As another non-homework-doer I also am here for this! I've never seen any grading plan with choice like this before, but it sure would have made my life a lot easier.
I always found that if homework wasn't weighted high (which happened in college) it was a trap. If I didn't do the homework I was gonna get in trouble on the exams.
Did she do the homework? The benefit would have been that she could just forgo the homework entirely and spend all that time doing something more valuable; the homework comes at a huge opportunity cost.
@@idontusenumbers She did! Homework takes a lot of time so has big opportunity cost, especially in the context of college social life. But in a calculus class its also one of the most effective ways to learn the material- sometimes even better than going to class.
@@ChrisStaecker Thank you for including this important detail. The whether she loaded up on the homewards or not is kind of irrelevant if she never actually did them. (And depending on the professor, she might have had the details available to be able to.)
As a computer science undergrad in around '81, an architecture student wandered in... He wanted to make a drawing sheet to allow him to sketch "circular perspective" drawings for his thesis. The idea was to roll the drawings into a cylinder, with the viewer at the centre, resulting in a 360 degree perspective panorama. Being more interested in these sorts of projects than achieving good grades, I accepted the challenge. I ended up plotting this beautiful A1 sheet covered in sine waves of various densities - it sort of looked like sine log paper. I never saw what he did with it... (The project was all the more interesting because networks weren't yet a thing and I had to write data to a mag tape and run to the other side of the campus to plot the results)
6:15 this ability to perform computations was the source of a dispute in a programming contest I participated in… The rules allowed a binder with paper, including "graph paper." After much debate, the judges settled on a way to differentiate between permissible "graph paper" and forbidden "engineering paper": the smallest gap between two lines. At the time, I found it absurd. In retrospect, it seems like a decent 'rule'
I went to a technical HS in the early 60's for electronics, we could buy individual graph sheets at the school bookstore.. I can remember buying their graph paper to plot antenna patterns, I'd have 2 or 3 pages of calculations (done with my K&E slide rule) with a plot of what the calculations proved.
I'm a bit surprised you didn't mention log-log paper, but I guess you had a limited time to talk. It was probably more useful than log paper, and the two of them together were what were used about 85% of the time in general engineering, where you didn't need one of the really specialized papers for your discipline. There were three classes of people that used these papers: PhD's, Engineers, and Draftsmen. PhDs either plotted things by hand with wavy hand-drawn "straight" line, or maybe advanced to the stage of using a ruler or the side of their slide rule for straight lines. Engineers usually had a selection of triangles and transparent scales, usually including a roller scale to draw parallel lines and a set of French Curves. Draftsmen would in most companies have a drafting machine, which made straight and square lines trivial, including making isometrics trivial. The progress of a chart was from a hand-drawn version from an engineer or PhD, then passed to the drafting department, where someone would tape a sheet of this graph paper down to a drawing board and plot it legibly. BTW, the perspective and isometric paper may have been plotted in squares, but nobody would have distorted Legos as a result. They would have measured the height of the Lego as 50% of the length, and then drawn fractional-height blocks. Using a compass or divider would have made it trivial to mark a stack of points all the same height, and then a drafting machine or rolling ruler would have turned those dots into parallel lines. See what you can know just by being older than the formation of the Earth?
Here's some lego trivia from a lego nerd: the ratio of length to height of a 1x1 brick (without considering tolerances) is 5/6. As you may know, a lego plate is 1/3 the height of a standard brick so you get a 5/2 ratio too. Actually, a lot of lego pieces have units half of a plate height, 1.6 mm, and some have even finer proportions. Advanced builders can make complex pieces fit together nicely.
Back in the day, when the dinosaurs roamed the Earth, I remember using log-log paper for analyzing experimental data. Those were the days when Engineers had to actually think.
On semilog paper, any exponential relation turns into a straight line--but on log-log paper, any power law (regardless of exponent) turns into a straight line! Amazing.
Typically only math and science teachers would understand the mathematics necessary to make such an offer. Not because teachers of other disciplines are 'stupid', but typically because their own strengths and values leading them to be a specialist in their own field.
I have some more graph papers to select for electronics use. A very handy one for dealing with chokes and capacitors is sone on a Log-Log chart. The impedances are plotted as straight lines versus frequency on groups. Capacitor impedances decay with frequency, so their lines slope from left high to right low. Inductances behave the opposite, from left low to right high.. You can instantly see which values produce a resonance at any desired frequency. Or where your low pass filter stops working. Another version of circular graphs appear on Smith-charts, used for radio applications, like determining effects of TV antenna cables.
These videos are amazing! The whole Playlist / series on 'Calculating Devices Reviews How Tos' is a fantastic treasure trove, a must see by any maths fan. This video is particularly a gem Mathematics, obscure devices wrapped up with dry comedy and a huge celebration of the mundane with the greatest enthusiasm The only down side is that the videos don't come in the ORIGINAL PACKAGING
This is one of your best Chris. I don’t understand it but I have always had a bit of a fascination with graph paper. I still have a box of K&E. Not the fancy stuff like you showed us though. I guess someone engraved these lines on the printing platen at one point in time so they could crank these out. Thanks for recreating some of them for us to enjoy. You need to do your calculus class as a series on one of the channels. I was bad at calculus and math in general but I love it. I would take your class just for fun. I would definitely put 60% of the grade on homework 😂
Wow what a channel!! It's been a week-long evening of bindging on old calculating and computing devices with Chris. Love all these devices and paper-oriented discussions. Was a real thrill to learn how important graph paper was and the many ways it's been used. Even though I'm in software, I use paper and pen/pencil all day. I've got stacks of vintage notebooks I've filled. It's easier to find old large-format books than new ones. Thank you so much for keeping this information alive and presented in an entertaining way. Love your sense of humor 😂
Brit here. Thank you. I think I now know how to pronounce 'Keuffel & Esser'. I've never heard of their products being big over here but my GF got me a rather nice Log Log Vector Slide Rule for my collection a few years ago. I had a couple of 5" Picketts and a Post but nothing from 'K+E'.
