How Archimedes Almost Broke Math with Circles

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  • Опубликовано: 23 дек 2024

Комментарии • 685

  • @bensyversen
    @bensyversen  Год назад +261

    Thanks for watching! I am looking forward to making more videos like this, so drop a comment if there's anything you'd like to see.

    • @bensyversen
      @bensyversen  Год назад +4

      @CUJ-RUclips Ooh that's interesting I haven't heard that before. I'll have to look into it.

    • @Grateful92
      @Grateful92 Год назад

      ​@@bensyversenyeah please make an intuitive video about it for us 🙏

    • @eldduva
      @eldduva Год назад +2

      Great video, love this! A video about pythagoras and his gang would be interesting. Also, maybe complex numbers.

    • @FrankoChakma
      @FrankoChakma Год назад +1

      Please make a video on integration 😊😊

    • @johnlarson505
      @johnlarson505 Год назад +4

      An obvious one is the correspondence between Pascal and Fermat that birthed probability theory. The suggestion about Descartes is also a good one.

  • @calebmcurby8580
    @calebmcurby8580 Год назад +1705

    Centuries later, Cicero visited Syracuse in search of Archimedes' tomb, which had been described having a giant cylinder and a sphere marking it. He finally discovered it hidden among the brambles, and had to tell the Syracusians with him the significance of it, because they didn't know who Archimedes was.

    • @placebojesus5652
      @placebojesus5652 Год назад

      Fuckin Sicilians lol

    • @lightlingzooma-69
      @lightlingzooma-69 Год назад +23

      interesting

    • @fatherpucci6111
      @fatherpucci6111 Год назад +20

      Do we still have it?

    • @mandala-YIN.YANG-
      @mandala-YIN.YANG- Год назад +9

      Could you provide some links where can I read that in detail?

    • @JenksAnro
      @JenksAnro Год назад +25

      ​@@mandala-YIN.YANG-either in Plutarch's life of Cicero, one of his Parallel Lives, or in Cicero's own Tusculan Disputations, he mentions finding it.

  • @billshiff2060
    @billshiff2060 Год назад +552

    General Marcellus was very upset at Archimedes death. He took only 2 things from Syracuse , 2 machines made by Archimedes which are said to accurately show the positions of all the planets. Until recently it was considered an exaggerated legend but with the discovery of the Antikythera mechanism we now know that it was certainly true.

    • @BalderOdinson
      @BalderOdinson Год назад +29

      I feel like I recently saw a documentary on this...wasn't there a dragon that people jumped out of?

    • @burnstick1380
      @burnstick1380 Год назад +3

      The Antikythera mechanism is actually a moon calendar...

    • @billshiff2060
      @billshiff2060 Год назад +19

      @@burnstick1380 No it is a planetarium that accurately tracks all the known planets as well as the moon.

    • @burnstick1380
      @burnstick1380 Год назад +8

      @@billshiff2060 whats your source?
      Mine is clickspring on youtube, he literally rebuild the antikythra (He's a watchmaker) and studied it and found that it is a lunar calender (well it does predict the moon phases too but not entire planets)

    • @billshiff2060
      @billshiff2060 Год назад

      @@burnstick1380 Dr Tony Freeth and company which is where clickspring gets HIS information.
      Michael Wright which is where Freeth got a lot of HIS information.
      Look up "A Model of the Cosmos in the ancient Greek Antikythera Mechanism"
      Click spring could not complete his model because Freeth came to a different conclusion about the display and it has to be re designed.

  • @zetaprnt262
    @zetaprnt262 Год назад +108

    His last words "μη μου τους κύκλους τάραττε" meaning "do not disturb my circles" are used to this day in Greece when we want to get rid of someone who's annoying us or disrupting our work

    • @TurtleTurtle-ii3lq
      @TurtleTurtle-ii3lq Год назад +1

      Interesting. I first thought it is in honour or to remember Aristoteles. But could it not rather be that the saying is older, and so the point of Aristotele's last words is this double meaning? Think it's not so easy to tell what was first ?

    • @schawo2
      @schawo2 6 месяцев назад +1

      It is also used in Hungarian, in the meaning of leave me alone.

    • @ParDiss-e4i
      @ParDiss-e4i 6 месяцев назад

      The Mughals disturbed him apparently already back then.

    • @goekhanbag
      @goekhanbag 6 месяцев назад

      Obviously his actual last words are unknown, and we have a text from 30 AD that mentions this legendary utterance in Latin.
      Thousands of years later, in the 19th century, it was translated into an archaizing form of Greek, what it might have been like.
      This legendary saying was not passed on over 2000 years. It was merely rediscovered and popularized in the 19th century.

