Why do calculators get this wrong? (We don't know!)

2024 ж. 15 Мам.
2 156 915 Рет қаралды

Women in Trading and Technology: www.janestreet.com/witt.html
21 to 23 September 2020 (deadline to apply: Friday 7 August 2020)
These are all of the almost-π calculations I showed:
11^6 ÷ 13 ≈ (156158413/3600)π
17^5 ÷ 11 ≈ (366494029/8920)π
11^6 ÷ 17 ≈ (119415257/3600)π
19^9 ÷ 2^3 ≈ (65249503235207/5082)π
5^9 ÷ 3 ≈ (1226819353/5920)π
7^9 ÷ 19 ≈ (2623750469/3881)π
13^5 ÷ 7 ≈ (154266801/9137)π
21^6 ÷ 5 ≈ (27818908094/5095)π
23^9 ÷ 5^4 ≈ (4030701961529/4394)π
Sheena's tweet
/ 1129114614321618951
The reddit post
/ got_this_while_doing_s...
Farey sequence
en.wikipedia.org/wiki/Farey_s...
This is the 'best rational approximation' algorithm I used:
www.johndcook.com/blog/2010/1...
I've tested it on the Casio FX-83GT PLUS and Casio FX-991EX CLASSWIZ. Let me know what calculators you have checked!
CORRECTIONS:
- At 8:30 I say "13" when I mean "11". Ignore what I say: the on-screen number is correct!
- Let me know if you spot anything else.
Thanks to my Patreon supports who do support these videos and make them possible. Here is a random subset:
Alan Flett
Nikola Studer
Philippe von Bergen
Alan McNea
Derek Chandler
Jeremy Buchanan
Alan H.
Malcolm Rowe
Glenn Watson
Patrick Stover
Support my channel and I can make more videos:
/ standupmaths
And of course thanks to Jane Street who support my channel. They're amazing.
www.janestreet.com/
Filming and editing by Matt Parker
Additional camera work by Lucie Green
That piano music is No.8 Requiem by Esther Abrami
All other music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/products/5b9f...
Nerdy maths toys: mathsgear.co.uk/
A transcendental number is not the root of any integer polynomial!
mathworld.wolfram.com/Transce...

Пікірлер
  • EDIT 1: I've figured it out! The reason why 11^6/17 didn't work was that it wasn't close enough! If we instead type 11^6/16.999999999995 (that's eleven 9s) we do indeed get a fractional multiple of pi. Obviously this is not an integer, but I'm sure if one tried hard enough they *could* find an integer that's close enough. Keep reading to see how I figured it out. I'm using the Casio fx-85GT PLUS, and I've noticed that there *is* in fact something special about the number 3600 (for a reason I don't understand). If we type a bunch of gibberish and divide it by 3600 (e.g. 4276161/3600), the calculator will return a bunch of gibberish (1187.8225), however if instead we multiply this gibberish by π (i.e. 4276161/3600 * π) the calculator does actually return a fractional multiple of π (475129/400 * π). If you try to divide by any number other than 3600 (say 3500), it won't work. Except that it does! This completely baffles me, but it also works with factors of 3600. Let's pick a random factor of 3600, say 240. 4276161/240 returns 17817.3375 4276161/240 * π returns 1425387/80 * π. As far as I could tell, the lowest denominator we can use is 15 (e.g. it works with 4572431/15 * π). All of this said, this still doesn't explain why the attempt where you divided by 3600 did not work. I'll keep trying, but in the meantime hopefully this helps in the quest to figure this out. BONUS: Just as I was proofreading this, I accidentally discovered that 3600 itself is a factor of an even bigger number that works, and that is 25200. So any factor of 25200 works! EDIT 2: Conclusion: If we want to find a number of the form a^b/c then we have to make sure that the result is approximately p/q * π, where q is a factor of 25200. If q is not a factor of 25200 then the calculator will never convert the answer to a fractional multiple of π.

    @smathlax@smathlax3 жыл бұрын
    • Congratulations!

      @buddyclem7328@buddyclem73283 жыл бұрын
    • This is an underrated post. Well done! Does this mean you've found another equation you can type into a casio and have it create a multiple of pi equivalent?

      @bryanandhallie@bryanandhallie3 жыл бұрын
    • I'm just spitting but 1x2x3x4x5x5x6x7 = 25200. Maybe that has something to do with how Pi is approximated

      @coasteringkid@coasteringkid3 жыл бұрын
    • Or more likely product of odd numbers, like 3×5×7×9... Looked up approximations of pi lol

      @coasteringkid@coasteringkid3 жыл бұрын
    • @@bryanandhallie Once you know that it's all about factors of 25200 generating solutions is somewhat trivial. You can try this on your own calculator. First, get a calculator that has more precision than the Casio (I just used the default Windows 10 calculator), then type a bunch of gibberish, divide it by a factor of 25200 and multiply by pi. Then type the exact figures that you obtain from the result into your Casio and it will return a fractional multiple of pi. This will not work if you divide by anything other than a factor of 25200! The only challenge at this point, if we want to go there, is to find some number in the form a^b/c which is close enough to one of these values.

      @smathlax@smathlax3 жыл бұрын
  • Plot twist: It's a deliberate bug in the code to quickly check if a competitor just ripped Casio ROM and used it in their calculator. Similar to the non-existent streets on maps.

    @UltimatePerfection@UltimatePerfection3 жыл бұрын
    • This answer is good and funny as it avoid admitting they use a buggy algorithm or implementation of it. Bad engineers with good excuses.

      @GildasCotomale@GildasCotomale3 жыл бұрын
    • @@GildasCotomale 'bad engineers with good excuses' is basically just programming lol

      @9volt65@9volt653 жыл бұрын
    • Or dictionaries with imaginary words!

      @DaMonster@DaMonster3 жыл бұрын
    • @@GildasCotomale eww linux

      @HEADSHOTPROLOL@HEADSHOTPROLOL3 жыл бұрын
    • This!

      @hiroshirako@hiroshirako3 жыл бұрын
  • In the Casio underground lair: "We did it! We drove mathematicians insane!" "Were they not a little bonkers before already?" "Yes, but not like this. They now step out of the house and get lost in thought in the woods."

    @uplink-on-yt@uplink-on-yt2 жыл бұрын
    • they actually touch grass

      @jacksonbird810@jacksonbird810 Жыл бұрын
  • I love how people find out about floating point standards. As a programmer myself, I can tell you this: the explanation that requires the least work to implement, is the most likely to be right.

    @TheLastCrankers@TheLastCrankers2 жыл бұрын
    • Not floating point but BCD. Still good comment

      @licht4808@licht48082 жыл бұрын
    • @@licht4808 is bcd not considered floarting point? I dunno coz I'm not a computer scientist or computer engineer, never took proper education in that field

      @TheLastCrankers@TheLastCrankers2 жыл бұрын
    • @@TheLastCrankers BCD and floating point are two different things. BCD is a way of doing base10 arithmetic with binary bits. Floating-point allows very large and very small numbers to be represented or approximated with a limited number of binary bits.

      @minispinakins2034@minispinakins20342 жыл бұрын
    • Occam’s razor

      @123coolmik@123coolmik2 жыл бұрын
    • No, when it's too simple it won't work and when it's too complicated it won't work either

      @Tuberex@Tuberex2 жыл бұрын
  • That one Casio engineer laughing after they intentionally added it.

    @slippery_gecko9274@slippery_gecko92743 жыл бұрын
    • That's how you know it's a genuine Casio

      @Nupetiet@Nupetiet3 жыл бұрын
    • @@Nupetiet yea i think it was an easter egg too, designed for several applications of science

      @koalastew9193@koalastew91933 жыл бұрын
    • Well it's kinda cool tho

      @NStripleseven@NStripleseven3 жыл бұрын
    • Wow, the 314th like, pi like

      @sjoerdstougie@sjoerdstougie3 жыл бұрын
    • It could have been intentional, like a trap for other devs.

      @RowanAckerman@RowanAckerman3 жыл бұрын
  • On the subject, calculator unboxings need to come back

    @munjee2@munjee23 жыл бұрын
    • Yes!

      @liv9589@liv95893 жыл бұрын
    • Yes!! For the sake of the calculator cult.

      @douglasmann4236@douglasmann42363 жыл бұрын
    • I asked for a shiny blue Casio Classwiz for Christmas and I must be the only person to get excited about that. Unboxings would make me feel less strange

      @claireloub@claireloub3 жыл бұрын
    • HP 32SII!

