Secrets to measuring a piece of paper - Numberphile

  • Added:  5 days ago
  • When Cliff Stoll sets your homework, there's always an extra lesson.
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  • Science & TechnologyScience & Technology
  • Runtime: 5:35
  • numberphile  paper  ruler  

Comments: 1 370

  • Jochem van Pamelen

    I've got a question, but first let me set the scene.

    So, I was calculating the limit of x->4 of (x²-2x-8)/(4x-x²) this would equal -1,5. Of course if x=4 there would not be a y-value because you would divide by 0. So wondered what it would look like if you zoom in on the the point A(4;-1,5). I took my calculator (TI-84 plus CE-T), put in the function and started to zoom in. Eventually I started to see something that looked like random spikes in the line.

    So my question is: why does this happen?

  • rolen47
    rolen47 13 hours ago

    For some reason this guy reminds me of Scott Bakula.

  • RicksGamerShelter RGS
    RicksGamerShelter RGS 20 hours ago

    what is 1110 to the power of 1111 ?

  • Alan Henness
    Alan Henness 22 hours ago

    You are cruel! I love it.

  • larrybud
    larrybud 22 hours ago

    He missed a couple of assumptions: Even if you caught the two 17's on the ruler, whose to say the ruler is calibrated correctly? And if you're using the other sheet of paper to check squareness, you better know that your source sheet is also square.

  • fang4643
    fang4643 Day ago

    Great video! Having that sort of mentality can get you into trouble at work sometimes, people just want instant results these days and consider curiosity a waste of time. I just had a shitty day at work because of that and I feel better now knowing there are different people out there.

  • awillers55
    awillers55 Day ago

    Legend has it that his brain is a Klein bottle

  • TheIgnobleSavage

    Why is it not a rectangular piece of paper? @1:45

    • TheIgnobleSavage
      TheIgnobleSavage Day ago

      Had he handed them a piece which was purposely cut differently?

  • Frank Harr
    Frank Harr Day ago

    Awwwww, Metriiic! Do I have toooooo!?

    I don't know how I would have handled this as a student.

  • Stephen L
    Stephen L Day ago

    I would conjecture that the likely enduring memory of his students would not relate to mathematics, but rather be something along the lines of, "Trust less".

  • Dingleburry
    Dingleburry Day ago

    theres holes in the paper

  • David Gillies
    David Gillies Day ago +1

    It was Hilbert: Wir müssen wissen, wir wereden wissen, in response the the Latin maxim igroamus et ignorabimus (we do knot know and we will not know).

    I hate not being able to solve a puzzle. It will consume me until I know. This is a trait I have in common with a very large number of scientists and engineers. I think it's innate rather than taught. Some people are happy not to know.

  • DB Fuller
    DB Fuller Day ago

    Paper size nerd. The second he gave the measurements, I knew something was off.

  • brian554xx
    brian554xx Day ago

    I think if you get Cliff Stoll and Matt Parker together, tell them "go off come up with something together in secret, you have 3-12 months, as needed," the result would be *spectacular!*

  • Charles Kevin Calipes

    Hey Numberphile, so I found this geometric "puzzles" called "Euclidea." You can feature some problems there. It will be interesting to watch mathematicians doing that game.

  • DeathrashWhiplash

    That guy is a beauty

  • Petra Kann
    Petra Kann Day ago

    How on earth can he forget Hilbert's name?

  • LateNightHacks
    LateNightHacks 2 days ago +1

    Cliff, if you teach a math class at school, I would gladly drop everything and go back to school, that school to be specific

  • Cyrus Tabery
    Cyrus Tabery 2 days ago

    Make a model of the paper and measure the paper with photographs and electron beams and write some simple software to measure the output and report on surface area. Measure model map I always say. Thanks for the Hilbert quote. We will know!!

  • Admiral Percy
    Admiral Percy 2 days ago +1

    This was exactly how I got a job as a sound tech in college! They asked why I wanted the job with no experience, I just said, "every time I walk by a sound board, I want to know what all those knobs do."
    The real answer was that I didn't want to work in the dish pit, but I got in regardless.

  • Diego Fischer
    Diego Fischer 2 days ago

    Can you fill a klein bottle with watter?

  • Admiral Percy
    Admiral Percy 2 days ago

    This man should be in every YouTube video

  • Julian Williams
    Julian Williams 2 days ago

    I don't really know about doing an integral, but couldn't I just measure and subtract the area of the triangles that are made when the papers are lined up? 1:45

  • juustgowithit
    juustgowithit 2 days ago


  • Max Whittle
    Max Whittle 2 days ago

    Homework every night? No thanks

  • ebulating
    ebulating 2 days ago

    I would use a scanner to determine the area. Would just need to determine how much area each pixel is.

  • cpovey1
    cpovey1 2 days ago +1

    Clifford Stoll is a Ph.D. astronomer. But back in 1986, while employed as a systems administrator at the Lawrence Berkeley National Laboratory, Stoll investigated a tenacious hacker, one who stole $0.75 of computer time (back when you had to rent computer time-no one owned computers back then)—later identified as a KGB agent—who stole passwords, pirated multiple computer accounts, and attempted to breach US military security.