    • @xristos.l4259
      @xristos.l4259 4 месяца назад

      No💀💀

  • @eeeee11235
    @eeeee11235 Год назад +191

    8:26 "do not disturn by circles." would be an awesome last words, like he defended something to his death, truly a great mathmatician and inventor

  • @VoightKampf
    @VoightKampf Год назад +976

    The genius of Archimedes is mind boggling and his demise was a monumental loss to science.

    • @bensyversen
      @bensyversen  Год назад +252

      He was absolutely extremely ahead of his time. I forget whether I said this in the video, but it’s worth noting that while his death was dramatic, he did live to the age of ~75.

    • @sphakamisozondi
      @sphakamisozondi Год назад +87

      That and the destruction of the library of Alexandra.

    • @bensyversen
      @bensyversen  Год назад +68

      Yeah this is something I’d like to research more for a possible future video

    • @VoightKampf
      @VoightKampf Год назад +9

      @@sphakamisozondi I was thinking of including that in my OC , but didn't want to digress too much.

    • @VoightKampf
      @VoightKampf Год назад +1

      @@bensyversen That would be an excellent choice.

  • @JonathanWhitmore
    @JonathanWhitmore Год назад +197

    Well done! The time that you spend on the visuals really makes the concepts clear. Looking forward to seeing more!

    • @bensyversen
      @bensyversen  Год назад +12

      Thanks Jonathan! And thank you for the help!

  • @coltonphillips7781
    @coltonphillips7781 Год назад +124

    Math usually scares me, it was always my worst subject. But as someone who is so passionate about astrophysics and other subjects that require math, this video was fun and comprehendable for me. You have a great talent, I wish you luck on your RUclips endeavors :)

    • @bensyversen
      @bensyversen  Год назад +10

      Thank you very much!

    • @fariesz6786
      @fariesz6786 Год назад +5

      maths is more often than not taught by people who, while passionate, can't for the life of them empathize with different mental approaches to things; and of course sometimes just by idiots to begin with.
      combine that with a society that vibes with the idea that maths should only ever be understood by nerds and it's easy to get scared by the subject.
      and yes, there are also people with dyscalculia, and they deserve help with their disability. however, the majority or people who are bad at maths are so bc of bad and discompassionate teaching methods, which is extremely sad.

  • @TurulHEMA
    @TurulHEMA Год назад +99

    The quality of this video does not match your subscription or view numbers! So under rated!

    • @bensyversen
      @bensyversen  Год назад +12

      Thank you so much for this! This is my first time making this kind of video but I’m looking forward to making more.

    • @qwertyuioph
      @qwertyuioph Год назад +1

      actually no, this was mid

    • @asdf14051
      @asdf14051 Год назад +3

      ayo wtf just checked the sub count and was shocked

    • @ananyomukherjeeixd281
      @ananyomukherjeeixd281 Год назад +1

      ​@@qwertyuiophmid compared to what?

    • @robertholtz
      @robertholtz Год назад +3

      @@bensyversenSubscribed! Please keep going. 👍

  • @henrikjørgensendk
    @henrikjørgensendk Год назад +110

    Great video, Ben! Love the concept of teaching math through the lens of history, dramatic music, and visuals. I'd like to see more videos like this.

    • @bensyversen
      @bensyversen  Год назад +5

      Thank you Henrik! I’m looking forward to making more.

  • @amichayr3418
    @amichayr3418 Год назад +108

    i just checked the view count, i thought this would be in the millions. This is very high quality work. both mathematically and storytelling ability

    • @bensyversen
      @bensyversen  Год назад +9

      Thank you, I appreciate that!

    • @brianvogt8125
      @brianvogt8125 Год назад +5

      Don't confuse quality with popularity. Most people just want quick amusement. Mathematics is a niche passtime.

  • @CreateSmarter
    @CreateSmarter Год назад +13

    Ben! I'm so happy to see this wonderful video of yours getting the recognition it deserves! Keep it up, man!

    • @bensyversen
      @bensyversen  Год назад +3

      Thank you Joel! You really helped me bring up the quality quite a bit with your feedback.

  • @stormmugger4719
    @stormmugger4719 Год назад +33

    This is unironically one of the highest quality math videoes i have seen, and the visuals really help!

    • @bensyversen
      @bensyversen  Год назад +1

      Thank you! Planning to make more

  • @William1w1
    @William1w1 Год назад +26

    We always called those proofs "epsilon delta stuff" in first-year calculus. We all dreaded it. I had no idea it wasn't invented until the nineteenth century! No wonder it stood out so much from what was otherwise a fun and relatively easy course.

    • @bensyversen
      @bensyversen  Год назад +11

      Yeah I really believe that giving people a sense of history with calculus (and math in general) would go a long way towards helping people appreciate it instead of thinking of it as something to dread.