      @ahfreebird@ahfreebird3 жыл бұрын
  • I have a theory: When you tried the more accurate calculations, the calculator didn't do the same thing, as it only has pi stored to 10 decimal places, so it would've been further away!

    @samuelcaskie@samuelcaskie Жыл бұрын
    • My Casio fx-570c, that I've been using almost every day since 1989, also stores pi to only ten decimal places. In the original example, 11^6 ÷13 × 3600÷156158413 results in 3.141592654. If I divide that by the calculator's stored pi value, it gives 1 as the answer.

      @polbecca@polbecca10 ай бұрын
    • hmm... if you'd asked me out of context how I thought a calculator stored pi, I would say as a floating point binary constant, probably one of the standard IEEE widths, and not as some integer number of decimals. but then I would start to doubt myself because I have this vague recollection of calculators using some kind of BCD to avoid certain rounding errors without having to escalate the amount of internal precision too much. so I dunno. I guess it should be possible to come up with test cases to distinguish. if I'm ever really bored... (EDIT: I saw the pinned comment and it does seem somebody got to the bottom of this)

      @jaapweel1@jaapweel1Ай бұрын
  • Shout out to the care and effort put into these videos. The marker and paper setup is good too but i love seeing creators get excited about the production and have fun with it.

    @threethousandbees7260@threethousandbees72602 жыл бұрын
    • agreed. its such a lovely wholesome dorkiness for him to add the bits where he's rumaging through a forest in despair. makes me smile.

      @dylanirt3905@dylanirt39052 жыл бұрын
  • TBH Matt, you're a big enough name that you could probably get Casio to look into this and get an actual answer.

    @FoxDren@FoxDren3 жыл бұрын
    • Agree. I say go for it. It would be interesting to see what Casio has to say about their own logic.

      @peterkelley6344@peterkelley63443 жыл бұрын
    • Then again, isn't it just more fun to have we minions of the interwebs completely reverse engineer a specific application circuit just because one small error bothers us?

      @seancampbell5751@seancampbell57513 жыл бұрын
    • @@seancampbell5751 while it may be "fun" it is not efficient and is unlikely to result in said bug inducing edge case to be rectified in future models

      @FoxDren@FoxDren3 жыл бұрын
    • What an amazing video that would be. Matt with unprecedented insight to how calculators work and Casio with an unprecedented reach into the smartest and most influential of the high school demographic.

      @mstout2u@mstout2u3 жыл бұрын
    • I am 99% sure that they will answer with " honestly we have no idea"

      @sWaRmBuStEr@sWaRmBuStEr3 жыл бұрын
  • The conclusion here is that Casio should publish their source code

    @FaliusAren@FaliusAren3 жыл бұрын
    • The only logical course of action is a Mission Impossible style operation where a team of mathematicians in tactical gear breaks in to Casio headquarters to steal the chip designs, CAD files and firmware code.

      @odw32@odw323 жыл бұрын
    • You can always pay for a teardown analysis. Or pull out the IDA tools to figure it out yourself. An old pocket calculator isn't going to be as complex (or as codelocked) as a modern smartphone.

      @pwnmeisterage@pwnmeisterage3 жыл бұрын
    • I figured Matt would just go ask them.

      @tonyennis1787@tonyennis17873 жыл бұрын
    • Like a242 vs. 232

      @brendawilliams8062@brendawilliams80623 жыл бұрын
    • @Etravagant Sobriquet - This is a special feature of Casio SYMBOLIC mode, which uses 25200 ( = 3600 * 7 ) as the original divisor. It is that simple ...

      @MrSummitville@MrSummitville2 жыл бұрын
  • What we need to know is the exact way the Casio calculator approximates and stores pi. My guess is that 11^6÷13 is special in this case, not because it's closest to actual pi, but because it's the only one that exactly nails the calculator's version of pi.

    @GaryIV@GaryIV2 жыл бұрын
    • This. It's not finding Pi by accident, it's finding the calculator's approximation of Pi by accident.

      @bable6314@bable631411 ай бұрын
    • Most likely it just stores its value as a double, then when getting an answer, it also computes the error with the PI answer (if the resulting fraction has been simplified), if that error is under 1^-10, it takes the PI result.

      @youuuuuuuuuuutube@youuuuuuuuuuutube9 ай бұрын
  • He almost has an existential crisis because he found the last digit of π

    @huhneat1076@huhneat10762 жыл бұрын
    • ???

      @lucaswiese6@lucaswiese6 Жыл бұрын
  • I've got a TI-83 from 1996 and it gave me the correct decimal result right away. I think your Casio just decided to be pi-curious.

    @manlyadvice1789@manlyadvice17893 жыл бұрын
    • i loved the pi-curious pun, amazing

      @e-towncuber5522@e-towncuber55223 жыл бұрын
    • I have a Ti-30X IIS It gave me the correct answer

      @_creare_2742@_creare_27422 жыл бұрын
    • TI is clearly the superior calculation device... I have a sibling TI-83 from the same timeframe.

      @matthewwagner4042@matthewwagner40422 жыл бұрын
    • I have the fx-82 AU Plus II, it also gave the correct answer

      @MrPokination@MrPokination2 жыл бұрын
    • My Casio fx-9750GII gave me the correct answer.

      @haonghephu4895@haonghephu48952 жыл бұрын
  • Even stranger, dividing the answer by pi makes the calculator give a decimal answer instead of the fractional coefficient.

    @crynon612@crynon6123 жыл бұрын
    • The correct answer?

      @zaraak323i@zaraak323i3 жыл бұрын
    • Did you multiply that decimal number by pi to see if it shows the original surprise answer again? It *should* but sounds like it won't.

      @KarstenJohansson@KarstenJohansson3 жыл бұрын
    • @@KarstenJohansson It will, I checked it!

      @user-en3xx7bl6v@user-en3xx7bl6v3 жыл бұрын
    • @@KarstenJohansson It shows the surprise you mentioned.

      @monnamonsta@monnamonsta3 жыл бұрын
  • Here are the priorities in the Casio program algorithm: 1. Display the result as a factor of pi, if any. 2. If the display is adequate, show this as a fractional number. If possible, show it as a fraction and associated with pi . Because when solving problems at school, show the result as pi related or fractional (or both). 3. It will give the result as Decimal when SD key is already pressed. In scientific machines with other Brand WriteView, the 1st priority usually gives a fractional result, if there is pi in the question, it gives a fractional result associated with pi. It gives decimal results with the SD key.

    @CafarYukeri@CafarYukeri2 жыл бұрын
  • It’s my first time watching one of your videos. You explained everything really well!

    @vamp97@vamp972 жыл бұрын
  • You know you're a true mathematician when you interrogate your calculator. ...and then have a breakup with it. lol

    @noahgiamei@noahgiamei3 жыл бұрын
    • That can be true aswell

      @Redditard@Redditard3 жыл бұрын
    • Not mathematicians. It's the calculator fanciers who do that.

      @pjaxy@pjaxy3 жыл бұрын
    • Somewhat obsessive compulsive .

      @markdemell3717@markdemell37173 жыл бұрын
    • HaHa LOL

      @thekabablord143@thekabablord1433 жыл бұрын
    • I've seen few college math professors that 'interrogated reality' with their maths, then promptly divorce themselves from reality because reality refused to capitulate to their views of what it should be. Looking back, I have to wonder if it had anything to do with them also being practising commi marxist types.

      @illbeyourmonster3591@illbeyourmonster35913 жыл бұрын
  • The fact that the denominator is 3600 just screams that it tries an approximation in RADIANS.

    @DukeBG@DukeBG3 жыл бұрын
    • He already tried another calculation that results in a multiple of pi with a denominator of 3600.

      @matthewschad6649@matthewschad66493 жыл бұрын
    • @@matthewschad6649 it was not precise enough. see the pinned comment

      @DukeBG@DukeBG3 жыл бұрын
    • @@DukeBG 25200 has nothing to do with the radians, though?

      @KuK137@KuK1373 жыл бұрын
    • @@KuK137 Just run around in circles.

      @Fudmottin@Fudmottin3 жыл бұрын
    • a degree is ¹/₁₈₀π or ¹⁴⁰/₂₅₂₀₀π radians

      @groszak1@groszak13 жыл бұрын
  • This is the most Dramatic Maths video I've ever seen, love it!

