Derivative measuring tool from the 1950s

The Gerber Derivimeter, made in the 1950s by the Gerber Scientific Instrument Company.
This is episode 58 of my video series about old calculating devices.
Claw machine photo by Wikipedia user Nlan86, CC-BY-SA-3.0
End song inspired by "Hotter than a Molotov" by The Coup.
Chris Staecker webarea: cstaecker.fairfield.edu/~cstaecker
#gerber #derivative #knobs

[@matthewholzner9526]

"Longtime fans of this channel will both know..." LOL!!!

[@nashvillain171]

His parents 😂

[@pablorepetto7804]

me at the beggining of the video: "isn't that just a fancy protractor?" me at the the end of the video: "that is a _genius_ invention! it's a _really_ fancy protractor!"

[@bennmurhaaya8518]

At high school, we were taught to find a tangent in a following way: You would position a small mirror on the curve in such a way that the curve and its reflection would line up perfectly and then you'd trace the mirror's edge. This would get you a line crossing the curve at the point where you want the tangent to be. Then you'd just use a compass to draw a line perpendicular to the line traced along the mirror's edge and et voila.... a perfect tangent.

[@RandomMan1]

That's really smart, but couldn't you just use the mirror as a straight edge at that point? (And flip the result afterwards)

[@bennmurhaaya8518]

@@RandomMan1 I am not quite sure how you picture it. The mirror is used as a straightedge, but drawing alongside the mirror will not give a tangent line but line perpendicular to the tangent line at that point of the graph.

[@aajpeter]

@@RandomMan1 the point being that the curve as it hits the mirror is easy to make exactly perpendicular by making the curve appear smooth, as even small deviations from perpendicularity will show up as a kink in the curve. When smooth, draw the line against the mirror, then get the perpendicular to that perpendicular to get the tangent.

[@ChrisStaecker]

(I discussed this in my Caliputer video)

[@r0cketplumber]

"The longtime fans of this channel will both know that I'm a big fan of the Gerber scientific instruments company." That made me laugh out loud, well played man.

[@ventility]

Praise to the almighty algorithm for introducing me to this channel. I enjoy the gadgets and tools you showcase but there's more to it than just neat things. Your personality comes through and makes your videos pop! I went on a little Staecker binge last night. Looking forward to more and a lot of catching up.

[@I967]

What an interesting device. I'm not very math-inclined, but I like all things mechanical. What a clever solution. Your subscriber and view count should explode any time now.

[@lucasconner621]

this is the first video of yours ive seen. i called out of work to the clear the next couple hours so i can watch more.

[@antiphlex]

Man, you are hilarious. I'm so glad to have stumbled on this channel.

[@portlyoldman]

Just found your channel and am in the process of gleefully binge watching 😁😁😁

[@defeatednamer8306]

Love all your videos! Great humor and love the ending song. You really deserve more subscribers.

[@Mural]

Incredibly elegant device. Great vid!

[@idcanthony9286]

Discovered you this evening. Totally love the channel. Keep it up!

[@paulkolodner2445]

I used the Gerber Variable Scale all the time back when data came out on paper (early 80s). If I recall correctly, I think I had one that was double length. I also had a whole file drawer filled with every kind of graph paper, carefully sorted. And I could get 4 digits out of a slide rule.

[@ChrisStaecker]

Nice- I wasn’t aware that the variable scale came in different sizes.

[@Gunbudder]

3:49 holy shit i had to do this SO MANY TIMES in calculus. my professor was obsessed with making us hate "the old way" so we really appreciated "the new way" of doing anything in calculus

[@adissentingopinion848]

Dude, you should have seen my face when the bar curved.

[@karl-heinzbirkenbeil1331]

Hi Chris, very nice vid and a top channel! Greetings from Germany 🇩🇪! From my chemistry teacher I learned around 1992 an easy method to estimate the slope of given curve at a distinct point, for example a reaction plot. You lay a capillary tube roughly perpendicular to the curve through the point of interest. Adjust the angle of the tube so that you get a symmetrical image of the graph when looking through the tube. Then you take a pencil, draw a thin line along the tube and measure out dy and dx.

[@ChurchOfThought]

The ol' Joe Gerber hasn't let me down yet. Neither has his reincarnation Chris Staecker ☺️

[@theshuman100]

a similar mechanism is also used to measure the radius of a curve, with couple big differences. one is that it measures by how much you push out the bendy bar. but the other thing that interests me is that it deforms the bar uniformly while this lets you set the deflection on iether side seperately. kinda wonder how that doesnt affect how you measure the curve.

[@MrDavid4998]

I'm currently going through your devices playlist and I think it would be awesome if you did a video where you compared the use of multiple devices to achieve a certain goal. For example, you could use a compass to draw a circle with a defined radius and then use area and length measurement to find out the value of pi and compare the accuracy. Also, thank you for these videos, they are very enjoyable.

[@ChrisStaecker]

Thanks for watching! I did do this one: kzbin.info/www/bejne/r4e5hpWkbc6Eh6M

[@Iomomozoe]

Just found your channel, these devices blow my mind lol

[@ukranaut]

Impressive.

[@suem6004]

Hey, just discovered your channel. Hubby was a math geek but cannot explain anything to me. But you sound like you explain math well. Sure wish I had you for mathematics. Never did calc because of bad teaching but with you AND using these fancy dancy devices, I would enjoy it. They are tactile pleasing as opposed to buttons on graphing calculators. Anyway, hubby and I are enjoying these videos and gadgets.

