Calculator Sticks from the 1600s

Napier's bones, invented in the 1600s. They multiply a big number times a single digit.
This is episode 8 of my video series about calculating devices.
Chris Staecker webarea: faculty.fairfield.edu/cstaecker/
Page about the bones: faculty.fairfield.edu/cstaeck...

Пікірлер: 557

  • @ChrisStaecker
    @ChrisStaecker2 жыл бұрын

    Related videos: RETORTS! I respond to my favorite comments from this video: kzread.info/dash/bejne/iKyM05Jvn6fJZrw.html Numbring Nines Rods- a variation from 1684: kzread.info/dash/bejne/eJyAmrOReqrAfbw.html Genaille Rods- a variation from 1891: kzread.info/dash/bejne/fHeJsqiTYMyuj9Y.html

  • @brianjones9780
    @brianjones97802 жыл бұрын

    The way he says "the bones" is one of a kind

  • @cavemanooga

    @cavemanooga

    2 жыл бұрын

    Came into the comments just to say I like the way he says bones

  • @ChrisStaecker

    @ChrisStaecker

    2 жыл бұрын

    Doesn't everybody say it like that?

  • @nubidubi23

    @nubidubi23

    2 жыл бұрын

    @@ChrisStaecker bawwwwns (no)

  • @ARCtrooper8248

    @ARCtrooper8248

    2 жыл бұрын

    Almost like 'Billy bones'

  • @cl-l_m5022

    @cl-l_m5022

    2 жыл бұрын

    Me say "Booouuuaans"

  • @matthewrooke819
    @matthewrooke8192 жыл бұрын

    Small things like this are what medieval/fantasy films are missing.

  • @gokul_ml

    @gokul_ml

    2 жыл бұрын

    Yeah, the authenticity ... In avatar, Navis had eight fingers. So their number system was base 8.

  • @ChrisStaecker

    @ChrisStaecker

    2 жыл бұрын

    I have never seen Napier's bones used in a film. Get on that, Hollywood!

  • @DieselpunkMachine

    @DieselpunkMachine

    2 жыл бұрын

    maybe real people were much smarter than movie makers?

  • @edwardmaginot

    @edwardmaginot

    2 жыл бұрын

    Not appropriate for medieval settings at all. It's largely an Early Modern thing from when there were intellectuals not necessarily part of a clergy, and after getting access to islamic knowledges. Two things not even close to relevant to Middle Ages.

  • @mondaysinsanity8193

    @mondaysinsanity8193

    2 жыл бұрын

    @@edwardmaginot um...mideavil isnt just europe js. Also banks existed since the crusades atleast which this is def a banker kinda thing

  • @Mural
    @Mural2 жыл бұрын

    You got a real good giggle out of me with the calculator.

  • @ohheyitscyber2848

    @ohheyitscyber2848

    2 жыл бұрын

    Same

  • @folasadeosibodu7119

    @folasadeosibodu7119

    2 жыл бұрын

    Yea that got me too.

  • @TheBookDoctor
    @TheBookDoctor2 жыл бұрын

    Awesome. I never understood how Napier's Bones worked, but this makes it super clear and super obvious. The connection to lattice multiplication is excellent too.

  • @Anti-Alphabet_Mafia

    @Anti-Alphabet_Mafia

    2 жыл бұрын

    You know what I say? Screw math. Math can suck my clit, my nuts, my nipples, and my ass.

  • @KujiraFEl

    @KujiraFEl

    2 жыл бұрын

    i can't understand a thing, it easier to learn another language, then math for me, it never was my thing you know

  • @d_1044
    @d_10442 жыл бұрын

    I like that you not only explain this interesting mathematical object but tell us how to use it and that the Home Depot people will get suspicious of you ask for too many free materials

  • @jingusflorpus4274
    @jingusflorpus42742 жыл бұрын

    I learned lattice multiplication in school and it’s actually been my preferred method to multiply since third grade, so I recognized it on the bones immediately and felt extremely vindicated when you confirmed it for me later lol

  • @AliceTheNeko
    @AliceTheNeko2 жыл бұрын

    Seeing these awakened long-buried memories in me of elementary school. I don't think we had these in particular, but we had similar things. I remember long, flat plastic rods with numbers along the side next to notches in the side that a small string would nest in as you wrapped and weaved it around the rod.

