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.
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.
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.
@@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)
@@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.
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
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 ?
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.
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 TH-cam endeavors :)
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.
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.
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.
@@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
@@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.
@@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.
“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
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
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!
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.
This is an excellent combination of history, mathematics, story-telling, and visual presentation of information. If there was an Oscar 🎥🏆 for TH-cam videos, you would have won by a wide margin!
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.
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.
"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.
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.
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
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.
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.
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...
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.
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.
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
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.
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 😅
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"
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!
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.
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
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.
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.
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
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.
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.
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.
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
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.
@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).
@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.
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 TH-cam page...I hesitate to post it in the comments to avoid any spam bots.
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.
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.
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: th-cam.com/video/gMlf1ELvRzc/w-d-xo.html
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
I want to believe that Archimedes was really just making his own Sonic OC when the Roman soldier entered his house. Guy sure did have a obsession with blue circles 🔵💨
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🙆🏽♂️🙆🏽♂️.
I just realized how to square a circle! If you cut the circle into 100 pieces, make a rectangle. then measure half the heighth of the bumps on top and bottom to get heighth of the rectangle, then do L X W, you get both the exact area and circumference of the circle.
Squaring a circle is a problem of converting a circle to a square of the same area with only a straightedge and a compass in a finite number of steps. This exact problem has been proven not to have a solution.
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.
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.
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.
@CUJ-TH-cam Ooh that's interesting I haven't heard that before. I'll have to look into it.
@@bensyversenyeah please make an intuitive video about it for us 🙏
Great video, love this! A video about pythagoras and his gang would be interesting. Also, maybe complex numbers.
Please make a video on integration 😊😊
An obvious one is the correspondence between Pascal and Fermat that birthed probability theory. The suggestion about Descartes is also a good one.
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.
Fuckin Sicilians lol
interesting
Do we still have it?
Could you provide some links where can I read that in detail?
@@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.
The genius of Archimedes is mind boggling and his demise was a monumental loss to science.
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.
That and the destruction of the library of Alexandra.
Yeah this is something I’d like to research more for a possible future video
@@sphakamisozondi I was thinking of including that in my OC , but didn't want to digress too much.
@@bensyversen That would be an excellent choice.
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.
I feel like I recently saw a documentary on this...wasn't there a dragon that people jumped out of?
The Antikythera mechanism is actually a moon calendar...
@@burnstick1380 No it is a planetarium that accurately tracks all the known planets as well as the moon.
@@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)
@@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.
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
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 ?
It is also used in Hungarian, in the meaning of leave me alone.
The Mughals disturbed him apparently already back then.
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.
No💀💀
Well done! The time that you spend on the visuals really makes the concepts clear. Looking forward to seeing more!
Thanks Jonathan! And thank you for the help!
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
Do not disturb my circles. *
"Get off my spheres"
@@JO-ch3el"get off my balls"
@@JO-ch3el😂😂
"Dont touch my balls"
The quality of this video does not match your subscription or view numbers! So under rated!
Thank you so much for this! This is my first time making this kind of video but I’m looking forward to making more.
actually no, this was mid
ayo wtf just checked the sub count and was shocked
@@qwertyuiophmid compared to what?
@@bensyversenSubscribed! Please keep going. 👍
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 TH-cam endeavors :)
Thank you very much!
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.
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
Thank you, I appreciate that!
Don't confuse quality with popularity. Most people just want quick amusement. Mathematics is a niche passtime.
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.
Thank you Henrik! I’m looking forward to making more.
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.
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.
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.)
noooo euclid what did the tier list do to him 😢
@@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
@@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.
@@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.
“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
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
Thank you!
This is unironically one of the highest quality math videoes i have seen, and the visuals really help!
Thank you! Planning to make more
Ben! I'm so happy to see this wonderful video of yours getting the recognition it deserves! Keep it up, man!
Thank you Joel! You really helped me bring up the quality quite a bit with your feedback.
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!
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.
This is an excellent combination of history, mathematics, story-telling, and visual presentation of information. If there was an Oscar 🎥🏆 for TH-cam videos, you would have won by a wide margin!
Thank you so much!
I just love seeing great high-level content coming from small channels. Great work! Expecting more videos from you 😀
Thank you! I’m looking forward to making more
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
Thank you!
Fantastic video - well edited and well explained!
Thanks Elias!
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.
Or no sides at all.
Congrats.... A well done video. Good luck and success to you and your future content.
Thank you very much!
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.
"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.
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.
Those last words are something else “do not disturb my circles” absolute legend
man!! you deserve more, really good video
Thank you so much!
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
Thank you! Yes, math history is full of great stories and I will do my best to do them justice.
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.
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.
Thank you!
bro dropped the hardest maths video and thought we wouldn't notice
Circle and pie is something where we can see and feel infinity. This makes mathematics beautiful.
Amazing! Good narration and the video quality looks like it was made by a channel with millions of subs 👍👍👍
Thank you very much!
imagine if that roman didn't stab Archimedes
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...
This video is going to pop off and receive millions of views
Thank you I hope so!
Good video! This Ben Syversen guy seems smart.