  • @Grateful92
    @Grateful92 Год назад +8

    Man, where have you been all these years?
    The city needs you!
    Keep uploading to help me and my generation winning the mathzilla fight.
    Please don't ever let anyone delete these videos, these are life saviours

  • @se7964
    @se7964 Год назад +16

    The creativity, pacing and visual energy of this video were all incredibly excellent! However I did feel underwhelmed by the video’s denouement, wherein Cauchy’s epsilon solution turned out to be the same as Archimedes. Felt like there is a lot more to be explored in the concepts of infinity - hope to see more in future videos!

    • @bensyversen
      @bensyversen  Год назад +2

      Thank you, I appreciate this comment. I'll be the first to tell you that I've greatly simplified the history here in order to give a quick throughline. I did try to be careful to say that Cauchy's "strategy was remarkably similar" to exhaustion -- similar type of strategy, but not the same. I'd love to explore it further in another video.

  • @DisisSid001
    @DisisSid001 Год назад +28

    I just love seeing great high-level content coming from small channels. Great work! Expecting more videos from you 😀

    • @bensyversen
      @bensyversen  Год назад +2

      Thank you! I’m looking forward to making more

  • @hello-rq8kf
    @hello-rq8kf Год назад +3

    i failed calc 2, but as a classical musician i appreciate how you fit the background music to the time period. that chopin prelude is one of my favs

  • @eliasschock6571
    @eliasschock6571 Год назад +11

    Fantastic video - well edited and well explained!

  • @kitcutting
    @kitcutting Год назад +25

    my top 10 maths greats list:
    10) Alhazen (optics)
    9) Leibniz (binary code)
    8) Descartes (coordinates)
    7) Ramanujan (fractal proofs)
    6) Russell (math philosophy)
    5) Euclid (geometry)
    4) Newton (calculus)
    3) Euler (e^[iπ] + 1 = 0)
    2) Archimedes (π)
    1) Gauss (non-Euclidean geometry, FFTs, Normal curve, etc.)

    • @larevolution13
      @larevolution13 Год назад +2

      noooo euclid what did the tier list do to him 😢

    • @kitcutting
      @kitcutting Год назад +2

      @@larevolution13 i think all of these guys are very close to each other in terms of importance. I also realize now that there are names I may have forgotten to mention that have also contributed greatly to the expansion of mathematical knowledge.
      Bernoulli (fluid dynamics), Listing (knot theory), Hamilton (multidimensional complex numbers), Al-Khwarizmi (algebra), Riemann (integral calculus), and Galileo (astronomical measurements) are a few of the names that definitely should have muddied this list

    • @darthmath1071
      @darthmath1071 Год назад +2

      @@kitcutting Leibniz has done so much more than binary lol. Same for Euler, he probably didn't care that much about e^ipi+1 because he knew it was a special case.

    • @kitcutting
      @kitcutting Год назад

      @@darthmath1071 Obviously all of these mathematicians have done more than what I have put down. I am just listing examples of some of the fields of maths that they have contributed to. I have a tremendous level of respect for all of these guys but after careful deliberation, I would personally rate them as you see them.

    • @kitcutting
      @kitcutting Год назад

      “calculus: Leibniz vs Newton,” “did Archimedes really come up with pi and prove that it was transcendental,” “did Euler even come up with that equation or was it just an extrapolation of one of his proofs,” there are so many things up for debate here that I have no time to talk about lol. Just take the original comment for what it is

  • @astratothemoon262
    @astratothemoon262 Год назад +6

    man!! you deserve more, really good video

  • @hkumar7340
    @hkumar7340 Год назад +17

    This is an excellent combination of history, mathematics, story-telling, and visual presentation of information. If there was an Oscar 🎥🏆 for RUclips videos, you would have won by a wide margin!

  • @singularsquids5753
    @singularsquids5753 11 месяцев назад +2

    Those last words are something else “do not disturb my circles” absolute legend

  • @BXBZ88
    @BXBZ88 Год назад +5

    Congrats.... A well done video. Good luck and success to you and your future content.

  • @johnlarson505
    @johnlarson505 Год назад +4

    Nice video. This is your first big banger. The pressure is on to follow it up with another one. You're fortunate that math history is full of cool stories. I'll give you a shot. +1 sub

    • @bensyversen
      @bensyversen  Год назад +2

      Thank you! Yes, math history is full of great stories and I will do my best to do them justice.

  • @1TakoyakiStore
    @1TakoyakiStore Год назад +7

    I remember in Calc I that my professor talked about the implications of pi. It didn't mean a lack of sides or just 1 side, but an infinite number of sides.