Very cool! When I was an undergrad in the early 1990s, I typed papers for Mathematicians in AmsTEX (like Latex, a typesetting program), and postscript (even "Display Postscript") was hot. PDFs were not quite mainstream. Anyway, I learned postscript and wrote some fun programs, but kept the one that prints graph paper and occasionally use it. The fancy graph paper was fun to see, but boring rectangular paper is super useful for day to day math and learning new math.
Hi, Oh boy. Superbe flashback. I used the semi log paper a lot in the early 80s to plot bacterial growth. I wanted the straight line to determine the growth rate and any indications of levelling off. The orange lined paper stuck into the hard bound lab notebook. Right thru that decade I’d use it. And I’d babble enthusiastically to the bored and smarter folk around at how cool it was. :-) Moved on k with an overlap, to cricketgraph on an se30. As an aside, I have to say that cricketgraph was the best graphing program I’ve ever seen. Simple to use but with features that for me were valuable. All about bacterial growth, exponential and slopes were key to maintaining the conditions for continued good growth. I’m by no means any where near math competent, seriously, but I discovered in cricketgraph I could take derivative to get slope, then second derivative change in slope. This was an epiphany. You’re laughing at the obviousness of this. But the second derivative allowed me to feed my culture ( batch sizes up to 5000l ) at the right time to maintain exponential growth. Feeding was tricky thing, to much or too soon inhibited, too little or too late never got growth back to initial slope. I have seen the other graph types in other notebooks and never Kniewärmern just hwo they were to be used. Thanks for explaining it all. Cheers Alistair
The triangle graph paper can be used for 3 metal alloys. A nice example is the graph of copper, gold and silver, where they show the color of said alloy. Each point is a metal and the opposite side has a scale of the percentage of that metal. What I've seen the most is, for a given temperature, what phase the alloy will be. This allows you to know what the composition your part will be at room temperature. (and thus, how strong, or hard it is)
My first job in the 1970s was Draftsman in a Civil Engineering office, plotting existing ground cross-sections on D sized orange graph paper. Exaggerated scale, don’t remember the actual scales but for example, 1”=20’ horizontal, 1”=2’ vertical. Then the Junior Engineer would cut a template of the design cross-section out of plastic sheet, calculate a key elevation (such as flow line of a trapezoidal canal), lay the template on there and trace the design cross-section over the existing. After that someone “buggied” the cross-section with a planimeter to get the cut areas and fill areas (square inches times horizontal scale times vertical scale equals square feet). Average the areas between cross-sections and multiply by distance between them (usually 50 feet). This would all be totaled up on a mass diagram to get total volume of earthwork in cubic yards, cut and fill.
The most incredible thing about this channel to me is how effortlessly you make your videos entertaining and hilarious. This is a serious talent that many professional "content creators" on YT wish they had. How do you get 6k views on videos like this instead of 600k is beyond me.
I hated the first couple years of high school, but the high point (for me) was drafting class - I don't remember exactly how many items we used from the Keuffel & Esser catalog, but it was _a lot_. I think I even had a pad of their log paper at one time. Thanks for the blast from the past!
Một bài hát rất hoài niệm , nhớ những ngày bồng bột của tuổi trẻ, chút kỷ niệm của tình yêu, lời chia tay vội vàng đúng như cái bồng bột ấy. Đức Phúc cover lại bài hát này tâm trạng quá !
In the mid 60s, without any computers, we used semi-log paper to graph the frequency response of aircraft flight control systems. I still have some of those sheets.
I've seen it in my chemistry class just the other week, and we often use isometric paper to draw in engineering Log paper is the one out of these that seems a little dated, since it's a lot easier to just take the logarithm of the data
11:24 There were drafting tables with angled and counter balanced rules on them. I would think this paper makes it easier to align those, rather than setting up your own perspective lines with string - which tends to make very strong foreshortening. (source: am old)
If you'd have told me 20 years ago that I'd have been watching a video about "graph paper" I'd have laughed in your face!!! This video should have been really boring - amazing job making it anything but boring - fantastic video Chris :-) Now I need to go get me some "graph paper" and plot some stuff..............
Engineering computation pads actually have the grid on the back. The paper is thin enough that when it’s on the pad, you can clearly see the lines, but when you pull it off and scan it, the lines disappear.
I took draughting back in high school, on paper with T-squares and set squares, which should tell you how old I am. Most of the paper was blank and bordered, but we also had paper with squares and triangles, great for drawing oblique angles. But this was also in the days of Dungeons and Dragons, so a lot of paper went "missing". 10:10 - THAT paper would have been handy for drawing buildings or mechanical objects.
@@ChrisStaecker Honestly, I probably would've put everything into exams if I could've since I generally did not show up to class when attendance was not counted. I ended up dropping out and I'm probably better off for it since now could I potentially retire, but I couldn't have even graduated yet if I stayed.
