serial number, call them they may be able to tell you when it was made. I had a General Radio Bridge gave them the serial number and they came back with march 1943. They even had parts for it.

[@kushpatel9911]

Ca you explain what you mean by "where there is no kink"? Why is that better than the subjective of trying to draw a tangent with the ruler?

[@ChrisStaecker]

This is a good question- both involve eyeballing it at some level. But I can say from experience that using the mirror gives much more repeatable results than just drawing the tangent with a ruler. Maybe some version of the "Vernier acuity"?

[@TheWinnieston]

Addiator multiplier book video WHEN??

[@aayush_deo_ranchi]

can you please publish some dimensions we can 3d print as analog computing is making a comeback so it will be very useful

[@Dad-l6i]

You don't have one next to the protractor?

[@Kihidokid]

I love analog so much

[@uwehardenberg830]

Hello! I'm desperately looking for a derivimeter, no matter what model. Maybe you can help me with that. Thank you very much!

[@ChrisStaecker]

I don't think I can give much useful advice. My strategy was: set a "saved search" on ebay with notifications, then wait about 5 years. If you're a maker, you can build your own Gerber-style derivimeter here: www.instructables.com/The-Gerber-Derivimeter-the-Ultimate-Tool/

[@uwehardenberg830]

@ChrisStaecker Thank you very much for your answer!

[@adcaptandumvulgus4252]

So basically it looks like a type of slide rule for calculus, yeah?

[@kkgt6591]

What was this used for?

[@chriswalford4161]

When experimental results were recorded graphically it could have been very useful to have a quick way to obtain an instant derivative; lots of answers in engineering problems are derivatives of curves.

[@ChrisStaecker]

Yes - data existing only as chart recorder output would’ve needed to be analyzed purely graphically

[@petergerdes1094]

Question for the mathematicians: what is the class of curves for which this procedure (applied ideally) gives you the right answer. Feel free to operationalize finding the perpendicular as a minimization problem.

[@landsgevaer]

Differentiable functions, I guess? (Locally differentiable suffices for local measurements.)

[@RicordiDellaRAI]

Fantastic!

[@kevinkauffman492]

how did you use the sundial while inside? doesn't make any sense!

[@nil2k]

I would just take a guess that the first two digits of the serial number are the year, so 1946.

[@laurencefinston7036]

It's a nice tool, but I think it's a misnomer to call it a "Derivometer". As someone else pointed out, and to the best of my knowledge, the derivative of a function is a function. The result of applying this device is (with greater or lesser accuracy) the tangent to a curve at a single point. It tells you nothing at all about the tangent at any other point on the curve. In addition, while the tangents only depend on the curve, the slopes also depend on the coordinate system. This implies that the curve would have to be plotted accurately (which is a big assumption). Even if you measured all of the infinite number of tangents along any segment of the curve, it still wouldn't tell you what the derivative function is. Besides, if I remember correctly, only the derivative of a quadratic function with a single independent variable would be a straight line. For example, the derivative of a cubic function would be a quadratic function. I like the mirror setup. It reminds me of how a sextant works. A much more impressive device is the Ott Integrometer. Unfortunately, very few were made and I have the only surviving one.

[@ChrisStaecker]

The derivative of a function is a function. The derivative of a function at a particular point is a number. Using the word "derivative" to describe either or both things is very common. You can see in their instruction sheet: "Applied to a sufficiently large number of points, this method enables the differential curve to be plotted point by point." So, like you say, you can draw the derivative function to arbitrary precision using this instrument. I'm not sure what you mean by: "it still wouldn't tell you what the derivative function is". This is used for graphically represented functions. If you can draw it, then that picture IS what it is. I'm not sure if you were joking about "Integrometer"- Ott and others did indeed make mechanical integrators, which are indeed hard to find these days- I don't have one, but they are basically planimeters.

[@laurencefinston7036]

@@ChrisStaecker I have limited mathematical skills, but according to my understanding, this device finds the tangent to the curve. The tangent can be considered, as you say, as a number, but often the term is used to refer to the straight line whose slope is the same as the instantaneous "direction" of the curve, if we consider the curve as the trace of a point moving through space (a plane, in this case). The angle of the line would be the arctangent of the number. I understand that you can plot a function using this device. My point was that it will not in general be possible to find the function, in the form of an equation, from the plot. Nor would it be possible to extrapolate for values even slightly beyond the boundaries of the original curve. I was joking about the Integrometer. I'd have to look up what a planimeter is. I would think that such a device (a mechanical integrator, that is) would only work for a very limited class of curves.