  • @ChrisStaecker

    @ChrisStaecker

    2 жыл бұрын

    Yes- those are “math wraps”! They don’t calculate for you, but you do a bunch of calculations as you wrap it up and then the string lets you check the answer.

  • @MurakenToo

    @MurakenToo

    2 жыл бұрын

    We had those back in the early 2000's in the school I went to here in Sweden :) I wonder if they're still used nowadays or if they've been replaced by electronics.

  • @getonthecrossanddontlookba5004

    @getonthecrossanddontlookba5004

    2 жыл бұрын

    Repent to Jesus Christ “In peace I will lie down and sleep, for you alone, Lord, make me dwell in safety.” ‭‭Psalms‬ ‭4:8‬ ‭NIV

  • @Not_An_EV

    @Not_An_EV

    Жыл бұрын

    @@getonthecrossanddontlookba5004 shoo shoo go away shoo

  • @austinevs
    @austinevs2 жыл бұрын

    The way he said "They get suspicious" at the end is kind of hilarious when you try and come up with a visual image of a home depot employee thinking what kind of nefarious things are you doing with paint sticks.

  • @ChrisStaecker

    @ChrisStaecker

    2 жыл бұрын

    my dude had no idea…

  • @adrianbilodeau1241
    @adrianbilodeau12412 жыл бұрын

    I never learned how and abacus worked until now… it’s actually quite beautiful in its own way.

  • @f3player
    @f3player2 жыл бұрын

    "Wanna use my calculator?" Nah, i got the bones

  • @JustSway
    @JustSway2 жыл бұрын

    I actually like that. I wish in history class they would teach us some older stuff like this... "evolution of math", instead of going over the same history we have been and barely adding anything new. Honestly, I can learn more about History on the internet than my High School history class.

  • @cracno1125

    @cracno1125

    2 жыл бұрын

    Remember, History class is usually a summary of the History of your country. Which society at large feels you should know as a citizen of X country. But don't worry. You can still learn more at home! I suggest you looking for trust worthy books on various historical subjects. You might even have a few at your school's library. Otherwise, order them at a public library or order them online.

  • @JustSway

    @JustSway

    2 жыл бұрын

    @@cracno1125 School is out of the picture as of now. High school graduate. I am currently working a factory job so any knowledge of history I would have to do online anyways.

  • @cracno1125

    @cracno1125

    2 жыл бұрын

    @@JustSway Why so?

  • @JustSway

    @JustSway

    2 жыл бұрын

    @@cracno1125 I am trying to control my spending habits and I work at a factory. I also said "as of now", I still have potential of going to a good school.

  • @cracno1125

    @cracno1125

    2 жыл бұрын

    @@JustSway Ok, that's cool. Remember, it's one's goal to enrich oneself in this life before going unto the next alongside Christ.

  • @tonyennis1787
    @tonyennis17872 жыл бұрын

    The Japanese abacus is awesome. Check out videos of them using it. They are amazing. You can also be very good on the Japanese abacus and not know how to add. It's all about patterns.

  • @Kameron-The-Crafter

    @Kameron-The-Crafter

    2 жыл бұрын

    Abacus are Awesome as Well.

  • @rebucato3142
    @rebucato31422 жыл бұрын

    Seeing that you mentioned the abacus at the end, I think the Chinese/Japanese abacuses (?) are also worth talking about. Instead of using rows of 10 beads, they use columns of 5/7 beads separated by a bar in the middle, with the top beads representing a value of 5 and the bottom beads representing 1. A lot of children in Japan still learn to use the abacus, and both the Chinese and Japanese have used it to take mental calculations to the next level (6-digit multiplications in their head).

  • @ChrisStaecker

    @ChrisStaecker

    2 жыл бұрын

    I featured the Japanese abacus in this video: kzread.info/dash/bejne/eJmouLmMo82dZ7A.html

  • @rebucato3142

    @rebucato3142

    2 жыл бұрын

    @@ChrisStaecker Yeah I realised that after going through your videos a bit more. Thanks for taking the time to respond though!