@@ChrisStaecker Yep. As a college prof. (Chemistry) a LOT of folks are surprised that I advocate so strongly for trade schools. But kids are told they "have" to go to college if they want a "good" job.
Thank you so so so much for the pdfs! I love K&E's catalogs, I personally have a turn of the century (1900) drafting machines catalog, which is pretty cool but this beats it hands down!
I suspect that the key to using perspective paper is to run a ruler between the top and bottom grids, the left and right grids, and the front and back grids, whenever you need to draw a line. I can't see it being much help for freehand drawing. Great video!
Yep. Going through my father's type catalogs from BB&S and ATF, I come across not only some beautiful typography but also some very interesting social commentary notes that most people of the time probably didn't think about at all. Back when there was more hands on maybe. Some day you ain't got better to do, check out an old Goes Litho certificate catalog. Now that's some serious art. . . . And, of course, I found your explanations of the various graph straightening functions reminding me of trying to figure out how to use two transistors & a handful of variable resistors to make a meter scale with with an antenna rotator so that half way around the rotation was in the middle of the meter and not skewed to one end or the other. (I actually did it but I didn't use graph paper ;-) ) . . . Nice history & math lesson, amigo. Thanks!
Chris, I just found your channel a couple of weeks ago, and I'm going to cover your entire back catalog. Great stuff. BTW, I'm not in the field, but I have seen graph paper consisting of hexagons, better for doing stuff in organic chemistry, where most everything is based on carbon, usually represented as a hexagon.
The way to use perspective paper is to sketch the shape on the planes represented by the faces of the grid. These sketches are then projected to determine the intersections of the vertices of the sketches. Honestly, it is easier to do it by hand than to use graph paper for this.
I'm so glad I found your channel... It's like Dr Steve Brule explaining stuff I'm actually interested in! Thanks for posting... liked, subscribed and trying to think of some one else to share this with who's as interested in these weird and wonderful relics as I am ;)
Visual measures for EDA (exploratory data analysis) are still important and were championed by Tukey. Any distribution can be plotted on a Q-Q plot, plotting theoretical versus actual quantiles against each other. R has this functionality builtin and a special function for the case of Gaussian distribution. Of course as a statistician I prefer to use ggplot2 which also can do this.
When you think about it maybe the graphing sheets probably don't cone in blue to avoid problems while photocopying and you choose between green and orange depending on how it looks after photocopying
I remember getting that 10x10 green-lined paper (probably not K&E brand but the same kind of stuff) and just vastly preferring it to the blue-lined stuff they sold at the drug store. I don't think I actually had any log-log or semilog paper but I coveted it. Got around it with digital calculation, just taking logs of things, which I guess in hindsight I should have seen as the crack of doom for most of this stuff.
I was unfamiliar with probability paper. This requires investigation as I often need to evaluate the probability of accumulated variations in mechanical system.
I was thinking... how often do I need to know the length of a curve, anyway? And then, I realized that if the "curve" is a cross-section of a piece of metal that I need to bend into that shape, then there have been many times I just took a wild guess, and ended up either a little short or a little long, and wasted material either way.
The "Blue Graph Paper" phenomena is probably down to the prevalence of the CMYK printing process. To get really nice sharp, crisp lines you want to only be using one color (i.e. one ink with one plate / press / drum / head / whatever) and any slight misalignment on a 2 or more color process would stand out like a sore thumb. This being so, the printers have a choice of either loading up a single color press with a single spot color ink in a nice green or orange, or just using one of the existing inks in their massive CMYK++ 3000ft/min web fed monster press, of which Cyan and Black are the only "sensible" options.
@@ChrisStaecker I like that you were completely willing to let me try to print tracing paper. I actually *do* appreciate you monitoring videos from years ago. Yet another reason I like ya.
Your videos are incredible. It must have taken ages to reproduce all the paper types. The conclusion remarks are hilarious. PS: there should be a name for retrofuturistic fictional universes where digital computers have not been invented and people have pished analog calculation aids to exquisite sophistication. A bit like atompunk in terms of the overall zeitgeist but with more weight on the engineering tools and less on the cold-war-ey stuff. How about analogpunk?
This made me think of Disco Elysium, with their radiocomputers and the fabled "prototype tape computer". I think the idea is supposed to be that they never went digital, and never invented the CRT so it's all paper printouts. The computers seem to be mostly electronic though. I want to call it radiopunk cause everybody listens to the radio, and even uses it like social media in what they call "milieus".
@@ChrisStaecker As soon as I saw that dot my guess was that she has ADHD like me. Homework (or anything) is a real struggle with executive dysfunction if it doesn't check one or more of the ICNU (Interesting, Challenging, Novelty, Urgency) boxes I would enjoy my math work in high school; I enjoyed learning new concepts, I found it interesting, it challenged me mentally, and it was a thing I (ideally) had to get done by the end of class. This satisfies all ICNU boxes However I usually grasped the concepts during the class period, and the same exact worksheet became awful, tedious, & I couldn't even bring myself to work on it as soon as I got it home As much as I like math, the problems take the same basic forms, just different numbers; they're no longer Interesting. I grasped the concepts in class; they're no longer Challenging. The concepts were new to me when the teacher did the demos, but now I've absorbed them; they're no longer Novel. I don't have to do it tonight, it's not due until next class overmorrow; it's no longer Urgent My teachers recognized that I was a good student, and even topped the class most of the time, but some of them had an absolute hell of a time trying to get me to actually do ny homework bc of the Executive Dysfunction. If I had the choice for weighting, I absolutely would've skewed more towards quizzes & tests like she did
@@shoofle I was going to blow this off, but then I found out the catgirls are involved! Unfortunately my university webserver is having persistent networking issues. I'm working on it!