What a coincidence, you have the same last name as me!
archimedes has the level of autism/adhd that I want as an aspiring mathematician
Very underrated video, keep going!
Thanks!
Bare in mind the two soldier's sent to capture Archimedes were explicitly told not to kill or even harm him.
Incredible animations! What are you using to make them? A video of this quality like this looks like it would take a long time
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.
Very impressive! Keep it up man
THank you!
This youtube channel is so underrated
Wonderful! Best video on the subject!
Thank you very much!
Wow!! Very interesting!!
Thank you!
Great video, you have gained a subscriber
Thank you!
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.
This channel is underrated
Thank you!
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
I wasn't thinking of that but I do love hip hop!
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.
When they overlap can you even say there's two points? Or do you have just one?
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 😅
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"
@@lorenzoputignano8829
Where can I read about this
You can have adjacent points if you have a non-continuous space.
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.
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!
Thanks! Working on it!
You could make a video on calculating the sun's angle at a given time and one's latitude.
Thank you!
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.
This is a masterpiece. More videos like this please.
Thank you! Hoping to do more
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
I strongly agree with this comment. I hope to tell more of those stories here in the future!
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.
Make more great videos like this one please
Thank you, I'm planning on it!
not even 3 k subs? damn man keep making videos like this and you'll be 300k soon. best of luck
Thank you!
Beautiful and educational video! I hope you grow in the future, seriously quality content.
Thank you very much!
Your video is so good that let me think your subscribers are 2M instead of 2k for a second there
Thank you!
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.
No shit bro he just explained that in the video
@@rogumann838 yep, the video cover is a clickbait, that's why I said that before watching it XD
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
this needs more views
Thank you!
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.
Excellent video, very interesting. Thank you 👍😊
Thank you
Keep uploading Ben, Love your Videos ❤
Thanks!
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.
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.
This is top tier quality. You should have millions of subs
Thank you! Someday I hope. I’m working on more as we speak.
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
Thank you very much!
I just looked at subs and assumed something about 500k not 40 you deserve so much more
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!
Great video.
Thank you!
Great video. I would like to ask you something. What exactly do you use for those drawings?
Thank you! I made the circle sectors in Inkscape and the animations in Keynote. Some of the background images come from Midjourney.
Thank you!
Kudos on this episode!
More please!
Thank you!
You got your 403th subscriber, still late but fine. Wish I could know about this channel earlier then now
Before Wednesday I had only been posting boring explanation videos, so you haven't missed much! Hoping to do plenty more.
Loved the video. Just one thought, you could let go of the background music during your explanation! Looking forward to more
Thank you! Yeah I was back and forth about the music in that section
Loved the video
Thank you!
He also proved the lever, the center of gravity, the law of buoyancy, worked with stereometry etc
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
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.
@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).
@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.
@bensyversen curious about any other way we could stay in contact.
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 TH-cam page...I hesitate to post it in the comments to avoid any spam bots.
Great video .. encouraged me to study for my maths test...😂😂
Thank you and good luck with the test!
😊 very informative 👏 and useful video and your visuals are fabulous 👌
Thank you!
Very cool Video, quite interesting! However, the "Calculus in the modern World" part with the stockfootage felt like a bit much xd
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.
Very good video, the opening music is a little too prominent but that’s about it.
Thank you
cool! very fascinating!
Thank you!
I, too, am a fan of circles. And I, too, dislike them being disturbed.
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.
The spectrum go crazy lol
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.
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: th-cam.com/video/gMlf1ELvRzc/w-d-xo.html
commenting cause this deserves more attention
Thanks!
Seems like you found a winning video format bro. =]
Thank you!
“Do not disturb my circles.” 😵💫
Subscribed 😊
Thank you!
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
This is great. I’d like to read more about Fermat. Do you have any favorite books about his work?
Honestly blew me away. Archimedes, can I marry your brain? 🤯😍😂
THANK YOU FOR YOUR CIRCLE
Alessi showed with ruler and compass:
pi = 4*sqr[1/phi] = 4*sqr[phi-1] = 4*sqr[2/(1+sqr[5])]
I want to believe that Archimedes was really just making his own Sonic OC when the Roman soldier entered his house. Guy sure did have a obsession with blue circles 🔵💨
You have 5k subs right now. Remember me when u hit a mil ❤
Haha thank you. Hoping to get there! Gotta finish my next video first…
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🙆🏽♂️🙆🏽♂️.
I love this. I think that Archimedes, like Newton, are actually still underrated to this day even with all that is said about them.
@@bensyversenTrue
I just realized how to square a circle! If you cut the circle into 100 pieces, make a rectangle. then measure half the heighth of the bumps on top and bottom to get heighth of the rectangle, then do L X W, you get both the exact area and circumference of the circle.
Well... the top half of the little bump is smaller than the bottom half, I think.
Squaring a circle is a problem of converting a circle to a square of the same area with only a straightedge and a compass in a finite number of steps. This exact problem has been proven not to have a solution.
If you get the top and bottom measurements right you have the exact solution!@@Kycilak
Great video, love this kind of content. Thank you!
Thanks!
I friggen love that guy
Awesome video and very informative. Thank you
Thanks!
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.
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.