  • @jeremyrutenberg7087
    @jeremyrutenberg70876 жыл бұрын

    This guy makes me laugh out loud I love it

  • @krishnachoubey8648
    @krishnachoubey86482 жыл бұрын

    Maths Teacher : Why did you bring "Ice-Cream Sticks" to the examination hall? Me : *"My goals are beyond your understanding"*

  • @pipespb

    @pipespb

    2 жыл бұрын

    Мы в школе сдавали экзамены на счетной (логарифмической) линейке. kzread.info/dash/bejne/aoGor7yvZrjSpcY.html

  • @tenofhearts99
    @tenofhearts992 жыл бұрын

    I used the lattice method all through school, I couldn't long multiply any other way and I still can't long divide. I always wondered if there was a whole school of thought in math that was like the lattice method. That drawn out grid helped me out so much as a person who is hands-on but I failed at math and nothing else was like the lattice method to me.

  • @zubirhusein

    @zubirhusein

    2 жыл бұрын

    Same, lattice is how my primary school teacher taught. If I don't do the lattice method, I do another method where I split up one of the operands by tens place. So 1234*1234 becomes 1234*1000 + 1234*200 + 1234*30 + 1234*4

  • @mujipanda1947

    @mujipanda1947

    2 жыл бұрын

    my school did not teach it but I used that method as I found it better

  • @layleedayne4772

    @layleedayne4772

    2 жыл бұрын

    Same. My teachers hated grading my tests and homework when you have to show your work. And I had cubes with numbers and slashes all over my papers. They also work really nicely for decimal point multiplication as well.

  • @zubirhusein

    @zubirhusein

    2 жыл бұрын

    @@layleedayne4772 oh yes true, makes it easy

  • @miradesnan38

    @miradesnan38

    2 жыл бұрын

    I would like teachers to teach this method when they see a child struggling with the usual way to calculate. But strange enough most teachers will give you less points on a right answer if the way you got this answer is not exactly the same way they teached! Isn't this totally wrong?

  • @themaddtatter6679
    @themaddtatter66792 жыл бұрын

    Love that "Ah-ha" (eureka) moment when you explained how to do the lattice method! Makes super sense and saves a TON of space. Can't wait to show my 13 year old who loves math as much as I do! Thankyou for sharing this!

  • @bennapier9260
    @bennapier92602 жыл бұрын

    John Napier was my ancestor. Everyone in my family has a gift for math.

  • @causewaykayak

    @causewaykayak

    2 жыл бұрын

    Thats pretty Special

  • @justinfufun5483

    @justinfufun5483

    2 жыл бұрын

    except Kate. (She replied here too)

  • @B1Boomer
    @B1Boomer2 жыл бұрын

    I did not realize it at the time, but my 5th-grade teacher taught us lattice multiplication to demonstrate the fun of mathematics.

  • @Stranger_Strange_Land
    @Stranger_Strange_Land2 жыл бұрын

    This is a prime example of how techniques/formulas have changed over time. Each generation seems to have been taught a different way to find the answer to math problems. A lot of them over complicate it, confusing people and making people, like me, _hate_ math.... This is really neat!

  • @jacklimestone2559
    @jacklimestone25592 жыл бұрын

    One of my first comp sci projects in college was making some of these out of cardboard and photographing me using them. What an odd professor, but he got the point across well.

  • @katenapier5477
    @katenapier54772 жыл бұрын

    John Napier: *invents extensive multiplication tools* Me, a distant relative: *traumatic war flashbacks of memorizing multiplication facts in 3rd grade*

  • @TroutBoneless
    @TroutBoneless2 жыл бұрын

    The personality on display here is captivating. That Burroughs calculator bit was a 10/10

  • @michaelrabich9635
    @michaelrabich96354 жыл бұрын

    I watched a lot of your videos, amazing stuff. Napier was the man

  • @Skeeter51244
    @Skeeter512442 жыл бұрын

    I began a career i8n surveying in the early 1960's, several years before electronic calculators were available. Each field crew had at least one Curta mechanical calculator. If you can put your hands on one, I think many of your viewers would find it interesting.

  • @christinageraci9172
    @christinageraci91727 жыл бұрын

    This channel is really cool. Definitely deserves more subs... and hoagies.

  • @ChrisStaecker

    @ChrisStaecker

    7 жыл бұрын

    Thanks! ... meatball for me.

  • @pratefplayzgaming160

    @pratefplayzgaming160

    2 жыл бұрын

    True bro you are very good

  • @Ten_522
    @Ten_5222 жыл бұрын

    The intro background music made medieval calculators sound as sick as a skateboarding ad.

