Secrets to measuring a piece of paper - Numberphile
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- Опубліковано 10 жов 2017
- When Cliff Stoll sets your homework, there's always an extra lesson.
More links & stuff in full description below ↓↓↓
More Cliff videos: bit.ly/Cliff_Videos
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Sign up for (occasional) emails: eepurl.com/YdjL9 - Наука та технологія
That's the opposite of clickbait
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Simply, content. Rare on UA-cam these days
Why should I believe the purple sheet is the rectangular one?
Use this protractor to test all the corners
[Protractor actually labels 90 at the 87 degree point]
O_O We must go deeper! Seriously, though, you can confirm that something's a rectangle without a fixed measuring device. You can get right bisectors on opposite sides with a compass and straight edge (IF IT'S TRULY STRAIGHT! :O) and check if they coincide. With some fiddling, you can do it with just a compass to decent precision, to avoid trusting the straightness of the straight edge, though it's a bit messy. Fun challenge, though! :)
Neil G. Dickson if the diagonals are congruent and bisect each other, it's a rectangle.
@grandoldrunner: The challenge there is how to determine whether "the diagonals are congruent and bisect each other" when you can't trust any of your measurement devices. Even the approach I suggested with just a compass doesn't work if the table isn't flat. ;)
Come on guys, to get a right angle: just fold any piece of paper twice. Once to get a straight edge. Another to half the half tau angle.
I don't know why I clicked on this video judging by the title but I'm glad I did.
I would have clicked much faster if Cliff was in the thumbnail. If he's in the video, I GOTTA know.
Because you didn't know what it was about, but you JUST HAD TO!
now you have to subscribe
I didn't expect the klein bottle guy; now I like the video so much more.
I know why: It helps to forget the BS floating on the tube...
I love how enthusiastic he is every time!! I wish he was my
teacher back then.
You can just see the passion he has for math/science!! :)
Yeah, he’s like the real-world version of Doc Brown, it’s great
false..
They must have used the imperfecto ruler when they built my house.
if i gave anyone an imperfecto ruler, they'd see it immediately.
no one trusts me lol
old soul. Wow
I am subscribed to your channel, glad to see you with a top comment haha
hahaha
The real question is - would it really matter tho? Everything would be equally off by 1cm, hence everything would come out even and fine. You would actually have a bigger house for the money of a smaller one (assuming the ruler was longer and not just added at the end of itself, in which case your house would be way bigger)
This title is the opposite of a click bait. And the video content is the opposite of a click bait video content.
Xano Trevisan Kothe this should became a numberphile brand/meme kind of thing... Like parker square but anti-clickbait
Great lesson about life ! Thanks Cliff !
Maths moi ça ! Eh mais j'ai déjà vu une de tes vidéos haha
J'espère que ça t'avait plu ;) N'hésite pas à revenir, de nouvelles sont sorties depuis !
Maths moi ça ! Allez c'est parti, je vais les regarder, je me souviens plus pourquoi je m'étais pas abonné à l'époque 🤔
Je t'en veux pas ;) N'hésite pas si tu as des remarques ou des idées de vidéos ! Merci pour ton abonnement !
false..
I really wish he was my math teacher
btw, "I didn't think you'd be an iphone guy-"
"IT WAS DAVID HILBERT!"
oh .. the guy that invented that funky space filling curve
Mihai Lazar Sounds like you know 3Blue1Brown :-D
Dragon Curve Enthusiast But of course
Mihai Lazar Hilbert did A TON. He was one of the most influential mathematicians of the late 19th and early 20th centuries. The more you study math, the more you tend to hear his name pop up :)
And yes, the Hilbert Curve is awesome (as is the 3B1B video on it)!
OrangeCreeper Google him and you see you probably wouldn't want him
The difficulties of measuring a Parker Square
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There's an extra twist to that double 17th cm, it's only 9 mm wide!
Oh, like I'd trust *anything* about that ruler once I noticed it had two 17s. For all I know the millimeters are actually 0.95mm wide.