  • @GIRGHGH
    @GIRGHGH Год назад +39

    I think my biggest disappointment in mathematics is that points cannot be adjacent to each other. Points either overlap, or they're separated by infinitely divisible space, and it drives me nuts.

    • @caffiend81
      @caffiend81 Год назад +3

      When they overlap can you even say there's two points? Or do you have just one?

    • @aogasd
      @aogasd Год назад +3

      If you wanted an adjacent point, you'd basically have to invent new math I guess. And the neighbour points would have to be undefinable / described by limits essentially. I'm not sure what use they'd have but ye that does conceptually sound annoying 😅

    • @lorenzoputignano8829
      @lorenzoputignano8829 Год назад

      There actually are particular topologies where points can be adjacent to eachother. You basically have to rethink the notion of distance, or even more fundamentally, of "separation"

    • @ronflypotato4242
      @ronflypotato4242 Год назад

      ​@@lorenzoputignano8829
      Where can I read about this

    • @Dellvmnyam
      @Dellvmnyam Год назад +1

      You can have adjacent points if you have a non-continuous space.

  • @TuorTheBlessedOfUlmo
    @TuorTheBlessedOfUlmo Год назад +4

    Bare in mind the two soldier's sent to capture Archimedes were explicitly told not to kill or even harm him.

  • @Aloysius_Roy
    @Aloysius_Roy Год назад +1

    bro dropped the hardest maths video and thought we wouldn't notice

  • @vishakjayakumar248
    @vishakjayakumar248 Год назад +1

    Circle and pie is something where we can see and feel infinity. This makes mathematics beautiful.

  • @guest3440
    @guest3440 Год назад +5

    Amazing! Good narration and the video quality looks like it was made by a channel with millions of subs 👍👍👍

  • @alidenizoguz6228
    @alidenizoguz6228 Год назад +2

    Very underrated video, keep going!

  • @zerksari
    @zerksari Год назад +1

    Wow.. Rarely I get the flyback feeling after 7 years of uni studies. You did that perfectly and reminded me why I did that to begin with randomly stumbling over your clip, solid thanks.

  • @aproc_
    @aproc_ Год назад +2

    Okay, this is silly, but I love how much his cadence seems to line up with the background music. It's like he's rapping Archimedes' praises. And he even got killed by a cop-a true OG

    • @bensyversen
      @bensyversen  Год назад +1

      I wasn't thinking of that but I do love hip hop!

  • @erictaylor5462
    @erictaylor5462 Год назад +5

    This is something that helped me to understand different sized infinities.
    Imagine you have a pair of totally fair dice. You throw each pair and you ger a number of pips between 2 and 12. However, you are more likely to get some numbers (like 6) than others (like 2 or 12). Because some numbers result from more combinations.
    If you threw the dice an infinite number of times you will get an infinite number of each result. However, the dice will follow the same statistic. You will have more 6's than you have 2's or 12's, even though you have an infinite number of both.
    This is possible became infinity is not a number.

    • @Benson_Bear
      @Benson_Bear Год назад +2

      "You will have more 6's than you have 2's or 12's, even though you have an infinite number of both." No you won't, you will have a countable infinity of each of them.

    • @bensyversen
      @bensyversen  Год назад +1

      I really appreciate both of these comments. That idea of “countable infinity” vs “uncountable infinity” is one that could he interesting for me to explore in a future video.

  • @fridmamedov270
    @fridmamedov270 9 месяцев назад +1

    That is because the people did not understand fully the idea of limit. The paradox like when the arrow is thrown, it should stay in equilibrium and should not move because it is stationary in very very small amout of time, and it should be stationary in another small time interval, and it keeps going. When you add up all the infinitesimally small pieces, you add up to get the whole thing. Seems Archimed had understood this and that is why he is GREAT.

  • @EyeLean5280
    @EyeLean5280 Год назад +2

    Wonderful! Best video on the subject!

  • @TektektektektekhaHAA
    @TektektektektekhaHAA 27 дней назад +1

    Archimedes is what happens to people when you take their phones away

  • @guitar0wnz
    @guitar0wnz Год назад +5

    Incredible animations! What are you using to make them? A video of this quality like this looks like it would take a long time

    • @bensyversen
      @bensyversen  Год назад +2

      Thank you! Believe it or not, I made most with Keynote, the Apple version of Powerpoint. There's one little animation in the intro that someone made for me using Manim, the math animation programming language. Yes, it was kind of time consuming! Hoping to get better at that with practice though.

    • @guitar0wnz
      @guitar0wnz Год назад +2

      Very impressive! Keep it up man

    • @bensyversen
      @bensyversen  Год назад

      THank you!

  • @karstensyversen
    @karstensyversen Год назад +4

    Good video! This Ben Syversen guy seems smart.