"100% long fiber highest grade new rags" might legitimately be the funniest (non-intentional) promotional copy I've ever heard 🤣 shut up and take my money!
Lego instructions are not isometric. Isometric projections are set up such that each axis is 30° from horizontal, which has a surprising number of useful properties (notably that the z axis (vertical) has demarcations of the same length as the x and y axes. I believe lego instructions either dimetric, where one side is a different angle than the other - they could also be trimetric to normalize the z axis, as legos are not cubes. Orthographic projection was the term you were looking for, where everything is drawn in true length without regards for perspective.
Yes I agree- I didn't realize these specific angles had their own names. In mathematics more generally "isometric" means preserving the distances, so I think in that sense the lego instructions are isometric. But looking it up, I see there are other more specific terms for different types- thanks!
The intermediate positions are interpolated linearly (more or less, with a brief acceleration and deceleration at the ends). So it’s just something like (1-t)x + t log(x) where t ranges from 0 to 1. This is default behavior in Blender.
I love old scientific measuring devices. The items you review fit well enough next to those as a collection. Plus I suspect they are much more budget friendly. I’ll have to start me a collection.
I've never seen a commercially produced log paper using base e. Everything in this booklet is base 10. If only powers of e were labeled on the axis, it would basically become impossible to use for plotting data by hand- like if my value was at y=8, how do I know where to draw it on the powers-of-e scale? But I suppose the logarithmic scale could be spaced out with base e, while the grid lines and labels were drawn base 10. I think it could work, but I've never seen it. The logarithmic paper in the video has no scale markings on the vertical axis, so you could label them using powers of e if you wanted. Or any other base- I can imagine some cases where maybe powers of 2 might be helpful, so it's not such a crazy idea.
@@physiqueDrummond 10**(kx) would look like a straight line with slope k. But e**x = 10**(xlog(e)), so e**x would look like a line with slope log(e) [this is the base-10 log].
As I've become used to with your videos by this point, your first pronunciation attempt for the company name was the most correct (which I presume you already knew since it's the one you repeated in the body of the video, so... guess this comment was pointless!)
As the kid who never did homework but was fine on the tests, I am with you, Margaret!!
As another non-homework-doer I also am here for this! I've never seen any grading plan with choice like this before, but it sure would have made my life a lot easier.
I always found that if homework wasn't weighted high (which happened in college) it was a trap. If I didn't do the homework I was gonna get in trouble on the exams.
UPDATE: Margaret finished with a good grade. But she would've done better if she loaded up on the homeworks like most of them.
Did she do the homework? The benefit would have been that she could just forgo the homework entirely and spend all that time doing something more valuable; the homework comes at a huge opportunity cost.
@@idontusenumbers She did! Homework takes a lot of time so has big opportunity cost, especially in the context of college social life. But in a calculus class its also one of the most effective ways to learn the material- sometimes even better than going to class.
@@ChrisStaecker oh, it's a college class? I thought it was highschool.
@@ChrisStaecker Thank you for including this important detail. The whether she loaded up on the homewards or not is kind of irrelevant if she never actually did them. (And depending on the professor, she might have had the details available to be able to.)
As a computer science undergrad in around '81, an architecture student wandered in... He wanted to make a drawing sheet to allow him to sketch "circular perspective" drawings for his thesis. The idea was to roll the drawings into a cylinder, with the viewer at the centre, resulting in a 360 degree perspective panorama.
Being more interested in these sorts of projects than achieving good grades, I accepted the challenge.
I ended up plotting this beautiful A1 sheet covered in sine waves of various densities - it sort of looked like sine log paper.
I never saw what he did with it...
(The project was all the more interesting because networks weren't yet a thing and I had to write data to a mag tape and run to the other side of the campus to plot the results)
This was unexpectedly fascinating.
I remember K&E paper and other materials from my time in university. It is amazing how useful log paper is for analyzing data.
I never did any homework, I'm right there with you Margret!
I’m with Margaret. Absolutely hated homework.
Homework was rough; if you could get an A on the test, the homework was a total waste of time and sanity.
I"m 100% with Margaret. I had ADHD and my home life sucked, so homework was awful but I loved math and learning so tests were easy for me.
Besides, who wants to do schoolwork when not at school? It's not like you do job work after you get out of work, that's called wage theft.
6:15 this ability to perform computations was the source of a dispute in a programming contest I participated in… The rules allowed a binder with paper, including "graph paper." After much debate, the judges settled on a way to differentiate between permissible "graph paper" and forbidden "engineering paper": the smallest gap between two lines.
At the time, I found it absurd. In retrospect, it seems like a decent 'rule'
I went to a technical HS in the early 60's for electronics, we could buy individual graph sheets at the school bookstore.. I can remember buying their graph paper to plot antenna patterns, I'd have 2 or 3 pages of calculations (done with my K&E slide rule) with a plot of what the calculations proved.
I'm a bit surprised you didn't mention log-log paper, but I guess you had a limited time to talk. It was probably more useful than log paper, and the two of them together were what were used about 85% of the time in general engineering, where you didn't need one of the really specialized papers for your discipline.