LOL yeah, and maybe with a hyperbolic geometry so distances aren't even linear...
speedbump0619 My thoughts exactly :D
I have a midterm to study for, but I see a new Numberphile vid, so I'll just see what it is - jackpot : it's Cliff !!
He's just the best. Thank you. I needed the break.
Same here haha
That is so awesome. I'm totally gonna use that on my students.
KamiKuzi YESSSS
That's going to be fun for you and the students. xD
Probably your students also watch Numberphile. :P
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Suggestion: make one of the centimeter increments have one more or one less millimeter.
This is the type of assignment I would hate my teacher for, but it's also the one for which I would one day love him!
This video probably had a larger impact on me than 4 years of high school teachers. Education is so much more than standardized tests and memorization. It's about learning how think and feel and react. This was beautiful.
Is he open to Grand-son applications?
Sorry the queue is already full
Glad that Hilbert never got to know about Gödel's incompleteness theorems. He would have been devastated.
Socialist Squirtle
He did. (No reference provided) The two men didn't interact, but it seems Hilbert mostly dismissed them. The theorems (and Gödel) were particularly controversial and generally misunderstood then (and still now).
Cliff is the type of Prof that would create a generation of scientists. This wonderment is what's missing in science curriculums, what has always been missing but for a few exceptional teachers that took the time to get their students excited about science.
Shoutout to Mr. Omar and his fourth grade science class for launching my school career.
Unfortunately, the curiosity and drive for knowledge he wants out of his students is the very thing schools have spent 12 years beating out of them.
That's exactly why he's fighting back against it.
I disagree with you, I would say more than 20 years
too bad many people go on to a fulfilling life of education and knowledge for your statement to even stand on its own.
@Fernando Lavalle
where are you from? why did you go to school for 20 years? is that normal in your country?
Its hard to get a PhD without at least 20 years of school.
Please tell me Cliff's immortal. I don't want to hear about him passing away :(
then don't think about it
Wish him a long and healthy life.
toropazzoide please tell me where to find your profile picture
mtndewman1022 google "dr house meme", it should be one of the top results :)
toropazzoide
That's not actually the original Cliff, though it's an enormously faithful replica.
Cliff Stoll is a fantastic man! the way he explain things is easy to understand, and his passion makes me so excited!
I can relate to this guy so much.
Growing up in my house we had a bookshelf in the living room with a dictionary, an atlas, a set of encyclopedias and a series of "How Things Work" books. If something came up that we didn't know the answer to we would look it up right then and there. The internet has made this habit nearly a compulsion.
Also, that homework assignment is brilliant!
Cliff is truly inspiring. Thank you for highlighting him and his work!
That guy is a complete lunatic! I love it!
This is so touching on how passionate he is about learning and teaching.
He wants everyone to look at the details and pay attention to the details.
*I’d love to have him as a teacher, seems like it would be hard but also fun!*
Who else wants a teacher like him? XD
Toni Burón i
In practice yes. But knowing myself I would completely try the East way out and fail the class.
Easy not east
I definitly do. But I teach physics, and by knowing my students, they wouldn't unfortunately. It's hard to get them intrested
Not me. I don't want someone jumping around and screaming at me for no reason, he would definitely assume i'd be totally disinterested but that's just my nature, there were always problems like that in school and i am surely not the only one. On behalf of all of those kids don't let the superficial appearance of 'enthusiasm' or interest for the class influence your evaluation of the student
"My idea of teaching is everyday have the kids go home and do an experiment" [Pause video, like video, unpause video]
I love that, "homework" nowadays is dreaded as its simply busywork. Doing the same thing you did in class except without a teachers guidance. The fact we grade on how correct the answers are is insane. All that does is reinforce the students who already have a 100% understanding of the subject and alienate those who need help.
I love that he prescribed something fully expecting "failure" and seemed genuinely proud of the students who figured out some of the issues of the problem. And I have no doubt in my mind that every student who did the work got full marks even if they didn't notice anything wrong.