    @ChrisMMaster0@ChrisMMaster03 жыл бұрын
  • In the table at 8:37, it is worth noting that the "Pi" that you get out of the calculations 1 and 3 is the exact same number, hence we can conclude that the important difference is the way that the initial results (11^6/13 vs. 11^6/17) are rounded. No matter whether you use binary or decimal numbers, any non-integer fraction with a denominator of 13 or 17 is wrong when expressed with a finite number of digits, and it is wrong in different ways for both fractions. Since (and this aligns with the results that I got pushing my Casio FX-82 Solar to the limit as a kid) the internal accuracy of (I guess) any Casio is limited to around 10^(-12), you can seemingly get these results at random when the resulting Pi is within about 10^(-12) of the correct value - with two more points to add: 1) I'm pretty certain that you could reverse engineer the rounding algorithm that Casio used when you apply your test rounding algorithm to the initial fractions (i.e. 11^6/13) to find the one that makes this particular fraction a sufficiently precise fraction of Pi (and doesn't for the others). 2) I'm also pretty certain that Casio didn't implement a Farey algorithm, but simply defined a set of denominators that are most likely to appear as an exact value in front of an irrational number. So for example any fraction of 25,200 (as pointed out in another comment) = 2^4 * 3^2 * 5^2 * 7^2 - which includes any integer up to 10 plus virtually all degree values that commonly appear in geometric problems: 15, 30, 45, 60, 75, 90, 180, 360, 540, 720, ... - plus "round" values like 100, 1000 etc. is tested as the denominator (likely starting with the smallest), and if there is an EXACT match with the number of Pi stored this result is displayed. If you randomly generate fractions that are sufficiently close to Pi, I would think that around 3.5% (=2^(-40) / Pi * 10^11) of them do actually come up as a fraction of Pi, which is probably enough to make an adult scientist give up before he finds a second example. Tldr.: The Casio only displays a result as a fraction of Pi if its internal computation EXACTLY matches this fraction, with the error resulting from rounding the initial result with an infinite number of digits to an intermediary result with a finite number and the inherent accuracy limits of the calculator. A lot of denominators will never appear in a result containing Pi (or another constant) since they aren't part of a predefined set.

    @james64ibm@james64ibm Жыл бұрын
  • I did not expect this to be a cliffhanger. Now I got a hole in my soul.

    @Epppi1@Epppi13 жыл бұрын
    • well it says so in the title

      @DiapaYY@DiapaYY3 жыл бұрын
    • It does say in the title, "(We don't know!)"

      @Huntracony@Huntracony3 жыл бұрын
    • Pi is always a cliffhanger.

      @geoffstrickler@geoffstrickler3 жыл бұрын
  • Here's something to consider: if you compute both sides of the 11^6 / 13 equation in single-precision floating-point arithmetic, you get exactly the same 32-bit result. This doesn't happen with the 11^6 / 17 example. My suspicion is that it's a combination of this and the fact that the denominator is 3600, which is a fairly nice number, being a product of the three lowest primes.

    @WhirligigStudios@WhirligigStudios3 жыл бұрын
    • This sounds like an answer, folks! So casios use 32-bit floats, good to know.

      @timh.6872@timh.68723 жыл бұрын
    • How can we find other pairs of numbers that have the same 32-bit result to verify that?

      @notwilwheaton@notwilwheaton3 жыл бұрын
    • PI in the result on CASIO fx-991ES PLUS 500*10/(22.977*10^-3) = 436382531/6300 * PI I found this while calculating how long would my device work with a 500mAh battery if I know it uses 22.977 uAh in 10s extracting pi=3.1415926535905471363222... 10 exact decimal places, or 11 if you round it there

      @music99matt@music99matt3 жыл бұрын
    • @@timh.6872 32-bit float is only 6 significant digits of precision. This calculator has significantly more than that (12-15).

      @movax20h@movax20h3 жыл бұрын
    • Perhaps something about the 3600 is yelling "CIRCLE" to the calculator? Given it's 360*10. In combination with this, perhaps 🤷‍♀️

      @Hades948@Hades9483 жыл бұрын
  • Interesting video. I remember doing number processes at college (I did computer science, and have worked as a developer for 30 years) - as soon as I saw the mistake the calculator makes, I thought "this is down to binary coded decimal truncation" - and yes - the threads elsewhere go straight to the same conclusion. Bookmarking this one - it's interesting :) There are some great videos about the Sinclair calculator online, where the source code is broken down to show some of the mathematical gymnastics computers go through to do arithmetic operations. Anyway. Great video.

    @jonbeckett@jonbeckett2 жыл бұрын
    • This is not a "mistake". This is a feature of the Casio, when in SYMBOLIC Mode. In Decimal mode, you will get the value that you want to see ...

      @MrSummitville@MrSummitville2 жыл бұрын
    • @@MrSummitville yes - bad wording - a feature in the classic sense of unexpected outcomes :)

      @jonbeckett@jonbeckett2 жыл бұрын
  • I've tested the bounds for Casio-π using their online emulator for the fx-82/85/350ES Plus. When entered directly, Casio-π symbol is displayed for any values in the range 3.14159265358918 and 3.14159265359042. The pre-defined stored value of Casio-π is the exact middle of these two values at: 3.1415926535898.

    @wag-on@wag-on Жыл бұрын
    • can you do (pi_exact - pi_min)/eps(pi_exact) and (pi_max -pi_exact)/eps(pi_exact), where eps(x) returns the smallest value that can be added to x?

      @SomeStrangeMan@SomeStrangeMan5 ай бұрын
  • Parker: doing tons of iterations of Farey Algorithm to get 1213/3600 Me: the first two decimal points are 0.33 so imma just call it 1/3.

    @fulltimeslackerii8229@fulltimeslackerii82293 жыл бұрын
    • Same I was even lazier. I figured 1213=1200 So it's 1/3

      @leadnitrate2194@leadnitrate21943 жыл бұрын
    • No it's called 33/100

      @milestailsprower4555@milestailsprower45553 жыл бұрын
    • Pfff, it is bigger than 0, I can just approximate it to 1

      @eduardlopezplans5814@eduardlopezplans58143 жыл бұрын
    • @@eduardlopezplans5814 Third

      @milestailsprower4555@milestailsprower45553 жыл бұрын
    • Nah. It’s 1 % x > 0 so call it x - (1 % x)

      @ryanisacuc8381@ryanisacuc83813 жыл бұрын
  • I do prefer a Gaxio calculator personally.

    @Martin95274@Martin952743 жыл бұрын
    • It is the only logical choice.

      @standupmaths@standupmaths3 жыл бұрын
    • Yeah, what were those Casio copycats thinking?!

      @GRBtutorials@GRBtutorials3 жыл бұрын
    • only because you've not tried the Kadio yet.

      @ramirofalco@ramirofalco3 жыл бұрын
    • Texas Instruments 👍🏻

      @AgentSmith911@AgentSmith9113 жыл бұрын
    • @@standupmaths it must be hardcoded. Now the question is, why? Surely there's some bit of math out there that uses some part of this anomaly to generate pi, and YOU MUST FIND IT WITH YOUR BRAINS AND WIT

      @DrKaii@DrKaii3 жыл бұрын
  • as someone who's used the fx-83GT PLUS for the past 6 years almost every day of my life, it felt so nostalgic when you took it out.

    @Sednas@Sednas3 жыл бұрын
  • This is a perfectly executed video. The retreat to the forest for contemplating a universe's weight of the philosophy behind a cryptic response to a reasonably simple quandary made this as epic as this run-on sentence is long. I imagine scores of your predecessors taking a nature hike for much the same reaon. Newton, Huygens, Socrates, Pythagoras, et cetera... and now Parker. Briliant.

    @darinheinz@darinheinz9 ай бұрын
  • This Matt Parker's math(s) puzzle seems harder than usual.

    @sirgermaine@sirgermaine3 жыл бұрын
  • This may well be a software "anti-theft" strategy, I use it a lot in my software... Thief: I didn't steal this your honour! Casio: Check 11^6/13 your honour!

    @microtools1318@microtools13183 жыл бұрын
    • we've found the maths version of paper towns. this is casio's Algoe.