    • @bensyversen
      @bensyversen  Год назад +3

      What a coincidence, you have the same last name as me!

  • @user-hpdengs
    @user-hpdengs Год назад +1

    not even 3 k subs? damn man keep making videos like this and you'll be 300k soon. best of luck

  • @jeannyong8563
    @jeannyong8563 Год назад +3

    Wow!! Very interesting!!

  • @leonardschrock4987
    @leonardschrock4987 Год назад +1

    Question for Ben Syversen. Near the end you mention Archimedes said the volumn and area of a sphere is 2/3 of a closely enclosing cylinder. This reminded me of what I think is a similar fact. The volumn of the intersecting of two cylinders is 2/3 that of a closely enclosing cube. What would the surface area of this shape be? Thanks for interesting video.

    • @bensyversen
      @bensyversen  Год назад

      Hmm I'm not if I can picture what you're describing, or if I'd be the right person to answer your question to be honest. I think you'd be able to calculate it with multivariable calculus, but mine is quite rusty I'm afraid.

  • @kiku000
    @kiku000 10 месяцев назад +2

    archimedes has the level of autism/adhd that I want as an aspiring mathematician

  • @nostrum7278
    @nostrum7278 6 месяцев назад

    I was wholly disheartened to see that you do not have 50 more videos for me to binge watch. Marveling content and presentation, thank you for sharing this with us!

    • @bensyversen
      @bensyversen  6 месяцев назад

      Thanks! Working on it!

  • @Brugosovi
    @Brugosovi Год назад +3

    Great video, you have gained a subscriber

  • @akshatchobdar3038
    @akshatchobdar3038 Год назад +2

    This channel is underrated

  • @mrelizeus2261
    @mrelizeus2261 11 месяцев назад +1

    This youtube channel is so underrated

  • @second_sheep690
    @second_sheep690 Год назад +1

    Your video is so good that let me think your subscribers are 2M instead of 2k for a second there

  • @kujojotarostandoceanman2641
    @kujojotarostandoceanman2641 Год назад +2

    I hate how school really undersale how powerful Archimedes and Neton are, they just do a "ohh they invent this" and did not and can not eleborate on how truly amazing the details are

    • @bensyversen
      @bensyversen  Год назад

      I strongly agree with this comment. I hope to tell more of those stories here in the future!

    • @amazinga7794
      @amazinga7794 4 месяца назад

      I think we also kinda oversell them.
      Yes these people were great but they were standing on the shoulders of giants. Einstein would be nothing without newton, newton nothing without people like Kepler and so on. We would all be nothing without those who came before us. Science is ultimately a gigantic collaboration that captures what is great about being a human.

  • @AlemMemić
    @AlemMemić Год назад +1

    Great video. I would like to ask you something. What exactly do you use for those drawings?

    • @bensyversen
      @bensyversen  Год назад

      Thank you! I made the circle sectors in Inkscape and the animations in Keynote. Some of the background images come from Midjourney.

    • @bensyversen
      @bensyversen  Год назад

      Thank you!

  • @Lawh
    @Lawh Год назад +6

    On Finnish we have a common saying, "to mess up ones shapes." Shapes on this sense refers to plans, but I would imagine it's origin is in Archimedes.

  • @lietreumchanomai
    @lietreumchanomai 5 месяцев назад

    Keep uploading Ben, Love your Videos ❤

  • @mitaskeledzija6269
    @mitaskeledzija6269 Год назад +2

    Beautiful and educational video! I hope you grow in the future, seriously quality content.

  • @ianprado1488
    @ianprado1488 Год назад +1

    This video is going to pop off and receive millions of views

  • @DanBurgess-Milne
    @DanBurgess-Milne Год назад +2

    This is a masterpiece. More videos like this please.

  • @melodymonger
    @melodymonger Год назад +1

    Excellent video, very interesting. Thank you 👍😊

  • @paddleman3131
    @paddleman3131 11 месяцев назад +1

    made an equation to calculate pi to 10 decimal places using the idea that a circle is a polygon with infinite sides. what I found is that how you approach zero (degrees for each tringle in the polygon) is really important. I had to approach zero with 2Pi/x while 1/x didn't work.

  • @speedyfps4170
    @speedyfps4170 Год назад +1

    What program did you use to make the math animations?

    • @bensyversen
      @bensyversen  Год назад

      I used Inkscape to draw the circle sectors and I made the animations using Keynote

  • @veramae4098
    @veramae4098 Год назад +1

    Can you help? I've been looking for a source that lists all 6 of Archimedes simple engines, and the 32 complex engines.
    Internet has some kids stuff on planes, levers and circles, but that's it. I can't find anything on the Michigan Electronic Library either. (All state libraries computerized catalogs combined.)
    Help!