My favorite math teacher had a similar understanding, and would give you some points back on homework if you wrote a sentence about why you got the problems wrong, not just redoing the question and getting it right, he wanted you to understand HOW you got it wrong. He said he was basically forced to follow the curriculum and give graded homework, and allowing students to get points back for attempting to learn the content better was the only thing he could do.
I was told in maths to always show your working out. Even if you get the answer wrong, they can award most of the marks if the logic is correct. It also makes it easier for you to check your answers if you have extra time at the end.
msclrhd Here in Sweden you're basically expected to show your working out of most nontrivial math questions; just putting down the right answer on, say, a problem worth 5 points on a national math test might get you one single point for not being wrong and "SHOW YOUR WORK!" scribbled in red pen while writing down your working out of the problem and doing it right but getting the wrong answer at the end because you missed a minus somewhere could get you 3-4 points if your work is otherwise correct.
Oh, we get a 0 failing grade if you don't show your work either.
Most of the time we get 0 points for showing our work, we get nothing for showing work because its expected. You have to show your work AND get a correct answer for most schoolwork.
The only time showing your work actually matters is on placement tests for schools, and generally get 1 to 5 points depending on the mistakes you made. But again, only for placement tests for college and such.
99% of highschool is either 0 points or 1 points.
Don't show work? 0 points
Don't get the answer right? 0 points
Get the answer right but forget rewrite the answer in a sentence? 0 points.
Get the answer perfectly right? 1 point.
Its not like getting points for showing your work would help though because of the american grading system.
In most schools anything below a 60% is failing and 90-95% is considered "average". My school got rid of that and made it so any grade bellow 75% was a fail. So in reality partial credit would barely help anyways, its better just to get everything right lol.
Connor Hill Damn, 90-95% is average?! So does that basically make A the average grade then or how does that work?
I love Cliff. He's just so enthusiastic and it's contagious
This was so different from the other videos with Cliff, but I loved it. Great lesson.
I wanted to learn something about measuring paper but instead, i got some life lessons.
10/10 would fall for clickbait again
*numberphile is trending and i have never felt more happy i watch them*
Cliff is the embodiment of science enthusiasm. Not even the slightest detail must go unexplored. Even something as insignificant as the specific name of the mathematician must be discovered, even if we know by the description who it is.
I love these videos with Dr. Emmett Brown, he's great to listen to
Great Scott! The area isn't what you think it is!
If you take away the windows of the DeLorean, the area is gonna be different!
I really wish I had been a student in one of Cliff's classes. He has such great enthusiasm for everything and I love his take on maths and sciences! Every Numberphile video I watch featuring him makes me super happy and pumped! If he ever did an encore class, I'd do everything in my power to attend as I envy his former students!
The Bookcase has "Automatic Sprinkler Systems" and "M.C.Escher". This explains a lot
Doom NK Presumably, an Escher sprinkler system sprays water onto itself?
This guy is the first one who has the same passion to learn anything we don't know. It is great to see :D
Omg I love this Cliff guy so much! So full of energy and you can really tell he loves his work. I wanna be like Cliff when I grow as old as he is.
You don't wanna be an IPhone guy do you?
That double 17 ruler is pure evil. I love it!
Wait, there's more: they are 9 mm long, not 10. :D
I love this guy so much ! Mathematical way of life ♥
His enthusiasm and giddy excitement is so infectious. Videos with him never fail to cheer me up.
Maths moi ça ! Inquisitive mind kind of life, always looking for the joy of learning/understanding something
He reminds me of back to the future 😂😂
I have nothing but love and admiration for Cliff.
Cliff is just my absolute favorite person. he is just so into what he likes, and he is a great teacher. I really enjoy listening to him, and I'd love to spend a day with him just talking about math, science and life in general.
His enthusiasm is so contagious
Cliff you beautiful person
Brady's vids with this guy are like proper chill ngl
I feel this man. The only drive in my life is pursuing knowledge. More and more, every day. Pursuing perfection.