There were three classes of people that used these papers: PhD's, Engineers, and Draftsmen. PhDs either plotted things by hand with wavy hand-drawn "straight" line, or maybe advanced to the stage of using a ruler or the side of their slide rule for straight lines. Engineers usually had a selection of triangles and transparent scales, usually including a roller scale to draw parallel lines and a set of French Curves. Draftsmen would in most companies have a drafting machine, which made straight and square lines trivial, including making isometrics trivial. The progress of a chart was from a hand-drawn version from an engineer or PhD, then passed to the drafting department, where someone would tape a sheet of this graph paper down to a drawing board and plot it legibly.
BTW, the perspective and isometric paper may have been plotted in squares, but nobody would have distorted Legos as a result. They would have measured the height of the Lego as 50% of the length, and then drawn fractional-height blocks. Using a compass or divider would have made it trivial to mark a stack of points all the same height, and then a drafting machine or rolling ruler would have turned those dots into parallel lines.
See what you can know just by being older than the formation of the Earth?
Here's some lego trivia from a lego nerd: the ratio of length to height of a 1x1 brick (without considering tolerances) is 5/6. As you may know, a lego plate is 1/3 the height of a standard brick so you get a 5/2 ratio too. Actually, a lot of lego pieces have units half of a plate height, 1.6 mm, and some have even finer proportions. Advanced builders can make complex pieces fit together nicely.
Back in the day, when the dinosaurs roamed the Earth, I remember using log-log paper for analyzing experimental data. Those were the days when Engineers had to actually think.
On semilog paper, any exponential relation turns into a straight line--but on log-log paper, any power law (regardless of exponent) turns into a straight line! Amazing.
Oh wow, your pick-your-own grade category ratios concept is amazing! I wish more of my teachers had had something like that in place…
Typically only math and science teachers would understand the mathematics necessary to make such an offer.
Not because teachers of other disciplines are 'stupid', but typically because their own strengths and values leading them to be a specialist in their own field.
I have some more graph papers to select for electronics use. A very handy one for dealing with chokes and capacitors is sone on a Log-Log chart. The impedances are plotted as straight lines versus frequency on groups. Capacitor impedances decay with frequency, so their lines slope from left high to right low. Inductances behave the opposite, from left low to right high.. You can instantly see which values produce a resonance at any desired frequency. Or where your low pass filter stops working. Another version of circular graphs appear on Smith-charts, used for radio applications, like determining effects of TV antenna cables.
These videos are amazing! The whole Playlist / series on 'Calculating Devices Reviews How Tos' is a fantastic treasure trove, a must see by any maths fan. This video is particularly a gem
Mathematics, obscure devices wrapped up with dry comedy and a huge celebration of the mundane with the greatest enthusiasm
The only down side is that the videos don't come in the ORIGINAL PACKAGING
This is one of your best Chris. I don’t understand it but I have always had a bit of a fascination with graph paper. I still have a box of K&E. Not the fancy stuff like you showed us though. I guess someone engraved these lines on the printing platen at one point in time so they could crank these out. Thanks for recreating some of them for us to enjoy. You need to do your calculus class as a series on one of the channels. I was bad at calculus and math in general but I love it. I would take your class just for fun. I would definitely put 60% of the grade on homework 😂
If you're serious about the classes, you might check out the playlists here: www.youtube.com/@profstaecker6579/playlists
@@ChrisStaecker oh how fun! Indeed I will. Thanks!!!
Wow what a channel!! It's been a week-long evening of bindging on old calculating and computing devices with Chris. Love all these devices and paper-oriented discussions. Was a real thrill to learn how important graph paper was and the many ways it's been used. Even though I'm in software, I use paper and pen/pencil all day. I've got stacks of vintage notebooks I've filled. It's easier to find old large-format books than new ones.
Thank you so much for keeping this information alive and presented in an entertaining way. Love your sense of humor 😂
Brit here. Thank you. I think I now know how to pronounce 'Keuffel & Esser'.
I've never heard of their products being big over here but my GF got me a rather nice Log Log Vector Slide Rule for my collection a few years ago. I had a couple of 5" Picketts and a Post but nothing from 'K+E'.
Very cool! When I was an undergrad in the early 1990s, I typed papers for Mathematicians in AmsTEX (like Latex, a typesetting program), and postscript (even "Display Postscript") was hot. PDFs were not quite mainstream. Anyway, I learned postscript and wrote some fun programs, but kept the one that prints graph paper and occasionally use it. The fancy graph paper was fun to see, but boring rectangular paper is super useful for day to day math and learning new math.
Hi,
Oh boy. Superbe flashback.
I used the semi log paper a lot in the early 80s to plot bacterial growth. I wanted the straight line to determine the growth rate and any indications of levelling off. The orange lined paper stuck into the hard bound lab notebook.
Right thru that decade I’d use it. And I’d babble enthusiastically to the bored and smarter folk around at how cool it was.
:-)
Moved on k with an overlap, to cricketgraph on an se30. As an aside, I have to say that cricketgraph was the best graphing program I’ve ever seen. Simple to use but with features that for me were valuable. All about bacterial growth, exponential and slopes were key to maintaining the conditions for continued good growth. I’m by no means any where near math competent, seriously, but I discovered in cricketgraph I could take derivative to get slope, then second derivative change in slope. This was an epiphany. You’re laughing at the obviousness of this. But the second derivative allowed me to feed my culture ( batch sizes up to 5000l ) at the right time to maintain exponential growth. Feeding was tricky thing, to much or too soon inhibited, too little or too late never got growth back to initial slope.