    • @bensyversen
      @bensyversen  Год назад

      Hello, I'm afraid that I don't have any helpful information for you on that. But if there are any viewers with this specific knowledge maybe they would chime in. Good luck in your search!

  • @Nothingx303
    @Nothingx303 Год назад +2

    😊 very informative 👏 and useful video and your visuals are fabulous 👌

  • @jimday666
    @jimday666 Год назад +2

    Kudos on this episode!
    More please!

  • @eth6706
    @eth6706 11 месяцев назад

    This is top tier quality. You should have millions of subs

    • @bensyversen
      @bensyversen  11 месяцев назад

      Thank you! Someday I hope. I’m working on more as we speak.

  • @nuwang2381
    @nuwang2381 Год назад +1

    Brings back a good memory from freshmen year of highschool where I was stumped over the circle equation lol I think we had a math masters sub in man even though I had that guy for a day I miss his enthusiasm for math lol really made me feel less crazy in that class lol

  • @Todeeee
    @Todeeee Год назад +5

    imagine if that roman didn't stab Archimedes

    • @Bluesruse
      @Bluesruse 8 месяцев назад +2

      Would not make that much of a difference.
      Archimedes made much more discoveries than we know anyways. Most of his discoveries were lost by the time the Church got their hands on his manuscripts and decided to wash them and write hymns to God on 'em instead.
      So, I'll forgive the soldier. The priest, however...

  • @ButWhatIfIAteYourAppl
    @ButWhatIfIAteYourAppl Год назад +6

    I just looked at subs and assumed something about 500k not 40 you deserve so much more

    • @bensyversen
      @bensyversen  Год назад

      Thank you very much! This is my first video of this type that I’ve made and I just posted it yesterday. I’m looking forward to making many more!

  • @basedboy
    @basedboy Год назад +1

    An area is cut into infinitely small pieces: a / inf = 0
    An individual piece is zero.
    All the small pieces together add up to the original area
    small piece + small piece = big piece
    So if a the small pieces are 0 it‘s like saying 0 + 0 + 0… = a
    That is why a / inf is not 0. the individual pieces approach zero.

  • @Grateful92
    @Grateful92 Год назад +1

    You got your 403th subscriber, still late but fine. Wish I could know about this channel earlier then now

    • @bensyversen
      @bensyversen  Год назад

      Before Wednesday I had only been posting boring explanation videos, so you haven't missed much! Hoping to do plenty more.

  • @erik19borgnia
    @erik19borgnia Год назад +1

    If you approximate a circle to a rectangle by doing small slices, having half the slices in one direction and the other half in the opposite one, you end up with a rectangle with height equal to the circle radius, and length equal to half the circunference. The area of that square would be
    r * (pi*d/2) = r * pi*r = pi * r^2
    And thats the area of a circle.

    • @rogumann838
      @rogumann838 Год назад

      No shit bro he just explained that in the video

    • @erik19borgnia
      @erik19borgnia Год назад

      @@rogumann838 yep, the video cover is a clickbait, that's why I said that before watching it XD

  • @Davide0033
    @Davide0033 Год назад +1

    damn, onlt 350 subs
    the quality of this video is actually impressive, i'm happy that at the least it's getting traction with nearly 19k views

  • @flavertex658
    @flavertex658 Год назад +1

    Great video, love this kind of content. Thank you!

  • @The-Cosmos
    @The-Cosmos Год назад +3

    You could make a video on calculating the sun's angle at a given time and one's latitude.

  • @J_GamerSP
    @J_GamerSP Год назад

    Very cool Video, quite interesting! However, the "Calculus in the modern World" part with the stockfootage felt like a bit much xd

  • @The-Cosmos
    @The-Cosmos Год назад +6

    Mate, i loved it. I guess this is somewhat like the book by steven strogatz: Infinite powers-the story of calculus. Have you read that? In any case, looking forward for more videos like this. 3b1b, numberphile, mathologer are some other greats. A well rested dog made jist one video in its lifetime and I loved that one, it was #Some2. Lastly, if you could prove that the ratios of sides of a right triangle remain the same as long as the angles are same regardless of the lengths of the sides. Many commit a fallacy in doing so, they unwittingly assume that it must be so in proving it. I guess you are understanding what I say, english after all is not my native tongue

    • @bensyversen
      @bensyversen  Год назад +2

      Thank you very much! I'm glad you enjoyed the video. Yes, this was definitely inspired by Infinite Powers. I'd like to tell more stories based on the ideas from that book. I think Strogatz has a great way of talking about this stuff and deserves to be shared with more people. I tried to point people to Infinite Powers in the video description but maybe next time I'll find a way to put something onscreen that doesn't interrupt the storytelling.
      I love the channels you mentioned! Also, Veritasium is a big inspiration.
      I'll look into that proof -- I've got some ideas for next videos, and I'm trying to find ideas from math that specifically have an element of history or personal drama involved that makes for an exciting story as well as being educational.