      @daninjamonkey1@daninjamonkey13 жыл бұрын
    • Giving you a things up for the algorithm even though the word "theft" here represents an unethical and counterproductive line of thinking. Unfortunately, because this toxic idea is so pervasive, I believe you are correct in your guess as to Casio's motivation.

      @MatthewStinar@MatthewStinar3 жыл бұрын
    • Isn't it true that paper towns like that specifically *don't* count legally to determine copies? Idk if it's different for code than books/maps though.

      @Jigkuro@Jigkuro3 жыл бұрын
    • Ooooooh, a paper calculation! That's a new one for me

      @DanielVCOliveira@DanielVCOliveira3 жыл бұрын
    • Oh yeah. It's big brain time.

      @heyandy889@heyandy8893 жыл бұрын
  • One thing to consider with most floating point representations is that more digits in front of the decimal reduce the number of digits held after the decimal. In many attempts to recreate the bug it looked like there would have been less precision held in the registers after the decimal, so just comparing what the full number would be is not good enough to predict what would happen. You'd want to consider what intermediate rounding is taking place.

    @cadaankaa@cadaankaa2 жыл бұрын
    • I tried to change the float on my ti-83 plus, as I had considered this a possibility as well.... I went from float up thru 9 (highest i can force it) and it didn't work.

      @Blinkerd00d@Blinkerd00d6 ай бұрын
  • after all these years you mister are still the best!!!!

    @keen4e@keen4e Жыл бұрын
  • Perhaps this is one of those intentional "mistakes" that any publisher would put in a textbook to see if another company copied them. Like how Genius sued Google for copying their lyrics. But in this case, Casio hard-coded this answer to test whether another calculator manufacturer copies their code.

    @SirVataqun@SirVataqun3 жыл бұрын
    • SirVataqun nah, its computer science

      @sunnohh@sunnohh3 жыл бұрын
    • A "paper calculation" I guess...

      @SweetChuckPi@SweetChuckPi3 жыл бұрын
    • Or it could have been an accidental miscoding in the initial creation before mass disribution.

      @billy4lifeify@billy4lifeify3 жыл бұрын
    • You beat me to it. Could well be a "copyright trap".

      @colinstamp9053@colinstamp90533 жыл бұрын
    • @@sunnohh like a map street! some roads are on maps which don't actually exist for copyright reasons.

      @leofisher1280@leofisher12803 жыл бұрын
  • the bit where he says "i thought i knew my casio" and then sad piano music starts is a fun moment for people who play casio pianos

    @saxrendell@saxrendell3 жыл бұрын
    • I am playing a casio piano, can confirm it was funny

      @theinternpianist1439@theinternpianist14393 жыл бұрын
  • ANSWER your calculator is always comparing the results with the saved constant PI for example on a CASIO fx-991EX the number: 5419351 / 6900132 will give PI/4 because it is PI/4 precise to 14 decimal places but 4559545 / 5805393 will only give a decimal because its PI/4 precise only to 13 decimal places this is because this particular calculator stores its value of PI precise up to 14 decimal places (which can be checked in the user's guide) PS. I enjoyed the video, it got me curious, thanks! 😀

    @ww.wojtek@ww.wojtek2 жыл бұрын
  • This might not be relevant but I have found that Casio calculators have more values that they tend to hide. For instance, when using pi, it only displays the first ten digits but actually uses fifteen digits for calculations. There is also weird stuff that happens when reversing a calculation you just did, to avoid losing accuracy, it makes sure the calculation gets the same result in reverse. So the square root of 9.999999999 x10^99 gets you 1 x10^50. If you square that again you just get the original 9.999 etc. But if you just take 1 x10^50^2 obviously you get 1 x10^100 which is just a math error. Casio’s are weird and do a lot of maths that they don’t show.

    @MogaTange@MogaTange Жыл бұрын
    • you seem to have greatly confused yourself about what the observed effects of base 10 display approximations would be - the number on display is nearly universally an approximation (unless its only factors are 2 and 5) in all cases - and the number of digits displayed is also disjoint from the value

      @styleisaweapon@styleisaweapon Жыл бұрын
  • Matt: Look at this! And it only works with this one combination! Casio: Oh crap... they found it! Change the launch codes!! NOW!!!!!!!!!!

    @AnimationGoneWrong@AnimationGoneWrong3 жыл бұрын
    • Lol I'm laughing so hard

      @monnamonsta@monnamonsta3 жыл бұрын
  • "I don't think the people online are correct" Oh how much better a world we would live in if everyone thought that way!

    @KKCryptic@KKCryptic3 жыл бұрын
    • says a person online ;)

      @vanagandr6425@vanagandr64253 жыл бұрын
    • Is thi videos streaming in a TV?

      @NiceEyeballs@NiceEyeballs3 жыл бұрын
    • "If it's in a book it's gotta be true!" - The Simpsons (pre-Internet)

      @CommodoreGreg@CommodoreGreg3 жыл бұрын
    • So you argue that world will be better if we don't believe people online as correct, but you're one of the people online so the world wouldn't be better based on your logic. So we should do the opposite and believe people online to make the world better, but then if we believed you then we shouldn't believe people online... Error: StackOverflowException

      @sth128@sth1283 жыл бұрын
    • "I'll just type up a short reply correcting them."

      @wheedler@wheedler3 жыл бұрын
  • This happened to me once on my Sharp Calculator. I was doing some financial maths question for secondary school exams and the result came out as a multiple of Pi. I don't remember the calculation but I remember thinking it was weird at the time

    @eoinmullally1531@eoinmullally15312 жыл бұрын
  • Beautiful cinematography in that take in the woods

    @bearcb@bearcb3 жыл бұрын
    • *SAD PIANO* :(

      @milestailsprower4555@milestailsprower45552 жыл бұрын
  • This is like a dramatic math version of captain disillusion and I love it. Really appreciate the quality of these videos

    @mrping2603@mrping26033 жыл бұрын
    • Are you kidding? I'm sending this directly to DrCap Disillisuion. How can there be two Matt'ses at once? And the whole calculator thing? looked straight up CGIed. This reeks I tell you.

      @vallov4188@vallov41883 жыл бұрын
  • Can't you get a casio contact for this? I'm sure they have an engineer who knows

    @Fs3i@Fs3i3 жыл бұрын
    • I’ve been asking around but nothing yet!

      @standupmaths@standupmaths3 жыл бұрын
    • I think it depends on how open Casio are about their Intellectual Property. If they have a policy of not revealing too much, asking them would be useless.

      @ismailb4334@ismailb43343 жыл бұрын
    • @@ismailb4334 maybe file a complaint? demand money back or something?

      @thinboxdictator6720@thinboxdictator67203 жыл бұрын
    • @@thinboxdictator6720 If you ask for a refund expecting a technical explanation of the bug, you're going to be very disappointed.

      @alxjones@alxjones3 жыл бұрын
    • @@thinboxdictator6720 they might give you a refund, but the customer support rep that deals with your complaint will either fob you off or give you a refund or some vouchers or something. It's not like it's even giving the wrong answer. It's correct to the precision required, it's just expressed in an unexpected way.

      @yadt@yadt3 жыл бұрын
  • 7:11 I love the way he looks up as though he can read the computer generated text above his head that was added after filming.

    @smokey04200420@smokey042004203 жыл бұрын
    • Yeah, it's pretty cool.

      @eekee6034@eekee60342 жыл бұрын
    • It’s called a fourth wall break.

      @exodus_20_15@exodus_20_15Ай бұрын
  • I had to try this with my old 991EX and the new 991CW. The CW one returned 136273.9231 as is, with no way to change formatting as a mixed fraction. The EX, or at least the VerB, returns with the pi fraction.