I have seen the other graph types in other notebooks and never Kniewärmern just hwo they were to be used. Thanks for explaining it all.
Cheers
Alistair
Ah! Cricket graph. Miss that guy. "what's it do?" "Graphs stuff...but really well"
The triangle graph paper can be used for 3 metal alloys.
A nice example is the graph of copper, gold and silver, where they show the color of said alloy.
Each point is a metal and the opposite side has a scale of the percentage of that metal.
What I've seen the most is, for a given temperature, what phase the alloy will be. This allows you to know what the composition your part will be at room temperature. (and thus, how strong, or hard it is)
My first job in the 1970s was Draftsman in a Civil Engineering office, plotting existing ground cross-sections on D sized orange graph paper. Exaggerated scale, don’t remember the actual scales but for example, 1”=20’ horizontal, 1”=2’ vertical. Then the Junior Engineer would cut a template of the design cross-section out of plastic sheet, calculate a key elevation (such as flow line of a trapezoidal canal), lay the template on there and trace the design cross-section over the existing. After that someone “buggied” the cross-section with a planimeter to get the cut areas and fill areas (square inches times horizontal scale times vertical scale equals square feet). Average the areas between cross-sections and multiply by distance between them (usually 50 feet). This would all be totaled up on a mass diagram to get total volume of earthwork in cubic yards, cut and fill.
The most incredible thing about this channel to me is how effortlessly you make your videos entertaining and hilarious. This is a serious talent that many professional "content creators" on YT wish they had. How do you get 6k views on videos like this instead of 600k is beyond me.
I hated the first couple years of high school, but the high point (for me) was drafting class - I don't remember exactly how many items we used from the Keuffel & Esser catalog, but it was _a lot_. I think I even had a pad of their log paper at one time. Thanks for the blast from the past!
Một bài hát rất hoài niệm , nhớ những ngày bồng bột của tuổi trẻ, chút kỷ niệm của tình yêu, lời chia tay vội vàng đúng như cái bồng bột ấy. Đức Phúc cover lại bài hát này tâm trạng quá !
In the mid 60s, without any computers, we used semi-log paper to graph the frequency response of aircraft flight control systems. I still have some of those sheets.
87a really made me chuckle.
I love your humor. "Ifinity! This is serious."
we still use the triangular paper often in material science for alloys or in chem eng for seperation of ternary mixes in distillation or leeching.
I've seen it in my chemistry class just the other week, and we often use isometric paper to draw in engineering
Log paper is the one out of these that seems a little dated, since it's a lot easier to just take the logarithm of the data
Isometric paper is my favourite type of paper to use for anything! I still use it today
I used K & EGraph Sheets extensively when I did my science degree in the 1970's. I still have some unused books of graph sheets.
11:24 There were drafting tables with angled and counter balanced rules on them. I would think this paper makes it easier to align those, rather than setting up your own perspective lines with string - which tends to make very strong foreshortening. (source: am old)
If you'd have told me 20 years ago that I'd have been watching a video about "graph paper" I'd have laughed in your face!!! This video should have been really boring - amazing job making it anything but boring - fantastic video Chris :-) Now I need to go get me some "graph paper" and plot some stuff..............
Engineering computation pads actually have the grid on the back. The paper is thin enough that when it’s on the pad, you can clearly see the lines, but when you pull it off and scan it, the lines disappear.
I took draughting back in high school, on paper with T-squares and set squares, which should tell you how old I am. Most of the paper was blank and bordered, but we also had paper with squares and triangles, great for drawing oblique angles. But this was also in the days of Dungeons and Dragons, so a lot of paper went "missing".
10:10 - THAT paper would have been handy for drawing buildings or mechanical objects.
What were you thinking Margaret?!
Hope she's not watching this...
@@ChrisStaecker Honestly, I probably would've put everything into exams if I could've since I generally did not show up to class when attendance was not counted. I ended up dropping out and I'm probably better off for it since now could I potentially retire, but I couldn't have even graduated yet if I stayed.
@@owendavies8227 More power to you- despite what American kids & parents think, college is not for everybody.
@@ChrisStaecker Thanks. Bold of you to do the opposite of marketing.
@@ChrisStaecker Yep. As a college prof. (Chemistry) a LOT of folks are surprised that I advocate so strongly for trade schools. But kids are told they "have" to go to college if they want a "good" job.
Thank you so so so much for the pdfs! I love K&E's catalogs, I personally have a turn of the century (1900) drafting machines catalog, which is pretty cool but this beats it hands down!
I suspect that the key to using perspective paper is to run a ruler between the top and bottom grids, the left and right grids, and the front and back grids, whenever you need to draw a line. I can't see it being much help for freehand drawing. Great video!
Yep. Going through my father's type catalogs from BB&S and ATF, I come across not only some beautiful typography but also some very interesting social commentary notes that most people of the time probably didn't think about at all. Back when there was more hands on maybe. Some day you ain't got better to do, check out an old Goes Litho certificate catalog. Now that's some serious art.
. . . And, of course, I found your explanations of the various graph straightening functions reminding me of trying to figure out how to use two transistors & a handful of variable resistors to make a meter scale with with an antenna rotator so that half way around the rotation was in the middle of the meter and not skewed to one end or the other. (I actually did it but I didn't use graph paper ;-) )
. . . Nice history & math lesson, amigo. Thanks!