  • @benjaminchance3311
    @benjaminchance33112 жыл бұрын

    if you put the smaller number on the right side you can also put decimals and get pretty accurate percentages. sometimes it can take some guessing to get the right decimal place in your answer.

  • @VAM_Physics_and_Engineering
    @VAM_Physics_and_Engineering2 жыл бұрын

    Never seen or heard of this before. I thoroughly enjoyed this... Well done!

  • @Southern.Nappiness
    @Southern.Nappiness2 жыл бұрын

    Your voice is very soothing. We learned about Napier Bones and abacus in history class in middle school. That's when they really taught history.🙂🙂

  • @sharishth
    @sharishth2 жыл бұрын

    I remember at studying this school text book under computer subject. With just a picture and a paragraph, happy to see after so many years someone showed us this calculator.

  • @1Isardo
    @1Isardo2 жыл бұрын

    I love how the bones are just the times tables for each number

  • @J3rs3y_G1rl
    @J3rs3y_G1rl2 жыл бұрын

    I learned so many methods of calculation today thanks to you. Much obliged.

  • @smexijebus
    @smexijebus2 жыл бұрын

    Wow, I spent a few years learning the Chinese abacus in my youth, got really quite fast at it, then never used it again and up until your demonstration, I had quite literally forgotten how it even worked. Kid me seemed like magic for most of my adult life.

  • @carriebishop8838
    @carriebishop88382 жыл бұрын

    Every Math teacher needs to refer their students to your videos

  • @CheaddakerT.Snodgrass
    @CheaddakerT.Snodgrass2 жыл бұрын

    Great. Just great. I'm randomly suggested this video. Now I have to watch more. Real great.

  • @CheaddakerT.Snodgrass

    @CheaddakerT.Snodgrass

    2 жыл бұрын

    In all seriousness those are really cool. Imagine if kids were taught how to use those before learning how to do math with a pencil. I feel like they would expand the mind.

  • @anthonywatts2033
    @anthonywatts20332 жыл бұрын

    One: you accent is awesome! Two: the bones...brilliant. I am just so glad the electronic calculator was invented by the time I came around....

  • @never-mind26
    @never-mind262 жыл бұрын

    Whoever you are, thank you for giving me something to do with my kid that's fun and pedagogic at the same time.

  • @whatsunderthetable
    @whatsunderthetable2 жыл бұрын

    this video has such a charm

  • @sharpiedory
    @sharpiedory6 жыл бұрын

    them Bones

  • @Lex60
    @Lex602 жыл бұрын

    My uncle did business with Chinese people in the mid-'30s and he told us how they used abacus in a very expert and quick way. Never had a problem.

  • @Delicate_Disaster
    @Delicate_Disaster2 жыл бұрын

    I've never seen this page, but I like it based off of this video. Especially The calculator part.

  • @Adamkilla9000
    @Adamkilla90002 жыл бұрын

    The most chill mathematician

  • @TheDitronik
    @TheDitronik2 жыл бұрын

    The form of multiplication was used in the 1202 Liber Abaci and 800 AD Islamic mathematics and known under the name of lattice multiplication. "Crest of the Peacock", by G.G, Joseph, suggests that Napier learned the details of this method from "Treviso Arithmetic", written in 1478.

  • @ChrisStaecker

    @ChrisStaecker

    2 жыл бұрын

    Yes I mentioned lattice multiplication around 2:50.

  • @Ligers81
    @Ligers812 жыл бұрын

    I didn't learn any of those methods! nice to see something new that I can still understand, except for the abacus.

  • @earthly_leopard6497
    @earthly_leopard64972 жыл бұрын

    I love seeing these sort of things

  • @vardoosh5305
    @vardoosh53052 жыл бұрын

    Hahahah first video I see from this KZreadr and pulls out the calculator joke 🤣 Subscribed and liked real quick.

  • @littlelyra754
    @littlelyra7542 жыл бұрын

    I have often used the lattice method since I learned it in elementary school, but after elementary school and I got a bit older, I used it in my scratch paper that I had to turn in for proof that I did the work, and the teacher was like “what is this?” And I got points counted off for it. I tried telling them what it was and they said they’d never heard of it. Smartphones weren’t common at the time, so I couldn’t just Google it and show them. Then I started asking other people and they had no idea what I was talking about, even when I wrote it down and showed them. For years I started thinking I was just crazy and had made it up in my head or something, but I kept using it because it worked. Now I know I’m not crazy, those other people were just dumb or forgot about it.