    Stoll was tenacious and needed to KNOW even then-I mean, how many people would devote months trying to find a $0.75 accounting error?

    After identifying the intrusion, Stoll set up a honeypot for Hess, eventually tracking him down and passing details to the authorities. It is recognized as one of the first examples of digital forensics. He described the events of his investigation in The Cuckoo's Egg: Tracking a Spy Through the Maze of Computer Espionage, which was a huge international best seller, and is an excellent book that I highly recommend.

  • Olga Garcia
    Olga Garcia 2 days ago +2

    This is sooooo cooooool!!!!

  • Greg Allan
    Greg Allan 2 days ago +1

    For a moment I thought I was watching Julias Sumner Miller. Those were the days.

  • Bradley Callaway
    Bradley Callaway 2 days ago

    I feel like noticing the trapezoid paper (and the innacurate ruler) is one of the few things that would be easier in American units, because our papers are all 8.5x11, so when you start measuring and it's 8.45x10.9, something's wrong. If it's 8.45x9.9, there's something very wrong.

  • S Oliven
    S Oliven 2 days ago +1

    i was a little sad about my future, but after i watched this, it encouraged me.

  • S Oliven
    S Oliven 2 days ago +1

    Awesome vid.

  • Imanol Toledo Sanz
    Imanol Toledo Sanz 2 days ago +1

    This guy is what indiana jones would look like when teaching

  • dam1en667
    dam1en667 2 days ago +1

    Cliff is great, would have liked to have had him as a teacher for sure. Enthusiasm is important

  • Vikrant Doshi
    Vikrant Doshi 2 days ago

    Can numberphile make a video on infinity - infinity =π

  • mrpalaces
    mrpalaces 2 days ago +1

    What a delightful person.

  • SuperJimmyChanga
    SuperJimmyChanga 3 days ago +1

    This is beautiful, Cliff

  • Valerio Vota
    Valerio Vota 3 days ago +1

    I want to be his student

  • Stuart Mortimore
    Stuart Mortimore 3 days ago +1

    Great advice for youngsters, and others too.

  • Jon McGowan
    Jon McGowan 3 days ago +1

    I actually hired someone not once, but twice for two different companies because he said in the first interview “I don’t know, but I know I can figure out the problem if I had more time and the right tools.” This was after he tried to trouble shoot a timed, and impossible to solve, hardware problem (yes I rigged it).

  • Brian Sierzega
    Brian Sierzega 3 days ago

    1.21 jiggawatts

  • FishBait
    FishBait 3 days ago

    Cliff both looks like and has the same speech patterns as Rick Sanchez.

  • Lara Tina Dias
    Lara Tina Dias 3 days ago +1

    I love him so much 💗💗💗

  • Max Larose
    Max Larose 3 days ago +1

    His students are lucky.

  • LuciaBiggles
    LuciaBiggles 3 days ago +1

    I loved this!! What an awesome guy! And super interesting

  • Sebastian Guzman Parrochia

    This guy should have a TV show only for himself

    CQUNC 3 days ago

    My first thought was the ruler tbh.

  • Robert Dunham Jr.
    Robert Dunham Jr. 3 days ago


  • Sebastian Elytron
    Sebastian Elytron 3 days ago +1

    How is this man still not knighted?

  • Ted Farwell
    Ted Farwell 3 days ago +1

    Cliff rocks!

  • rondle berik
    rondle berik 3 days ago +1

    I still don't know how to meassure the paper properly now.

  • Sebastian Perez
    Sebastian Perez 3 days ago +1

    This guy is AMAZING !!!!

  • timolsen75
    timolsen75 3 days ago +1

    I knew he was probably gonna tell me that measuring a piece of paper may not be as streight forward as I think... but this.. I didn't expect this..... awesome.

  • Jean Bonnefoy
    Jean Bonnefoy 3 days ago +1

    and no students notices that with that definitely Trumpfakish ruler, the usual 20x27cm sheet of paper measured... 20x26cm ;-) (check on the video)

  • Mahissimo
    Mahissimo 3 days ago +3

    There is an imperfecto ruler right now and nobody gets it either.

  • Random
    Random 3 days ago

    This guys brain is wired just like mine

  • weetgeen1
    weetgeen1 3 days ago

    Savage Klein bottle guy

  • Jack O'Scalpel
    Jack O'Scalpel 3 days ago

    I like that feeling

  • Lord Hamster
    Lord Hamster 3 days ago

    I want to ask that guy a question

  • Lord Hamster
    Lord Hamster 3 days ago

    I want to ask that guy a questiin

  • Barbarian UNO
    Barbarian UNO 3 days ago

    Is the Earth pear shaped?

  • Patrick Luy
    Patrick Luy 3 days ago

    Why don’t more teachers do this? You know, make students think. This man is brilliant.

  • Neeraj kumar
    Neeraj kumar 3 days ago

    So enthusiastic about his work.. I Really like him...mathematically speaking..