    • @The-Cosmos
      @The-Cosmos Год назад +2

      @bensyversen For one thing, you made my day, or rather I should say night! Only new creators bother to answer all comments but it is also understandable as they get well known the amount of comments gets grandeous. definitely veritasium must be a inspiration. Though he makes few strictly mathematical videos, the ones he makes are excellent (most thanks should be given to his math friend).

    • @The-Cosmos
      @The-Cosmos Год назад +2

      @bensyversen not any professional myself, but I would really like to recommend these science/Math/history books-
      Surely you are joking Mr feynman
      Homo sapiens by yuval noah Harare
      Higher Algebra by Barnard and Child
      Higher algebra by Hall and Knight
      I have all the books mentioned and I definitely liked them! Hall and Knight algebra is concise and most suitable for the first course of reading. The Barnard and child version is a big tome and suitable for those who have mastered the hall and knight. Again, Heartfelt thanks for the video and your reply.

    • @The-Cosmos
      @The-Cosmos Год назад

      @bensyversen curious about any other way we could stay in contact.

    • @bensyversen
      @bensyversen  Год назад

      Well I am definitely a new creator and I am very happy to see people writing in the comments!
      Thank you for those book recommendations. I read Surely You're Joking Mr. Feynman many years ago and was thinking of returning to it now that I'm starting to make videos like this. The others I'm not familiar with and I'll be excited to dig in.
      Are you on Twitter/X? I have an account there: @ben-syversen. Also, you can find my email in the about me section of my RUclips page...I hesitate to post it in the comments to avoid any spam bots.

  • @floatingfroggy
    @floatingfroggy Год назад +1

    5:40 I love the music here. It's entitled "Prelude in C" by Bach.
    It reminds me of God making the works with His own hands and fashioned the laws of math and physics.
    Throughout the millennia, scientists and mathematicians have worked hard to uncover God's hidden truths about logic, order, and reality. As they've come closer to understanding the laws that God made, their mathematical concepts have become more complex and intricate, like an ultra-detailed mosaic of tiles in a mosque, like the nature of God Himself. And it's lovely to see.

    • @bensyversen
      @bensyversen  Год назад +1

      I'm glad that you noticed the Bach excerpt. (Oddly, the recording I was using was pitched in B for some reason and I had to transpose it up a half step so it would connect properly to the Chopin piece that came after which was also in C). Yes, Newton and Bach both seemed to have an ineffable connection to some form of higher consciousness...many would say God. It felt right to pair them together in that moment in the video.

  • @cadence_wav2423
    @cadence_wav2423 Год назад +2

    Loved the video

  • @BadPixelArtist.
    @BadPixelArtist. Год назад +6

    this needs more views

  • @sumitdatta6421
    @sumitdatta6421 Год назад +1

    Loved the video. Just one thought, you could let go of the background music during your explanation! Looking forward to more

    • @bensyversen
      @bensyversen  Год назад

      Thank you! Yeah I was back and forth about the music in that section

  • @lorenzomizushal3980
    @lorenzomizushal3980 Год назад +2

    Literally the last thing this guy was quoted to have said was to a soldier, telling them not to disturb his circles, then the soldier killed him.

    • @McKae00
      @McKae00 Год назад

      The spectrum go crazy lol

  • @parkerstroh6586
    @parkerstroh6586 Год назад

    Imagine being so deep in thought that when your are violently awakened out of your waking dream the only sentence you can muster is “don’t disturb my circles” lmao

  • @ZyroZoro
    @ZyroZoro Год назад +2

    I, too, am a fan of circles. And I, too, dislike them being disturbed.

  • @ophikaktus1282
    @ophikaktus1282 Год назад +3

    Make more great videos like this one please

  • @cd8147
    @cd8147 Год назад +2

    cool! very fascinating!

  • @NegativeAccelerate
    @NegativeAccelerate Год назад +1

    Onw of my favourite things to do in high school was to prove where the formulae we were using came from. But I couldnt figure out the area of a circle formula.

  • @TG-to5nf
    @TG-to5nf Год назад +1

    Very good video, the opening music is a little too prominent but that’s about it.

  • @mutabazimichael8404
    @mutabazimichael8404 Год назад +2

    E.T.Bell ex president of American Mathematical association and author of "Mens of mathematics" ; says in his introduction to the chapter on Archimedes " that Archimedes genius is so great that from the number of math breakthrough that he anticipated ,if he rose up today (1965) and took an undergrad course in physics,he would understand Bohr, Einstein,Dirac better than they understand their own theories. "
    I mean damn that's some high praise more than 2 millenium after your death🙆🏽‍♂️🙆🏽‍♂️.