  • @DiegoJove
    @DiegoJove3 жыл бұрын

    This is the best video of this topic!!!

  • @petermach8635
    @petermach86352 жыл бұрын

    Ha ...... not just the 1600's, I learnt to use them at school in Edinburgh in the 1960's along with slide rules. Mind you, that was just down the road from Merchiston Castle, the family home of the Napiers.

  • @laurenkalibat357
    @laurenkalibat3572 жыл бұрын

    Napier's Bones are a great teaching tool. I used them in the classroom many years ago.

  • @Omegawylo
    @Omegawylo2 жыл бұрын

    This is a perfect youtube video. Perfection.

  • @BoneGoddess
    @BoneGoddess2 жыл бұрын

    Lol new to your channel. Loved how gitty you were over that calculator

  • @lenxx
    @lenxx2 жыл бұрын

    this was so much fun to watch. thank you.

  • @CoopyKat
    @CoopyKat2 жыл бұрын

    This was really COOL! i used to have an old mechanical pocket calculator, I loved it.

  • @juanjosemendivil1626
    @juanjosemendivil16262 жыл бұрын

    I didn't recognize the formula until he draw the box, I was stunned I was using it the whole time.

  • @hopefletcher7420
    @hopefletcher74202 жыл бұрын

    When I was in high school in the 1960s they still taught how to use a sliderule for the advanced students. In my first job in the 1970s I used the old manual calculator that had rows of numbers to punch.

  • @JimboLogic
    @JimboLogic2 жыл бұрын

    I enjoyed this video waayyy more than I thought I would. Subscribed.

  • @Southern.Nappiness
    @Southern.Nappiness2 жыл бұрын

    I subbed bcuz I love, used and understand the Napier Bones. We made small ones from popsicle sticks, just for fun in middle school. I loved the clicks of the Abacus.🙂🙂🙂

  • @drowningflamingo
    @drowningflamingo2 жыл бұрын

    So cool to see a demonstration of these! Btw, the sound level for the VO was a little low and the music a little high. Overall, another great video. Keep it up!

  • @Jamie_Pritchard
    @Jamie_Pritchard2 жыл бұрын

    I shall now and forevermore use the diagonal lattice system. It's so much easier 😲

  • @latiendadepaikawaii
    @latiendadepaikawaii2 жыл бұрын

    That music at the start got me thinking "why does this sound familiar?" And i saw a minecraft lego ad in my recommended and it was this same music it used.

  • @gonzalogarcia312
    @gonzalogarcia3122 жыл бұрын

    This is totally awesome. I'm not very good at math but I feel like if I was taught this as a kid I probably wouldn't be as bad at math! Hell maybe it might have boosted my confidence in mathematics. Definitely a good eye opener of a video!

  • @user-ho4tb5qe7v
    @user-ho4tb5qe7v2 жыл бұрын

    Sometimes I want to pick all ytubers and time travel them back to when I was a kid, this makes sooo much more sense

  • @Jcorella
    @Jcorella2 жыл бұрын

    How happy you were with your big calculator made me happy.

  • @kilgoretrout8896
    @kilgoretrout88962 жыл бұрын

    I haven’t subbed this hard in years

  • @mylehigh
    @mylehigh2 жыл бұрын

    When I was younger I could never figure out multiplication and only knew lattice, so it's interesting to see that other people used I'd more frequently for more applications

  • @vladstad8102
    @vladstad81022 жыл бұрын

    subbed this stuff blew my mind

  • @argonwheatbelly637
    @argonwheatbelly6372 жыл бұрын

    You could also use jetons on an exchequer table, or even calculi on a sand table or Salamis-styled board.

  • @bmanpura
    @bmanpura2 жыл бұрын

    I learned the abacus as a child, this thing is faster in operation speed but it needs time to setup. Plus, it can be arbitrary length - abacus is kinda limited and really unwieldy. Good abacus operator can calculate really fast and with enough practice, it's muscle memory. I wonder how fast can the calculation be if people practice using this enough.