  • Name Last Name
    Name Last Name 3 days ago

    have he done a video about everyone is 7 handshakes away from the president? i found that odd

    SPACE TOEST 3 days ago

    We love parker square!

  • Pablo A. Barros
    Pablo A. Barros 3 days ago

    i love this guy

  • Francisco Serrano
    Francisco Serrano 3 days ago +2

    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.

  • Sean Ehle
    Sean Ehle 3 days ago +2

    This 5 minute video conveys a sense of scientific rigor so amazingly well!
    I love this so much, I emailed it around the intro physics lab department at my university yesterday morning. This morning, we're talking about maybe using this as the first lab of the fall semester for next year's program.
    8th grade? The lessons in this video apply at all levels of research.

  • Ben John
    Ben John 3 days ago +1

    o didn't think you'd be an iPhone guHILBERT DAVID HILBERT

  • Tencinour
    Tencinour 3 days ago +1

    That's really educational!
    Btw, I was unintentionally expecting a cry of "Great Scott" lol

  • David DM
    David DM 3 days ago +1

    great advice! I was caught.
    er. why two '17' on the ruler? lol. about the wrong 'tool' to use?

  • Eagle Angelo
    Eagle Angelo 3 days ago +1

    He goes on about the desire to know things, only to go all around trying to find that mathematician's name. That's one way to show you stick to your philosophy!

  • Hristo.Bogdanov
    Hristo.Bogdanov 3 days ago

    This guy is sooo cool.

  • LearnAlliCan
    LearnAlliCan 4 days ago +1

    3:50 This is something that comes natural in CERTAIN areas. For some people its science others its math, others its English.

  • Anirudh M
    Anirudh M 4 days ago

    This man looks like Einstein on weed

  • jason dads
    jason dads 4 days ago

    Klien bottle guy!

  • wafflanjunior00
    wafflanjunior00 4 days ago +3

    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.

  • yuting liu
    yuting liu 4 days ago +1


  • orsettomorbido
    orsettomorbido 4 days ago +1

    Amazing! :D

  • GetGoodSkrub 420
    GetGoodSkrub 420 4 days ago +1

    Find the minimum value of (10a+13)^1/2+(10b+15)^1/2 given that a+b=10

  • Landrew0
    Landrew0 4 days ago

    Acting outlandishly can get you a fair bit of mileage.

  • p eibye
    p eibye 4 days ago


  • Kenneth Studstill
    Kenneth Studstill 4 days ago

    I thought that one of the interpretations would include measuring the depth of the paper by folding it and using the depth to find the area of its edge-like sides.

  • ZandarKoad
    ZandarKoad 4 days ago

    He should be collecting royalties off Dr. Emmett Brown.

  • Praepes
    Praepes 4 days ago +1

    This is the kind of teacher I aspire to be.

  • khanh huy
    khanh huy 4 days ago

    Do modulo inverse plssss :”((

  • proshot82
    proshot82 4 days ago

    Real life Doc. Brown

  • R.J. Lupin
    R.J. Lupin 4 days ago +1

    Can Cliff Stoll be my professor? Please?

  • aviphysics
    aviphysics 4 days ago

    the moment I saw the homework assignment, I immediately thought that I would measure it by attempting to cut a shape of known area, and weighing that piece. Then weighting the whole sheet and multiplying by the known mass per a unit of area (this is how we used to do it for figuring the area under a chromatography trace.)

    For the sides, I was thinking I would cut the paper into several pieces and stack them, to get the thickness of the paper, but I am not sure how precisely the cut edge of the paper matches its thickness.

  • Justin Richards
    Justin Richards 4 days ago +1

    I would assume there would be some chance that the students results in many cases would not match based on which edges they measured.
    So then, have them explain why . This would be interesting to observe.

    Might experiment on my kids ... now where do i get an imperfecto ruler. Must be one in my garage somewhere.

  • Austin Bryan
    Austin Bryan 4 days ago +1

    Mad genius

  • Jared Worman
    Jared Worman 4 days ago

    Cliff reminds me of doc brown

  • Cameron Bigley
    Cameron Bigley 4 days ago

    I feel cheated.

  • server642
    server642 4 days ago +1

    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!

  • liams923
    liams923 4 days ago +1

    I would love to have him as a teacher

  • OwlOfBlues
    OwlOfBlues 4 days ago +1

    I was surprised to see it’s not a rant by Matt Parker!

  • CryingWife
    CryingWife 4 days ago +1

    The one thing I must know is who would dislike this video.

  • mathew major
    mathew major 4 days ago +2

    Is there a place where we can get like a PDF copy or something of the imperfecto ruler he uses, or is it a secret of cliff only

  • Nick Combs
    Nick Combs 4 days ago +1

    I'm almost certain that drive for knowledge is learned, not a natural gift. If you've got it, some event in your past showed you learning how to discover a fundamental truth is empowering in any future dealings with the subject of that truth.

  • Adam Anderson
    Adam Anderson 4 days ago

    He is weird, but amazing!