    @MackyClemen@MackyClemen Жыл бұрын
  • Response from someone who has worked on similar calculation/approximation code, albeit not on an actual calculator: I'm gonna guess Casio is using IEEE floating-point math since it means they can use off-the-shelf components in their calculators. A really high-end calculator might use a custom solution with more bits or a different format, but this mass-market calculator probably doesn't. I imagine the issue here is that, in this particular case, the 64-bit floating-point result of 11⁶/13 actually matched the approximation 156158413π/3600 _exactly,_ bit-for-bit. Casio probably doesn't show the result as a multiple of π unless the bits match exactly, or perhaps with a one-bit epsilon to allow for rounding errors. Your other examples may have _seemed_ to match up to a certain _decimal_ place, but that doesn't mean they matched up to the very last _bit,_ or _binary_ place, of the floating-point result. It takes between 3 and 4 bits to represent a single decimal digit, so being off by one bit could result in rounding to the same last decimal digit while still being different in its last binary digit. If it helps to know, IEEE floating-point numbers are represented as *±1.m ⨯ 2ᵉ,* where *m* is the mantissa, a value somewhere from 0 up to, but not including, 1, and *e* is an exponent. How the sign and exponent are represented in memory isn't too important here, but the mantissa is: it is a finite number of bits (i.e. binary digits) that represent a fraction in the form *(0 … 2ⁿ-1) / 2ⁿ,* with *n* being the number of bits. Numbers are effectively always rational, and if you displayed them in binary, you would never get an endless string of digits like you do after you _try_ to represent them in decimal. Some quick examples: • 3 = 1.5 ⨯ 2¹ • 12 = 1.5 ⨯ 2³ • 48 = 1.75 ⨯ 2⁵ Same examples expressed in a simplistic 8-bit floating-point format, with 1 bit determining whether the integer portion of the expression is 1 or -1, 4 bits representing the mantissa, and 3 bits representing the exponent, and remember, all digits here are binary: • 3 = 1.1000 ⨯ 10⁰⁰¹ = 8-bit byte: [0|0 0 1|1 0 0 0] • 12 = 1.1000 ⨯ 10⁰¹¹ = 8-bit byte: [0|0 1 1|1 0 0 0] • 48 = 1.1100 ⨯ 10¹⁰¹ = 8-bit byte: [0|1 0 1|1 1 0 0] (Note: This is a simplified explanation that glosses over how 0 is treated as a special case, as it obviously can't be represented as 1.m ⨯ 2ᵉ, but that and negative exponents and other special cases like infinity, indefinite values, etc. are a story for a different time. If you're keen to know, I'm sure google can hook you up with reams of details.)

    @Felice_Enellen@Felice_Enellen3 жыл бұрын
    • Mantissa. Haven't heard that word in years.

      @Remls@Remls3 жыл бұрын
    • The two numbers, float64(11^6/13) and float64(float64(156158413*float64(pi))/3600), differ by exactly 1125 units in the last place.

      @edgarbonet1@edgarbonet13 жыл бұрын
    • As a computer programmer, am suspecting something along this line of thought.

      @JaimeWarlock@JaimeWarlock3 жыл бұрын
    • I feel like you are a better authority on this topic and thus should commence making math videos.

      @broodlyric@broodlyric3 жыл бұрын
    • @@edgarbonet1 I went and tried it myself. I see what you mean. It could be they aren't using IEEE floats. The number of formats out there, at least historically, is kind of staggering, so it's possible. For a lot more detail, see here: www.quadibloc.com/comp/cp0201.htm I also read something that claimed Casio uses decimal floats, which I'm guessing means BCD floats? But the article didn't seem super clueful and may just have been empirical guessing based on what the calculator is willing to display on what little screen real estate it has, along with considerations for humans not usually familiar with the quirks of binary and IEEE floats.

      @Felice_Enellen@Felice_Enellen3 жыл бұрын
  • Reverse engineering someone else's code is hard enough when you have the code in front of you...

    @rorykurek643@rorykurek6433 жыл бұрын
    • Fetching machine code is enough if you have descent tools. But they might have set up encrypted and protected boot to prevent dumping binaries.

      @suokkos@suokkos3 жыл бұрын
    • Reverse engineering MY OWN code from last year is hard enough :p

      @sourcererseven3858@sourcererseven38583 жыл бұрын
    • @@suokkos Highly doubt that for a calculator though

      @deoxal7947@deoxal79473 жыл бұрын
  • Interesting! I don't normally comment but it's my birthday today, this video was posted on my birthday last year, and I found it completely by accident. When the universe (or the YT algorithm) yanks your chain like that, you better follow. So (as a professional code trouble shooter and optimizer) my very first thought was this: Have you tried the 'obvious control' input of 121^3 / 13 ? If this does not give the same result as 11^6 / 13 then this suggests that the specific precise input of the latter is treated as a 'special case' input, in which case it's not a confluence of approximations and rounding errors but a simple if/then clause in the code. Could be an easter egg, or as I saw someone suggest in the comments, a quick way for Casio to test if someone copied their code.

    @BeamerMiasma@BeamerMiasma2 жыл бұрын
    • Very late for a comment, but 121^3/13, 1331^2/13, 14641^1.5/13, and 161051^1.2/13 all give the pi approximation result. It seems to be related to the 3600 denominator (using 11^6/16.999999999995 instead of 17 gives you a pi approximation)

      @airplaneniner@airplaneniner10 ай бұрын
  • It seems you don't even have to type in the Equation: When I just Type 136273.923077 into my Casio fx-82es and hit [=], it will also tell me that it is 156158413/3600*pi. The same also works for 136273.9230769, but not 136273.9230768 or 136273.9230771. Yet again 136273.923077018 does work, while 136273.923077019 does not. After that I stopped trying.

    @Robert-qo1qu@Robert-qo1qu3 жыл бұрын
    • i have a Casio fx-82MS and it does not use pi for any of these. This version has Chinese letters on the top and is from my Chinese friend (so its legit). Maybe! these are made in china.... and they slightly skew the ones they sell to the westerners?

      @cocorico128@cocorico1283 жыл бұрын
    • Hey can you do the 11^6/13 calculation again, but when it gives you that fraction, hit the S D button to turn the answer into a decimal number, then scroll along and type down the answer to 50 decimal places unless it repeats then just say what it repeats please.

      @prich0382@prich03823 жыл бұрын
    • @@cocorico128 It works on a range. not any higher. but as low as 136273.923076900, maybe further but I'm not messing with it any more.

      @kal9001@kal90013 жыл бұрын
    • @@christosvoskresye i don't see that. it does say S-V.P.A.M. most just say vpam and aparently the S stands for Super so whatever super can do is what mine can do.

      @cocorico128@cocorico1283 жыл бұрын
    • @@kal9001 i put tons of digits into it and couldn't get it to ever show pi

      @cocorico128@cocorico1283 жыл бұрын
  • it is possible that is a trademark to see if their tech has been stolen by another company like a waterstamp

    @MeisterReaper@MeisterReaper3 жыл бұрын
    • Oh! That’s an interesting theory. I suppose that, like a map, it would be very difficult to prove that your code had been copied if all you could show is that both calculators provide the correct answer for every calculation you tried. One thing though, and sorry for this terrible nitpick, but that’s not a trademark or a watermark - it’s a copyright trap. Trademark is a way of publicly branding yourself, and violating a trademark tends to be pretty obvious. If I was branding my calculators as KASIO, that would be a violation of Casio’s trademark. If I stole their calculator code and put it in my calculator, that’s a violation of their copyright. If I did that, and they could show that my calculator and their calculator gave the same unusual answer for a given input, and I couldn’t justify why my calculator does that, that can be used as evidence that I violated their copyright.

      @gormster@gormster3 жыл бұрын
    • Given Smathlax's discovery of the relationship to 25200 and factors thereof, the circumstances required to produce this 'bug' feels too general (as in not-specific) to be a copyright trap. But I will concede that it is entirely possible that you are correct. My bet is some sort of strange coding error.

      @superdupergrover9857@superdupergrover98573 жыл бұрын
    • Or this might be the pirate one. ;-P

      @LuizBHMG@LuizBHMG3 жыл бұрын
    • @@superdupergrover9857 Instead -- though this is a nifty suggestion that could be correct -- I bet it has to do with how the rational fraction discovery algorithm is implemented. I bet it's counting the amount of iterations, because that's what any sane engineer would do. And when I say counting, I don't mean actually counting, but instead the algorithm is limited in cycles, and if it doesn't yield a solution in a given amount of iterations, the operation is seen as futile, the solution is discarded and something else is tried instead, eventually falling back to displaying an irrational decimal number, which is a logical thing to do, given the inaccurate nature of floating point math in processors. This is the simplest explanation of what's going on (from the software engineer's point of view, and I am one), but to prove it we need the actual algorithm as it is implemented in Casio. Maybe someone could rev engineer it though, and I admire the host's effort in this direction, but he needs to be much more stubborn than that, and to think very low level. edit: In other words, he's obviously not a software engineer, but a mathematician. He fell into a trap of thinking the Casio must have surely compared the number to Pi, which is something you just never do, you never compare the two floating points naively. Not only it is unreliable, it is also incredibly slow. The numbers are internally represented in an IEEE 754 standard, which has nothing to do with how the digits are displayed in the decimal system, and you can't simply compare two base-2 sausages bit by bit and hope it works like plain text or integers would.