[@tajmahalfred]

A Gerber Graphanalogue just went up for sale on eBay (with case!) for more than I should really be spending. So while I look forward to your eventual Graphanalogue video, maybe not this week

[@haramanggapuja]

Wow! As a guy who can barely figure out how to get his iPhone to send a text to my wife across the room, this is really a cool video. Well, let's be real: all your videos are cool. But that device! Whoah. Betcha there were kids in school wishin' they'd had one back in the day. . . . And that mystery device? Hah! I saw it. I really did. Hardly wait to see that video, amigo.

[@chriswalford4161]

Cute and genius!

[@colinstu]

O R I G I N A L

[@co880]

TIL how to find a derivative, or maybe I knew, but have forgotten in the years since high school?

[@ragnarhairybreeks]

Hi, Man, that is clever…. The flexy strip . Thanks for making the vid. Alistair

[@ragnarhairybreeks]

So,many questions …. Immediate one is how the circular scale derived. Pun not intended. Obviously I’m a math dolt, but can you explain ? Another observation is how the flexture that is adjusted to follow the curve makes the pointer point true. It’s cool on many levels. Thanks again for the vid , it’s made me think about things during my workday . Alistair

[@ChrisStaecker]

@@ragnarhairybreeks You can easily convert standard protractor markings to the scale on this thing using the tangent function. If x is the angle (measured with 0 at the top), then the slope marking would be tan(x). Not exactly kid stuff, but this would be easily understandable to any engineering student. The pointer is attached to the crossbar so that it makes a right angle where it's attached. So if the bar curves, the pointer must move along with it to maintain the right angle.

[@plugplagiate1564]

i just think, where would have apollo ended if they would have taken this thing?

[@txikitofandango]

even in math with your abstract equations, you can have not only a tangent line, but a tangent parabola, tangent cubic, tangent whatever! just keep more terms besides the linear terms when tossing out the higher-order terms

[@christopherellis2663]

Slope, the Sine of the Angle 0/1 to 1/0

[@sujalgvs987]

Is that graph analog at 5:00 in the corner of the screen the "mind blowing acquisition" you're talking about towards the end of the video?

[@ChrisStaecker]

No spoilers!

[@sujalgvs987]

@@ChrisStaecker haha i love this channel

[@nicholasmastricola8145]

@@ChrisStaecker I always lover your vids because I'm a slide rule, gerber, and calculator collector too! I commented before about the GGA on another vid. If that isn't your mind blowing acquisition, let me know. I recently found a 2nd one. Looking forward to your next Gerber vid! Thanks!

[@ChrisStaecker]

@@nicholasmastricola8145 So you have 2 GraphAnalogues? That must be a record! (I have one, but had to wait a long time before seeing it on ebay) Where did you find yours?

[@nicholasmastricola8145]

@@ChrisStaecker I have had up to 3 at one time. Ebay, other online auctions, surplus sales at companies... one had to be scrapped for parts to complete the 3. One to keep, 2 to pass along. I have a manual if you need scans ( I'm not sure if that one is available online). Still looking for an original equimeter though

[@der.Schtefan]

Ah, you broke the 4th wall. Nooo. Anyway, GERBER! YAAAY!

[@manuelgolindanob.5381]

This is sOOOOo Nice, how can i make oneeeeeeeeee????????

[@Vallee152]

This will make physics class so much easier

[@ChrisStaecker]

Fact: Joe Gerber invented all his early gadgets because he was fed up with doing his engineering homework problems.

[@farpointgamingdirect]

Is this Gerber the same company that makes multi-tools and knives, or a different company all together?

[@ChrisStaecker]

Different company. (Also different from the baby food)

[@LuisRodriguez-vh6fg]

Where did you get the Derivimeter?

[@ChrisStaecker]

Ebay

[@Calbeck]

hol up are you saying this thing could precisely calculate a number between 0 and INFINITY with INFINITY being a specific point on a finite instrument

[@ChrisStaecker]

Infinity is not a real number, but "infinite slope" is a real thing- it just means the line is vertical. The instrument can read infinity as the answer, but practically speaking the answers are very imprecise for any values higher than 10. You can see on the scale that 100 is right next to infinity. Any large values will be practically indistinguishable from infinity. (Actually in this setting negative infinity and infinity are equal! 🤯🤯🤯)

[@pauljackson3491]

It's interesting to see strange tools I never thought would even exist. I don't know hows this channel got to me but the weird stuff is cool. You should try to find someone who actually used these; or more likely a descendant. They might be like 80 years old. Or try making one yourself. You said your were a mathematition - stupid spelling - but I don't know how much engineering you know.

[@alo1236546]

Gerber scientific was sold

[@portlyoldman]

….and subscribing …

[@vinesthemonkey]

this must be a new video because why do I have to see your face so much like other youtubers and why does it take up so much of the frame :P

[@ChrisStaecker]

Yes I just started doing those face shots- I didn’t have good enough lights before to do it well. I like the big head look, but for me it’s necessary because my space where I film is so small.

[@leesweets4110]

You call it genius to use a bendy line but I tell you what; even if I thought to use a bendy line, I wouldnt assume it would give me better results. And how do you verify the accuracy of the technology once built?

[@someonestolemyname]

Things this simple seems like cheating, no difficult maths and janky mechanisms, just pure simple physics and psychology trick. Hell, I can print this thing on a 3D printer and just use a protractor to measure the slope. Almost makes me wonder what the purpose of highschool calculus.