I am a simple guy.
I see Cliff, I hit like.
I am a simple guy.
I see "I am a simple guy.
I see 'x', I hit like.", I hit like.
You post a comment demonstrating your routine for if you see Cliff.
Let x(0) be "I am a simple guy. I see Cliff, I hit like"
and let x(n) be "I am a simple guy. I see x(n-1), I hit like."
you are not a simpel guy.
neverending story inspired.
There is a book about sprinklers in the background. This guy is so funny.
Bearziherl where? I can't find it
Bearziherl nvm commented too early. Found it in a closer shot
No, but seriously, this guy Cliff is AWESOME. Wish there were more people who were that interested in KNOWING. 👍🏽👍🏽
Someone make a petition that makes it mandatory for Cliff to be in every Numberphile video.
Love this guy!
This man is a national treasure
I'm touched by how genuinely happy you look when you speak.
This is perhaps one of my favorite videos. It gave me the chills (in a good way). Thanks Brady! -and Cliff!
Cliff Stoll would make an excellent Doctor Who.
I think Tom Baker's Doctor is pretty close. He's got the same kind of enthusiasm Cliff has.
You have ONE JOB, Science! Clone this man.
I love his enthusiasm and drive for knowledge.
Cliff is great, would have liked to have had him as a teacher for sure. Enthusiasm is important
"I didn't see you as an iPhone guy", is that because he's intelligent?
I want the same ruler !
Do you have Photoshop and a printer?
Especially if he borrows it for an exam !
Where as some people that get in "measuring" contests would like the reverse setup ruler. 1" 2" 3" 5" 6" 7"
I also thought the ruler's length might be wrong altogether, e.g. every marking is actually 0.9 cm apart.
there is only 9mm between the two 17s
I love Cliff videos so much, Cliff is so passionate, is an inspiration for me.
I love this guy. He is so insanely positive and passionate.
This guy is the best! I wish he started a podcast
Michael Rector he has one but it's inactive
It could be him commenting on and describing various problems. We could call it Cliff Notes
Anyone notice that between the two 17s on the ruler, that there are only 9 ticks instead of 10? The second 17 is therefore 17.9, then the 18 after that is really 18.9 and so on
Assuming the millimeters aren't actually 0.95 mm thick.
Cliff and James are my two favourite people who appear on this channel. They remind me very much of professors I had in late high school and early college, and I wish I had more teachers like them.
This is pure gold! I wish I had him as a teacher in elementary school. This little experiment should be required for all children in the world when they first start getting introduced into Math, Physics or any science for that matter. The world would be completely different if this was implemented.
master level troll
Easy way to calculate the area. Cut out a square centimeter of that paper (or ten for good measure), and weigh it. Then weigh the whole piece of paper, and just divide with the weight of the initial piece. Assuming that its density is uniform, you should easily get the total area. :D
Use this trick to calculate integrals. Print your graph on a millimeter paper, and weigh a square and then the whole graph. No need to use math or computer programs.
George Papadopoulos
An elegant solution. It still requires your mentioned assumption, but in general very effective and accurate. (I'm assuming weighing ink would be avoided)
Well, you have to cut the graph along the line. So, you can choose a thin line to print the graph. But I think it would have a minor effect!
For paper provided that isn't rectangular [while you are expected to think that], that came with a ruler that is wrong, can you assume that it is of uniform thickness?
It would be difficult to make 1 that wasn't of consistent thickness
I can't even handle how amazing Cliff is.
Best Cliff video yet.
I want an assignment from Professor Cliff!
How many life lessons did he manage to cram into this simples sounding homework assignment
I wish i had a teacher like him. His enthusiasm is infectious.
Hope there will be much more professors and teachers with his enthusiasm. what a good energy!
"Great Scott, Marty! As long as you hit that wire with the connecting hook at precisely 88 miles per hour, the instant the lightning strikes the tower... everything will be fine!"
LoL, was looking for this :D
I love him!