      @milanstevic8424@milanstevic84243 жыл бұрын
    • So any calculator that gets the right answer didn't steal from them. Clever.

      @daicon2k6@daicon2k63 жыл бұрын
  • Pi in a Casio calculator (fx-85GT Plus) is stored as 3.1415926535898 to 14 sf. This is why is you type 3.1415926535898 the calculator shows π. Proof if you are not satisfied: 8.729071001916644*3599 = 10000π. Or: 15,707,963,267,949/5x10¹² = π. Smallest aprox for π that works : 4272943/1360120 = π. (17^5)/11 = (366494029/8920)π does yield pi to 13dp , but they are only equal in this statement to 9sf On the other hand: (11^6)/13 = (156158413/3600)π yields pi to only 12dp , but they are equal in this statment to 13sf : far more than the other.

    @qrcode7504@qrcode75042 жыл бұрын
  • Don't know if it has been mentioned, but there is a common approximation that the number of seconds in a year is \pi\times 10^7.

    @chriskennedy9872@chriskennedy9872 Жыл бұрын
  • Haven’t been able to get my Casio fx-82AU PLUS II to do it, although I did find this in its manual: “The range for calculation results that can be displayed in π form when using Natural Display is |x|

    @cameronsteel6147@cameronsteel61473 жыл бұрын
    • My 82AU Plus II and 100AU plus won't do it, but they also cannot find exact values because of NSW examination rules. Is yours one where it can find exact values?

      @zachst3r_773@zachst3r_7733 жыл бұрын
    • @@zachst3r_773 elaborate on the examination rules, I don't get what you mean by that, why wouldn't it give the exact value (I am also a NSW student)

      @lindsaytang1017@lindsaytang10173 жыл бұрын
    • Documented bug = feature

      @juandesalgado@juandesalgado3 жыл бұрын
    • fx-350TL (from about 20 years ago) doesn't get it either

      @sandravukovic2901@sandravukovic29013 жыл бұрын
    • @@lindsaytang1017 NSW syllabus makes you find exact values by yourself, hence why they dont want calculators to do it for you

      @cam-gv2gf@cam-gv2gf3 жыл бұрын
  • If you look closely, you can see other Matt waving in the distant background from behind the tree at the end.

    @merlinmagnus873@merlinmagnus8733 жыл бұрын
  • You're funny & brilliant. Congratulations.

    @blood.mirror@blood.mirror Жыл бұрын
  • I’ve got a Casio FX-115 ES and it worked just like the video, giving a multiple of pi. But you have to have it in COMP mode (mode 1).

    @mwm48@mwm482 жыл бұрын
  • Back in the day, this kind of thing would be called an easter egg

    @stronzo5000@stronzo50003 жыл бұрын
    • @nuff sed or an easter boob

      @allthingsclick5167@allthingsclick51673 жыл бұрын
    • @nuff sed is that what a real Easter egg is? And I suppose dying actual chicken eggs bright colors and hiding them in the yard for kids to find is an idea inspired by it?

      @justinulysses@justinulysses3 жыл бұрын
    • Once the Easter Egg... now just the merengue on Casio's lemon-Pi.

      @jessecatrainham6957@jessecatrainham69573 жыл бұрын
    • No? Easter Eggs are supposed to be intentional.

      @kingacrisius@kingacrisius3 жыл бұрын
    • ​@@kingacrisius Oopster Eggs

      @jessecatrainham6957@jessecatrainham69573 жыл бұрын
  • Honestly I just enjoy Matt using the exact same calculator I used for my GCSES like 8 years ago. Once a classic, always a classic

    @Ninjamix2372@Ninjamix23723 жыл бұрын
    • GCSEs not GCSES. I take it you failed your GCSE English.

      @Locutus@Locutus3 жыл бұрын
    • @@Locutus This is the most pointless comment in youtube history. Even a broken pencil that hasn't been used since the second world war is less pointless than this comment. I feel bad for your parents, after celebrating the birth of you, that the child they treasure so much will, in the near future, make such a pointless remark.

      @kpp28@kpp283 жыл бұрын
    • @@kpp28 You're wasting your time challenging him - resistance is futile.

      @molletts@molletts3 жыл бұрын
    • We still use them now at my school

      @TomtheMagician21@TomtheMagician213 жыл бұрын
    • Locutus dude calm down

      @TomtheMagician21@TomtheMagician213 жыл бұрын
  • You probably saved my FX-82 :) I dag it out from a drawer just to notice it won't turn on. The battery leaked. Hopefully PCB is intact and it just needs some basic cleaning. Thanks! If it stayed longer with this leaked battery it could be severely damaged.

    @MrocznyTechnik@MrocznyTechnik Жыл бұрын
  • I love the math related existential dread scenes

    @raymondprendergast1084@raymondprendergast10842 жыл бұрын
  • Here i go again, watching KZhead videos about weird maths problems past 10pm.

    @Chrischi3TutorialLPs@Chrischi3TutorialLPs3 жыл бұрын
    • Switch over to ,how to make Pastrami like they did in the old days.

      @markdemell3717@markdemell37173 жыл бұрын
    • tirns out to be 11:02 for me would be neat to see how many watch during the same time frame

      @andrewbarnard3229@andrewbarnard32293 жыл бұрын
    • LMAO it’s literally 10:11 rn and I’m thinking that exact thjng

      @vaughnkhouri1364@vaughnkhouri13643 жыл бұрын
    • 3:28am, welp

      @mikef5951@mikef59513 жыл бұрын
    • Af least it isn’t 4am 🥲

      @arranmcgown2386@arranmcgown23863 жыл бұрын
  • I did a little bit of research as I was curious, you can quite easily replicate this by just using an accurate rational approximation of PI. I used the Farey Algorithm to calculate approximate fractions and it turns out that 3126535 / 995207 is displayed as a decimal but 4272943 / 1360120 is displayed as pi (on the Casio FX-85GT Plus). These approximations were calculated using 322 iterations and 323 iterations respectively, so that should hopefully be a decent indicator of where the precision boundary lies.

    @smitony2@smitony23 жыл бұрын
    • I got the same result on a fx-991EX

      @harmonicarchipelgo9351@harmonicarchipelgo93513 жыл бұрын
    • This makes me curious. Can you multiply the numerator by 2 and get 2*pi? Or multiply the denominator by 2 and get 1/2*pi?

      @OMGclueless@OMGclueless3 жыл бұрын
    • @@OMGclueless This is what I want to know too

      @cortexauth4094@cortexauth40943 жыл бұрын
    • Casio calculators store each number as 13 significant digits multiplied by a power of 10. I haven't checked, but I hypothesize that the first one you said stops equalling pi somewhere before the first 12 digits after the decimal (total of 13 digits including the leading 3.), but the second is equal to pi in at least the first 12, so as far as the calculator is concerned they are the exact same number.

      @NeatNit@NeatNit3 жыл бұрын
    • Casio printing pi in mathprint mode is nothing new, problem is with the fraction before the pi, can we do that by some change in fractional input? EDIT:- That sounded rude I guess, but just everyone is bringing the pi thing up and no one is discussing the fractional part, just saw another comment and people believed it to be a mystery solved

      @cortexauth4094@cortexauth40943 жыл бұрын
  • When I was at school I always thought it was annoying when the calculator tried to show the answer a different way. In the basic high school maths we were doing we always wanted the decimal

    @michael-h95@michael-h957 ай бұрын
  • This got all artsy independent short film REAL quick

    @gionnifer@gionnifer3 жыл бұрын
  • Two things to consider: - Binary Representation - Easter Egg

    @gordondurnell8248@gordondurnell82483 жыл бұрын
    • I didn't see the Easter egg but the binary representation is closer for pi

      @lightarmanov6266@lightarmanov62663 жыл бұрын
    • pi in binary?

      @JLo_24@JLo_243 жыл бұрын
    • Ondřej Majerech not exactly, floating point numbers are represented in a different way in memory. Not even sure Casio use floating point but probably yes

      @SuperSerNiko97@SuperSerNiko973 жыл бұрын
    • This is a 32 bit representation 00111111101101010011110100010101

      @SuperSerNiko97@SuperSerNiko973 жыл бұрын
    • I vote for easter egg: cheap/easy to implement & gives maths nerds something to talk about.