    • @bensyversen
      @bensyversen  Год назад +1

      I love this. I think that Archimedes, like Newton, are actually still underrated to this day even with all that is said about them.

    • @mutabazimichael8404
      @mutabazimichael8404 Год назад +1

      ​@@bensyversenTrue

  • @1Eagler
    @1Eagler Год назад +2

    Think about our civilization IF Archimedes' work was continued for 1800 years .

  • @connorkearley7789
    @connorkearley7789 8 месяцев назад

    Awesome video and very informative. Thank you

  • @anayshendey
    @anayshendey 9 месяцев назад

    Pioneers of trigonometry, pie and zero were Indians; concepts later moved towards Arabia-> Europe e.g., The history of the term “sine” in Trigonometry illustrates how we learn from each other. That trigonometric idea was well developed by Aryabhata, who called it jya-ardha, and sometimes shortened it to jya. The Arab mathematicians, using Aryabhata’s idea (400CE), called it “jiba,” which is phonetically close. But jiba is a meaningless sound in Arabic, but jaib, which has the same consonants, is a good Arabic word, and and since the Arabic script does not specify vowels, the later generation of Arab mathematicians used the term jaib, which means a bay or a cove. Then in 1150 when the Italian mathematician, Gherardo of Cremona, translated the word into Latin, he used the Latin word “sinus,” which means a bay or a cove in Latin. And it is from this - the Latin sinus - that the modern trigonometric terms “sine” is derived. In this one word we see the interconnection of three mathematical traditions - Indian, Arabic and European.

  • @cupatelj52
    @cupatelj52 Год назад +1

    Great video.

  • @FrankoChakma
    @FrankoChakma Год назад +2

    Subscribed 😊

  • @innosanto
    @innosanto Год назад +1

    He also proved the lever, the center of gravity, the law of buoyancy, worked with stereometry etc

  • @GPCTM
    @GPCTM 3 месяца назад

    1:00 I bet you have never thought why the area is side times side.

  • @aleattorium
    @aleattorium Год назад +1

    edit: This is a great video, this is just a comment about the "History after Archimedes" part.
    The chapter about history after Archimedes is such a wasted opportunity.
    There were several mathematicians during medieval times calculating pi by the Archimedes way, even up to 1500 Ludolph van Ceulen calculated 35 digits of pi and put it in his grave tombstone; In 1400 an Indian mathematician developed the so-called "Leibiniz formula" 250 years before Leibiniz was born. Btw that formula used infinity sums with exponentials. There's even more, I think it just brushed until Renaissance like no one went beyond Archimedes, it's just not true.

    • @bensyversen
      @bensyversen  Год назад

      Thank you for this comment. Yes, my history here is quite simplified for brevity's sake. I'd love to delve deeper into some of these stories in future videos.
      You may enjoy this video about the history of pi by Veritasium: ruclips.net/video/gMlf1ELvRzc/видео.html

  • @AndrewDangerously
    @AndrewDangerously Год назад +1

    Seems like you found a winning video format bro. =]

  • @SinghRishneet
    @SinghRishneet Год назад +2

    Great video .. encouraged me to study for my maths test...😂😂

    • @bensyversen
      @bensyversen  Год назад

      Thank you and good luck with the test!

  • @tomholroyd7519
    @tomholroyd7519 Год назад +2

    Guess it's worth pointing out that Fermat was the first to solve the paradox of the infinitesimal. Nowadays we use so-called "nilsquare" elements as infinitesimals. It's the correct theory. No paradoxes. Today it is used in LLMs under the name "automatic differentiation". So there's no paradox anymore, and it's all being using computationally constantly, billions and billions of times per second all over the world, one of the most used things ever

    • @bensyversen
      @bensyversen  Год назад +1

      This is great. I’d like to read more about Fermat. Do you have any favorite books about his work?

  • @Kanishk._7
    @Kanishk._7 9 месяцев назад

    You have 5k subs right now. Remember me when u hit a mil ❤

    • @bensyversen
      @bensyversen  9 месяцев назад

      Haha thank you. Hoping to get there! Gotta finish my next video first…

  • @VulpinetideCuteTimes0w0
    @VulpinetideCuteTimes0w0 Год назад

    General Marcellus: Capture this "Archimedes" fellow and bring him to me unharmed.
    Roman soldier: I brought his arm and his head.
    General Marcellus: 😠

  • @crazyman8472
    @crazyman8472 Год назад +1

    “Do not disturb my circles.” 😵‍💫