  • @ThePieOfTheUnknown
    @ThePieOfTheUnknown2 жыл бұрын

    My brain died in the abacus demonstration

  • @tomlongworth5387
    @tomlongworth53872 жыл бұрын

    I think a teacher would be impressed if you used this in highschool

  • @softcloudx7240
    @softcloudx72402 жыл бұрын

    In my school system we actually learn multiplication using the lattice method! We get taught the older method and the lattice so we could use what works best for us

  • @sohiln9076
    @sohiln90762 жыл бұрын

    Thanks man just found another way to multiply big numbers

  • @yee9167
    @yee91672 жыл бұрын

    I remember that my 3rd grade teacher taught my class how to make these: I completely forgot how, until now.

  • @connoranastasio
    @connoranastasio3 жыл бұрын

    How does this channel not have more subs wtf

  • @petergohan
    @petergohan2 жыл бұрын

    holy crap, that's magical.

  • @ichoboi
    @ichoboi2 жыл бұрын

    that's a pretty cool way to calculate things

  • @paulc6060
    @paulc60602 жыл бұрын

    This video is as though ripped from the internet of my childhood and brought here to the internet of my sad late 20's.

  • @DailySnuggles
    @DailySnuggles2 жыл бұрын

    this video was awesome as someone who like numbers its cool to see a old way of computation that works the way my brain dose math

  • @novopotato
    @novopotato2 жыл бұрын

    A well formulated video

  • @mikaelsza
    @mikaelsza2 жыл бұрын

    YT Algorithm: Wanna see a Stick Calculator from 1600s?? Me, watching in a sunday: WHY NOT?!

  • @kamo7293
    @kamo72932 жыл бұрын

    You could do multi digit with multi digit using the bones by writing out the rows on a different paper and doing lattice on them. Pretty sick. Also first time I ever saw someone explain the abacus

  • @CorruptPianist
    @CorruptPianist2 жыл бұрын

    Ok, you had me at the calculator. Liked, commented, and subscribed!

  • @remen_emperor
    @remen_emperor2 жыл бұрын

    I need these as a peak into our ancestors' strange, sideways ingenuity. It's stuff like this - not just swords, battles, and politics - that I love from history

  • @SirOliverKnox
    @SirOliverKnox2 жыл бұрын

    thank you for this cool video

  • @cinderclawz
    @cinderclawz2 жыл бұрын

    I don't care about the content. I just listen to him talk and relax.

  • @ChrisStaecker

    @ChrisStaecker

    2 жыл бұрын

    You'll love this guy: kzread.info/dash/bejne/gKtqtrupj6jNd5M.html

  • @OrcinusDrake
    @OrcinusDrake2 жыл бұрын

    I actually like that lattice multiplication method, I've never seen it before lemme try it out

  • @kevinalterman9749
    @kevinalterman97492 жыл бұрын

    I wondered why he didn't start with multiples of 1 when figuring out which numbers to put on the bones until I realized multiplying anything by 1 wouldn't require a device

  • @codycoyote6912
    @codycoyote69122 жыл бұрын

    Very good, very interesting.

  • @deanciaciura3153
    @deanciaciura31532 жыл бұрын

    I'm related to John Napier and I think this is the first time I've learned anything about him besides from family

  • @dooogides9176
    @dooogides91762 жыл бұрын

    “Let me use my calculator” Dame I laugh so much I didn’t expect that 😂 thx bro nice touch

  • @BokBarber
    @BokBarberАй бұрын

    Me: I would like 50 free paint sticks please. Home Depot employee: Sure, no problem sir. (Frantically presses the Napier's Bones Alarm under the counter.)

  • @FortuneXGamer
    @FortuneXGamer3 жыл бұрын

    they showed me this in my class i liked this video good job!

  • @dr.kinderman5290
    @dr.kinderman52902 жыл бұрын

    This is really amazing, Napier had to have been a genius

  • @pipespb

    @pipespb

    2 жыл бұрын

    Не зря его именем (Neper) назван один из параметров звука.

  • @xalynkx
    @xalynkx2 жыл бұрын

    "Let me check it on my calculator"... hilarious 🤣🤣🤣

  • @ollie4860
    @ollie48602 жыл бұрын

    You have just changed my math grades…. Thank you

  • @philippezevenberg1332
    @philippezevenberg13322 жыл бұрын

    I love how his horrible handwriting is almost as bad as mine! You got yourself a sub. The calculator is cool ig.

  • @chandasubba3502
    @chandasubba35022 жыл бұрын

    You are amazing 💖 Thanks 👍

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