Chris, I just found your channel a couple of weeks ago, and I'm going to cover your entire back catalog. Great stuff. BTW, I'm not in the field, but I have seen graph paper consisting of hexagons, better for doing stuff in organic chemistry, where most everything is based on carbon, usually represented as a hexagon.
From memory I think blue did not photocopy well with the photocopiers of the time.
The way to use perspective paper is to sketch the shape on the planes represented by the faces of the grid. These sketches are then projected to determine the intersections of the vertices of the sketches. Honestly, it is easier to do it by hand than to use graph paper for this.
you can get modern graph paper in green too
I'm so glad I found your channel... It's like Dr Steve Brule explaining stuff I'm actually interested in! Thanks for posting... liked, subscribed and trying to think of some one else to share this with who's as interested in these weird and wonderful relics as I am ;)
Lee Valley sells pads of isometric graph paper.
Visual measures for EDA (exploratory data analysis) are still important and were championed by Tukey. Any distribution can be plotted on a Q-Q plot, plotting theoretical versus actual quantiles against each other. R has this functionality builtin and a special function for the case of Gaussian distribution. Of course as a statistician I prefer to use ggplot2 which also can do this.
I remember isometric paper from my technology's class back in school, we never really used it past being taught how to draw on it.
Loving this channel.
When you think about it maybe the graphing sheets probably don't cone in blue to avoid problems while photocopying and you choose between green and orange depending on how it looks after photocopying
Blue does not print on diazo machines (blue line). So translucent paper with blue grids is handy if you don’t want the grids to print.
I remember getting that 10x10 green-lined paper (probably not K&E brand but the same kind of stuff) and just vastly preferring it to the blue-lined stuff they sold at the drug store. I don't think I actually had any log-log or semilog paper but I coveted it. Got around it with digital calculation, just taking logs of things, which I guess in hindsight I should have seen as the crack of doom for most of this stuff.
My new favorite!
I was unfamiliar with probability paper. This requires investigation as I often need to evaluate the probability of accumulated variations in mechanical system.
omg
its called graph paper because they used it to make graphs
honestly i shouldve realized that one sooner
I was thinking... how often do I need to know the length of a curve, anyway? And then, I realized that if the "curve" is a cross-section of a piece of metal that I need to bend into that shape, then there have been many times I just took a wild guess, and ended up either a little short or a little long, and wasted material either way.
This is incredible, thanks
The "Blue Graph Paper" phenomena is probably down to the prevalence of the CMYK printing process.
To get really nice sharp, crisp lines you want to only be using one color (i.e. one ink with one plate / press / drum / head / whatever) and any slight misalignment on a 2 or more color process would stand out like a sore thumb. This being so, the printers have a choice of either loading up a single color press with a single spot color ink in a nice green or orange, or just using one of the existing inks in their massive CMYK++ 3000ft/min web fed monster press, of which Cyan and Black are the only "sensible" options.
Blue lines did not reproduce on photo printing so the grid would disappear when the printed output was generated.
to be honest I was surprised there weren't any dots with minimal homework, because I would have absolutely gone all-in on exams if I could
Great review. I like your new microphone.
3:45
You think you can scan some of these tracing papers so I can print and try them as well?
@@OldManBOMBIN I don’t have any- I only have the catalogue.
@@ChrisStaecker I like that you were completely willing to let me try to print tracing paper.
I actually *do* appreciate you monitoring videos from years ago. Yet another reason I like ya.
Your videos are incredible. It must have taken ages to reproduce all the paper types. The conclusion remarks are hilarious.
PS: there should be a name for retrofuturistic fictional universes where digital computers have not been invented and people have pished analog calculation aids to exquisite sophistication. A bit like atompunk in terms of the overall zeitgeist but with more weight on the engineering tools and less on the cold-war-ey stuff. How about analogpunk?
This made me think of Disco Elysium, with their radiocomputers and the fabled "prototype tape computer". I think the idea is supposed to be that they never went digital, and never invented the CRT so it's all paper printouts. The computers seem to be mostly electronic though. I want to call it radiopunk cause everybody listens to the radio, and even uses it like social media in what they call "milieus".
In Germany, the standard colour for graph paper linings is orange and not blue. Seems like a thing that depends on the country you are living in.
When you said "42nd edition", i knew i have encountered the solution for everything.
And i was plotted right.
Iso metric paper is still used by welders to draw up piping
I love this guy!
"What are you thinking, Margaret?"
Dunno about Marge, but I'm thinking either heavy procrastination or absolute scholarly enlightenment
A little of both I think- she seemed to be a really good student.
@@ChrisStaecker As soon as I saw that dot my guess was that she has ADHD like me. Homework (or anything) is a real struggle with executive dysfunction if it doesn't check one or more of the ICNU (Interesting, Challenging, Novelty, Urgency) boxes
I would enjoy my math work in high school; I enjoyed learning new concepts, I found it interesting, it challenged me mentally, and it was a thing I (ideally) had to get done by the end of class. This satisfies all ICNU boxes
However I usually grasped the concepts during the class period, and the same exact worksheet became awful, tedious, & I couldn't even bring myself to work on it as soon as I got it home
As much as I like math, the problems take the same basic forms, just different numbers; they're no longer Interesting. I grasped the concepts in class; they're no longer Challenging. The concepts were new to me when the teacher did the demos, but now I've absorbed them; they're no longer Novel. I don't have to do it tonight, it's not due until next class overmorrow; it's no longer Urgent
My teachers recognized that I was a good student, and even topped the class most of the time, but some of them had an absolute hell of a time trying to get me to actually do ny homework bc of the Executive Dysfunction. If I had the choice for weighting, I absolutely would've skewed more towards quizzes & tests like she did
it seems like the links in the description are no longer working; can we get updated ones? :3
the catgirl delegation demands antique calculation methods downloads!!!