      @jrwjryan@jrwjryan3 жыл бұрын
  • The answer might be in the manual: www.sciencestudio.co.uk/wp-content/uploads/2019/01/fx-83GTX_85GTX_EN.pdf Page 103: "The range for calculation results that can be displayed in π form when MathI/MathO is selected for Input/Output on the setup menu is |x| < 10^6. Note, however, that internal calculation error can make it impossible to display some calculation results in π form. It also can cause calculation results that should be in decimal form to appear in π form." Page 31&34 explain when the result (for fractions) is shown automatically as decimal or as fraction. Maybe that applies to the π-form also somehow.

    @burnheart123@burnheart1233 жыл бұрын
    • This sounds like it's relevant, but you'd probably need to look at the actual internal logic for what form to display in order to figure it out.

      @Bootleg_Jones@Bootleg_Jones3 жыл бұрын
    • Ah, a classic case of RTFM.

      @NeatNit@NeatNit3 жыл бұрын
    • Never wanted to so badly look at calculator source code as I do now.

      @Ikantspell4@Ikantspell43 жыл бұрын
    • @@Ikantspell4 They have a PC simulator of several calculators which exhibit the issue. That might be a reimplementation of the firmware or an emulator + ROM dump?

      @SianaGearz@SianaGearz3 жыл бұрын
    • @@NeatNit Who knew that reading the fine manual could be so illuminating?

      @frankbaird8645@frankbaird86453 жыл бұрын
  • Can confirm that this happens on the 82-ES Plus second edition, just tried it out.

    @smaransuthar663@smaransuthar66310 ай бұрын
  • My favorite approximation for pi is the fourth root of 2143/22. It is accurate to nine decimal places and easy to remember.

    @ericmoore6498@ericmoore64985 ай бұрын
    • It's cool, but not really useful, right? It's just about as easy to remember the 9 decimal places

      @toast_recon@toast_recon5 ай бұрын
  • 8:27 That's an interesting way to pronounce "eleven"

    @Aarontti@Aarontti3 жыл бұрын
    • Rounding error. LOL!

      @hopelessnerd6677@hopelessnerd66773 жыл бұрын
    • Might be due to his Australian accent. They have some weird pronunciations down there.

      @anlumo1@anlumo13 жыл бұрын
    • Parker eleven?

      @rednammoc@rednammoc3 жыл бұрын
    • It's a baker's eleven

      @Ptylermon@Ptylermon3 жыл бұрын
    • Also an interesting way to pronounce 3600 at about 8:50.

      @jeffc5974@jeffc59743 жыл бұрын
  • I tried this on two calculators. My CASIO gives me the same strange result, my TI does not. CASIO fx-85ES: 156158413 / 3600 * \pi Texas Instruments TI-30XB: 136273.9231

    @NereosRenbur@NereosRenbur3 жыл бұрын
    • Hit the S D button to change the answer to decimal. NO ONE knows this for some reason

      @prich0382@prich03823 жыл бұрын
    • @Grant Grant Such as?

      @martind2520@martind25203 жыл бұрын
    • @@prich0382 wdym everyone is taught this in school aren't they?

      @AJ-rm2vh@AJ-rm2vh3 жыл бұрын
    • My TI-30X-IIS gave same answer as Dr Nereos' TI answer

      @fredericapanon207@fredericapanon2073 жыл бұрын
    • @@prich0382 what does that button do? I don't have that on my TI

      @fredericapanon207@fredericapanon2073 жыл бұрын
  • I don't know if anyone has written about this before: I tried it on my Casio FX-991DEX. It gave me a multiple of pi, when I entered it using the "fraction" (the one top left, below "OPTN") button. But when I used the standard "divide" (below the "AC"), it did NOT. So there's something about using the textbook entry mode to trigger the show-me-a-fraction-multiple-of-pi-square-root-of-whole-number algorithm.

    @MartinBeerbom@MartinBeerbom Жыл бұрын
  • I don't expect Casio to use Farey's algorithm, nor continued fractions. The number 3600 is quite suspicious. I assume it just multiplies by an integer with many divisors (e.g. 25200) and checks for a near integer; then simplify the fraction.

    @jurjenbos228@jurjenbos2282 жыл бұрын
    • He entered another example that should have also yielded 3600 in the denominator, but the calculator just gave a decimal answer

      @Muhahahahaz@Muhahahahaz Жыл бұрын
    • Read top comment

      @jdrmanmusiqking@jdrmanmusiqking Жыл бұрын
  • Calculator: *gives answer accurate to 12 decimal places* Average Joe: That's way more accuracy than I need. Mathematician: Not good enough!

    @GreatUSTreasureHunt@GreatUSTreasureHunt3 жыл бұрын
    • Not just average Joe. Also average engineer because they deal with practical matters and average scientist because they deal with precision limitations and significant digits, etc. BTW, we used to laugh at a physics professor who would always say things like "that results in 4.8, we'll call it 5, and then continues the problem with the 5."

      @justinjames3028@justinjames30283 жыл бұрын
    • @@justinjames3028 but wait, aren't we indeed supposed to approximate 4.8 with 5 and 9.8 with 10 in physics? hmmmm

      @OtherPony@OtherPony3 жыл бұрын
    • Me, uses 3

      @billylauwda9178@billylauwda91783 жыл бұрын
    • truth is binary..

      @MrMichaelfalk@MrMichaelfalk3 жыл бұрын
    • @@OtherPony not when it isn't the final answer and even the it depends on the starting values as well. 9.8 could actually be the correct answer for a calculation if the starting values were precise enough (2.82 and 14 for example).

      @yeet3279@yeet32792 жыл бұрын
  • I wonder if it’s deliberate like fake roads on maps to catch out people trying to clone the calculator.

    @desmondbloemers7276@desmondbloemers72763 жыл бұрын
    • Very likely. It's almost an Easter egg. Companies do some strange things to protect intellectual property. Or it could just be an artifact of the floating point routines they used.

      @hopelessnerd6677@hopelessnerd66773 жыл бұрын
    • I was thinking the same thing.

      @JokoarK@JokoarK3 жыл бұрын
    • like paper towns?

      @suryamohan3410@suryamohan34103 жыл бұрын
    • Going by the weirdly specific rules the guy found in the pinned post, I'm sure you're right. It had to be programmed in.

      @HipsterKitteh@HipsterKitteh3 жыл бұрын
  • I lost it at the walk in the forest bit

    @chrismpbuchholz@chrismpbuchholz3 жыл бұрын
  • Omg, the start of the video is Gold !

    @davidlecompte9467@davidlecompte9467 Жыл бұрын
  • This sounds like a good excuse to bring back your calculator review series

    @cupcakesandrose@cupcakesandrose3 жыл бұрын
  • How to throw a mathematician into an existential crisis: Give him a problem his calculator fails at gloriously for no apparent reason.

    @Celrador@Celrador3 жыл бұрын
    • It’s an existential crisis for programmers too

      @ottobass9193@ottobass91933 жыл бұрын
    • @@ottobass9193 If you get thrown into an existential crisis every time your code gives the wrong result for no apparent reason, you might have picked the wrong career :D

      @welltypedwitch@welltypedwitch3 жыл бұрын
    • @@welltypedwitch Am programmer. Can confirm.

      @Celrador@Celrador3 жыл бұрын
    • I mean it depends what you mean by fail. Technically the calculator got as close as it needs to

      @Hojahs@Hojahs3 жыл бұрын
    • @@welltypedwitch that's right 😂

      @ottobass9193@ottobass91933 жыл бұрын
  • Also fascinating, thanks - I was just using that method today to find more and more accurate values for something but with decimals not fractions, to get accurate to more and more decimal places. (Adjusting parameters in a formula to minimize its error compared with another set of data points) [- see the comment to your video on the perimeter of ellipses!]

    @yahccs1@yahccs12 жыл бұрын
  • I enjoyed this video so much ;)

    @pianodavid9676@pianodavid9676 Жыл бұрын
  • "bUt Pi Is IrRaTiOnaL" resonating through my brain

    @zeroartisan@zeroartisan3 жыл бұрын
    • Pi = circumference/diameter => Pi is rational Q.E.D. I see absolutely no problems

      @ethannguyen2754@ethannguyen27542 жыл бұрын
    • Because remember, it isn't a root of any polynomial with rational coefficients.