I would loved a teacher like Cliff. Passion, Energy, and a sense of humour and trickery THIS makes me curious and THIS makes me want more. Not the endless droning on that I got.
Numberphile, this guy is the best, MORE VIDEOS WITH CLIFF!
But the prof seems to have forgotten the largest unkown factor, the surface isn't completely flat. On a microscopic level it's an insane mess of fibers and binding materials. So with hand tools all we can say is that the surface is larger then the one we can measure.
R K shoo, dirty engineer
LOL. Not engineer, just a machinist ;-)
Fractals to the rescue!
I thought I had this things figured out but you caught an unconscious assumption I and almost everyone else missed (and yes, I caught the Euclidean Geometry assumption). You win sir! (Did you realize that the edges are probably jagged as well?)
Thinking about this some more, it's another aspect of what exactly he meant by "area". Is it the 3D surface area, or the area covered by its 2D shadow on a flat surface? We generally think of paper as a 2D surface, so that's another assumption to clear up.
I never found out what the area was - lol
The answer doesn't matter, its the question that matters.
Most schools in the US forget this, they hand our sheets of math problems and grade you based on your answers and don't give two shits about how you solved the question.
The fact that you care more about getting the correct answer is pretty much proof of what Cliff is saying.
You're actually amazing, Cliff. Much love.
Cliff, you must be an amazing teacher. Those tricks you added to the simple task of measuring paper were incredible, seriously makes people think.
An inclination for investigative curiousity often "comes naturally"
Such inclination can often be kindled where it is not noticeably present
Such inclination can always be nurtured
And sadly such inclination can easily be drowned
I wish he was my maths teacher
Cliff is so great at conveying a message. Just watching him gives me gooosebumps.
One of the most educating videos I've ever seen.
What about the roughness of the paper?
Wir müssen wissen
Wir werden wissen
"Was einmal gedacht wurde, kann nicht mehr zurück genommen werden."
"Ich liebe Titten." Mahatma Gandhi
This guy is a perfect teacher. he conveys enough enthusiasm so that you feel the thirst of knowledge
This is the type of teacher you want. He’d always have you think outside of the box, his way of teaching would be immersive. Not many teachers like that these days.
I would've caught the holes, but nothing else.
Looks like he enjoys his job.
I cannot, I will not ever have enough of Cliff Stoll.
I love the videos you make with Cliff Stoll. He's just so enthusiastic about everything he does and really inspires me to think about the way i look at things and gets me interested in mathematics. :D
Trolling at its best.
YOU WON'T BELIEVE NUMBER 4!
But they all believed number 17!
=24
Back to the Future number 4! You said it! It's one of my favorite trilogies and soon we will get part 4 and then it's not a trilogy anymore.
Rekko P. Nah, it's not a fourth part. It's a reboot with an all-female cast and a new soundtrack by Fall Out Boy.
Sounds like Douglas Adams, with his Hitchhiker's Guide To The Galaxy trilogy. There were five books in the story by the time he died, and a sixth part of the 'trilogy' was completed by Eioan Colfer a few years later. Minds being messed with!
I love your videos!
In my opinion, you make the best numberphile videos!
BRILLIANT. I wish my math teachers would have taught this way. I would have known about how much I love math WAY back then instead of figuring it out in my 30's....
2:34 who flinched?
a little...
I wouldn’t have thought of him as an iPhone guy either. Also for some reason I assumed he was gonna pull out a massive book to look stuff up in. I guess that’s my fault for stereotyping someone who has been around the sun many more times than I have.
Cliff's enthusiasm is so infectious. I bet he was a fantastic teacher for those 8th graders!
I just love how happy he is with his math. It reminds me of when I was a kid watching math programs. I clicked on this because I had to measure a part of my room using a sheet of paper. I didn't have standard measuring tools. What I did have was paper with it's size known. I taped sheets to the wall until the space left was smaller than the sheet of paper. Then I folded it in half repeatedly to get smaller units. It worked out well. The furniture sits perfectly in the space.