@@shoofle I was going to blow this off, but then I found out the catgirls are involved! Unfortunately my university webserver is having persistent networking issues. I'm working on it!
"100% long fiber highest grade new rags" might legitimately be the funniest (non-intentional) promotional copy I've ever heard 🤣 shut up and take my money!
I'm lovin it
I used to be given 1mm lined 5mm accented and 1cm bolded quite a lot in the '00s - why wouldn't you use that if you needed to graph stuff?
Lego instructions are not isometric. Isometric projections are set up such that each axis is 30° from horizontal, which has a surprising number of useful properties (notably that the z axis (vertical) has demarcations of the same length as the x and y axes. I believe lego instructions either dimetric, where one side is a different angle than the other - they could also be trimetric to normalize the z axis, as legos are not cubes.
Orthographic projection was the term you were looking for, where everything is drawn in true length without regards for perspective.
Yes I agree- I didn't realize these specific angles had their own names. In mathematics more generally "isometric" means preserving the distances, so I think in that sense the lego instructions are isometric. But looking it up, I see there are other more specific terms for different types- thanks!
I test well and I don't do any homework at all, I'd probably choose the same as Margaret.
Please tell me you have the scans still! The link is broken. I’d greatly appreciate a new link.
Sorry I had to move the pages. I just updated the link! It should work now-
10:49 this looks like a dimetric projection to me
What, no Smith carts? I'm disappointed.
you sound like Drue Langlois character plaugue roach.love you videos ^-^
87a ofc
what are the lyrics to the nifty outro song?
I’m here to start some static bout money, murder, and mathematics.
How about stereo nets?
Never heard of it, but just looked it up- very interesting, thanks!
Great Video!
Nice linear to log animation! What functions did you use in between?
The intermediate positions are interpolated linearly (more or less, with a brief acceleration and deceleration at the ends). So it’s just something like (1-t)x + t log(x) where t ranges from 0 to 1. This is default behavior in Blender.
@@ChrisStaecker Ah, that explains the zero at the bottom, which, as you know, is not present on a log axis.
@@ClausB252 Yes probably I should've made the zero fade out, but I didn't think of it at the time
Interesting 🤔
Lol, I'm a total Margaret. Didn't do a single piece of homework in my entire AP Calculus class. I was just in it for the fun of the math anyways.
I love this. The last part was the best
Where do you get all your stuff
eBay & Craigslist mostly. These things are mostly obscure, but not hard to find and get if you know what you’re looking for.
I love old scientific measuring devices. The items you review fit well enough next to those as a collection. Plus I suspect they are much more budget friendly. I’ll have to start me a collection.
Visit your local geology department and ask about THEIR graph paper.
I think it is pronounced as Koi-ful & Eszer Co. 🤔
Were you able to choose the base of the logarithm paper? Either 10 or "e" ?
I've never seen a commercially produced log paper using base e. Everything in this booklet is base 10. If only powers of e were labeled on the axis, it would basically become impossible to use for plotting data by hand- like if my value was at y=8, how do I know where to draw it on the powers-of-e scale? But I suppose the logarithmic scale could be spaced out with base e, while the grid lines and labels were drawn base 10. I think it could work, but I've never seen it.
The logarithmic paper in the video has no scale markings on the vertical axis, so you could label them using powers of e if you wanted. Or any other base- I can imagine some cases where maybe powers of 2 might be helpful, so it's not such a crazy idea.
@@ChrisStaecker then what happens when someone plot values from e**x ?
@@physiqueDrummond 10**(kx) would look like a straight line with slope k. But e**x = 10**(xlog(e)), so e**x would look like a line with slope log(e) [this is the base-10 log].
As I've become used to with your videos by this point, your first pronunciation attempt for the company name was the most correct (which I presume you already knew since it's the one you repeated in the body of the video, so... guess this comment was pointless!)
Pretty much all but the paper has returned. Bring back graphing sheet, GURPS / Warhammer / D&D games need it.
I want this. No particular reason. I just think it's neat.
That about sums up my feelings about all my videos!
I thought I was the only one who collected graph paper.
Margaret wants to do school work at school and wants to do whatever she wants to at home. But definitely not schoolwork at home.
Margaret is all of us.
Even this cannot flatten Ruble's curve
I never had a safe place to make homework a viable option. A’s on tests or bust.
So uh... good times never ended I guess?
>not using incompetech music
"now it's only available in blue" you should go find a Japanese stationary store
1:13 Joke’s on you and everybody who bought those dumb things. The universe is infinite, which means it cannot be divided.
"Joke’s on you and everybody who bought those dumb things" pretty much sums up my whole vibe.
11:07 Yep, "the paper" was less successful 😂
"... And the world was usually on the brink of nuclear disaster"...
Using a slide rule as a ruler? Shame on you.
The curious cowbell hopefully fold because vulture nearly search throughout a magnificent shame. wholesale, homely colombia