[@laurencefinston7036]

@@ChrisStaecker I just thought about this for a couple of minutes. At the risk of being persnickety, I think that there's no such thing as the derivative of a function at a point, there's only it's value at a point (or more precisely, it's value for a given x, assuming it's a function in x). The derivative of a function is always either a function or a constant, whereby the latter case is simply the degenerate case of a constant function (i.e., the derivative is always a function). The reason I care about this is that it's relevant to my work. I have a particular interest in the intersections of curves and plots don't do me any good, only equations.

[@ChrisStaecker]

@@laurencefinston7036 I'm not sure exactly what you mean, but I think you aren't using terminology in the standard way. Like for f(x)=x^2, I would say f'(x)=2x, and I would call that "the derivative of f(x)", which is a function. I would also say f'(3) = 6, and I would call that "the derivative of f(x) at x=3", or some such. That is a number. Both of these things are colloquially called "the derivative". If somebody started talking to me about the derivative with no context at all, I would probably assume they mean the whole function. But it's not strange at all to use the word derivative when talking about a single point. As for "plots don't do me any good, only equations", this is a fundamental difference with the intended user of the derivimeter. This was meant to be used on empirically produced graphical curves- say, from data chart recorders. If you have an equation for the curve, then you would just use calculus to find its derivatives. This instrument is meant to be used for a curve which exists only on paper.

[@laurencefinston7036]

@@ChrisStaecker Maybe I'm splitting hairs, but I would say the derivative of f(x) for x = 3 is f'(3) and the value of f'(x) for x = 3 (or more simply f'(3)) is equal to 6. However, I hardly ever discuss math with anybody, so I don't know what common parlance would be. Just using calculus would be nice. Unfortunately, it's not so easy in practice. Two problems are 1) that one often doesn't have an equation for a curve and 2) in computer graphics, the equations for spline curves aren't integrable. I don't know if they're differentiable (I doubt it), but I haven't needed to find tangents to spline curves (yet). I'm mostly interested in finding distances along the curves, as well as intersections. For anyone who doesn't know this, in general, integration is needed to find distances along algebraic curves. (It is not needed for straight lines or circles, but it is for ellipses). I will make a guess that if these devices were used in ballistics, then at least some of the curves it was used for were parabolae, so they probably had a good idea of what curve the plots were supposed to fit. Not sure I'm on target here. I appreciate this device very much and would use it for that reason alone. However, using it for a technical drawing of any complexity would be a pain in the neck.

[@LANless]

Damn, that's so cool!

[@MichaelMaxwell747]

Liked and subbed.

[@hockkhor4641]

"Lady I think you better come back to my pace". Oh-ho-ho. :)

[@erikziak1249]

3:56 Looks like 28,175° to me.

[@zbynekdolejsek8930]

great, I was wrong, it's not 31,85°

[@puzzlinggamedev]

I find this video very derivative.

[@ltva8781]

I am yet to see interferometry based exxxxtra precise derivimeter!

[@ErikBongers]

The protractor with slope markings isn't less accurate than the one with degrees. The visual accuracy is exactly the same. Don't be fooled by the fact that when you calculate the tangent you get a number of decimals.

[@ChrisStaecker]

Well I said "precise" which I'm using different from "accurate". I agree the accuracy is exactly the same. But the precision is nonlinear so it's hard to talk about in simple terms. A small deviation, say by 1 degree, doesn't change the slope value very much when it's small, but it can have a huge effect when it's big. Of course the calculator gives me false precision when I press the "tan" button, but that's not really what I was talking about.

[@BrianTRice77]

Also, you can get the tangent value with a slide rule pretty quickly to the same accuracy from the angle measurement. Anyway, the eye can read off graduations that are equally spaced like angles on a circle better than an uneven gradation which you would get for a tangent value. The slide rule is at least made for such a reading, and doesn't convey unwarranted digits of precision...

[@landsgevaer]

I agreed, until I saw this thing had a nonius. That would be difficult to achieve with unequal markings. PS, it is later mentioned on the vid, apparently called Vernier scale (as well).

[@BrianTRice77]

Oh, I bet the vernier scale is an additional motivator for the angle markings, because it wouldn’t work with an uneven scale. I have a number of slide rules, and the vernier scale would only work on a log/L scale or rulers on the edges 🤔 maybe I can try scoring a custom cursor window…

[@kim3982]

I need one ❤

[@aimlessweasel]

"Start the clock!" with the PiP of the sunwatch.💀

[@BrianTRice77]

“It finds the derivative or it gets the hose again!” (I’m sorry, but I had to get out the worst taste joke out once it occurred to me after seeing notifications. I’ll see myself out! 😬)