      @mjzudba5268@mjzudba52682 жыл бұрын
    • Lol

      @zedwolfcontent@zedwolfcontent2 жыл бұрын
    • Jesus Christ is God and is the only way

      @SquidBeats@SquidBeats2 жыл бұрын
    • @@ethannguyen2754 just making a ratio like that isn't enough to make a number considered rational yknow. The two numbers must be WHOLE and coprime to each other

      @adamqazsedc@adamqazsedc2 жыл бұрын
  • What if this was a unique Easter Egg, coded in by some engineer as their favourite approximation for pi? That would explain why the others don't work.

    @josephcorrigan6839@josephcorrigan68393 жыл бұрын
    • This is what I was thinking too, tbh.

      @bryantames3716@bryantames37163 жыл бұрын
    • No

      @TheRealFlenuan@TheRealFlenuan3 жыл бұрын
  • this feels like a moment that would cause a doubtful techpriest of mars to be born again

    @ItWasSaucerShaped@ItWasSaucerShaped3 ай бұрын
  • I haven't had many modern Casio calculators - in fact I don't even think my current one would be among those doing this, though I think I did briefly have one that would.

    @PhilReynoldsLondonGeek@PhilReynoldsLondonGeek3 жыл бұрын
  • that calculator is perfect for you. it almost always gives correct answers like a true Parker calculator.

    @HPD1171@HPD11713 жыл бұрын
    • i went looking for a "parker calculator" or "parker approximation" comment. thank you

      @logosking2848@logosking28482 жыл бұрын
  • Why didn't Matt ask a Casio engineer? That would've been fun to watch.

    @hgonzmart@hgonzmart3 жыл бұрын
    • Hugo Gonzmart My guess would be that’s confidential information they can’t share.

      @donatj@donatj3 жыл бұрын
    • My guess is that he has tried but has been unsuccessful in contacting them.

      @AnthonyJamesWood@AnthonyJamesWood3 жыл бұрын
    • I see what you did there.

      @andybaldman@andybaldman3 жыл бұрын
    • Matt used number of digits as a limit for the search of the fraction, maybe instead Casio uses a recursion depth limit for the search

      @rogerab1792@rogerab17923 жыл бұрын
    • That is left as an exercise for the reader.

      @Silwany@Silwany3 жыл бұрын
  • How the Casio could get to Pi times Pi (or a fraction in the sense of an equation as opposed to a number multiplied by Pi) is that BEDMAS would have you use exponents or divide before you multiply, which the question did not do, so the Casio expresses the circular argument that it would have to do each before the other, which is as infinite as Pi (or thereabouts) times Pi. Regards.

    @user-pq1cz9mo4y@user-pq1cz9mo4y7 ай бұрын
  • I experienced the opposite of this. I used an integral to find the area of a circle with radius 1 and the calculator rounded the result so much that it no longer recognized it as pi

    @younscrafter7372@younscrafter73725 ай бұрын
  • Wow, that fraction finding thing was enlightening. I have no idea how I’ve never seen that in all my days. This is why I love educational youtubes, it’s like a box of chocolates, never know what you’re going to get.

    @ObservationofLimits@ObservationofLimits3 жыл бұрын
    • That's a really popular practice in math and computer science.. A binary search is a similar way of narrowing down to a result and there is an algrothim to find a root of a function which uses the same idea of discarding half the data every time

      @monkey1346ful@monkey1346ful2 жыл бұрын
  • I love finding out about crazy functions or proofs that are blindly stumbled across and are weirdly interesting.

    @graefx@graefx3 жыл бұрын
  • Love the existential dread vibe 🤣🤘

    @krakhedd@krakhedd2 жыл бұрын
  • I want a sequel to this intriguing property

    @Kirmo13@Kirmo13 Жыл бұрын
  • Some people may have their favorite sports teams, but Matt Parker has his favorite calculator.

    @real.bingus@real.bingus3 жыл бұрын
    • He's not alone. Though I prefer Sharp vs Casio, personally.

      @pwnmeisterage@pwnmeisterage3 жыл бұрын
    • I've had the same TI-30Xa since high school and wouldn't trade it for anything. Nerdy to say, but I love it.

      @Mariorox1956@Mariorox19563 жыл бұрын
  • As we always say: Pi pops up in the darndest places!

    @seanm7445@seanm74453 жыл бұрын
    • Such an interesting comment! How about, "The London Underground"? Investigate how much longer the outside rail of the Circle Line is than the inside rail, given that the gauge is 4 feet 8 and a half inches.

      @stephentucker994@stephentucker9943 жыл бұрын
    • **3Blue1Brown has entered the chat**

      @Trent-tr2nx@Trent-tr2nx3 жыл бұрын
  • That intro was beautiful

    @Epinardscaramel@Epinardscaramel Жыл бұрын
  • As a programmer, I have a good idea of what's happening: 1) get the resulting number 2) try to make a fraction out of it 3) try the same as #2 with first divide by PI, if the resulting fraction has been simplified, then keep #3 It's that simple. Why is it even trying #3? Because otherwise PI would never appear in any answer since it's irrational, and if you do something like acos(-1), the calculator will output 3.14159265359, but in reality, the exact answer is PI, so the algorithm tries to find PI by checking if the result is very close to a multiple of PI.

    @youuuuuuuuuuutube@youuuuuuuuuuutube9 ай бұрын
  • Perhaps it's a proprietary phenomenon like the "paper towns" that exist only on maps.

    @shurikenmiasma@shurikenmiasma3 жыл бұрын
    • That's a neat idea

      @robertstuckey6407@robertstuckey64073 жыл бұрын
    • I imagine some poor guy sitting in an office in China, writing the software for the new Gaxio. He is doing every possible calculation (all of them) on a Casio, and then hardcoding the result. Casio, you are so evil!

      @renerpho@renerpho3 жыл бұрын
    • Genius!

      @geirtwo@geirtwo3 жыл бұрын
    • Is that like a trap street? en.wikipedia.org/wiki/Trap_street

      @IanTester@IanTester3 жыл бұрын
    • I was thinking the same thing. Perhaps it's a way to find out if somebody is building a calculator using stolen chip designs - or (more likely) stolen firmware. (Do these calculators run firmware? I would guess so, but I have no knowledge.)

      @russelllewis9215@russelllewis92153 жыл бұрын
  • As a software developer, I’m willing to bet that the answer lies in different number representations between your Python code (likely floating point) and the Casio (perhaps fixed point) or perhaps both are floating point, but different implementations. The “Pi detector” is surely tuned to whatever the Casio’s representation’s most accurate representation of PI is. Switching the Python code to a different implementation floating point (perhaps 24/32/64 bit) or a fixed decimal package may shed some light on this.

    @tommornini2470@tommornini24703 жыл бұрын
    • I suspect you're right. It's easy to get different results on different hardware/software from the same calculation when floating point numbers are involved. IEEE-754 provides standard for floating point arithmetic that everyone can develop against so that you can at least be confident that two different pieces of hardware or software will provide the same answer but even then it's possible for both of them to be wrong. To see what happens when you do it poorly just look to the patriot missile system failure in the first gulf war. That mistake resulted in 28 soldiers dying.

      @shawnsustrich7981@shawnsustrich79813 жыл бұрын
    • To add to this, I also suspect that "pi" is represented within the calculator as a ratio of two integers that are "close enough", since it's impossible to actually store an irrational number. Maybe they just happened upon this exact ratio?

      @clarinetJWD@clarinetJWD3 жыл бұрын
  • We just found the most elaborate easter egg in a place where we didn't know easter eggs could even exist

    @vale.antoni@vale.antoni2 жыл бұрын
  • Whenever I do math by myself, it's never this fun.

    @johnfitzgerald8879@johnfitzgerald8879 Жыл бұрын
  • Irrational numbers are the oldest conspiracy around, you've stumbled on something they don't want you to know. 😉

    @cariad561@cariad5613 жыл бұрын
    • oh shut it pythagoras

      @geekjokes8458@geekjokes84583 жыл бұрын
    • THEY tried to silence us. THEY tried to censor the Truth from our math books. be careful people, because THEY are the ones who teach our kids and throw those fantasies to them in order to hide what's actually happening

      @srpenguinbr@srpenguinbr3 жыл бұрын
KZhead