D C Your timeline ignores the use of the number 12960000 which is 60^4 by people several thousand years before the Greeks - your homework now could be to find out which culture was so mathematically savvy - and why. Reading Sitchin's books is the way I learned that. Good luck.
Just been shown your vid. In a year 9 math class. And found it online myself. And then I need to slow down the narrative voice. Cause I didn't catch that last uhhhh. I don't know. 8 MINUTES
This video is my childhood... Thinking about it now, I'll be going to university, majoring in math soon. This channel may actually be the one that will have the largest impact on my life as one of the things that gave me a love for mathematics. I guess I'll just have to see where this takes me. Thank you Vihart, Sincerely, a math enthusiast
@@isiahmattingly522 People enjoy different things. I for one am glad I grew up being fascinated with things like the way our universe works and the wonders we’ve managed to prove using logic and axioms. What sucks to me is that most people will never see how beautiful math can be (partially due to the way math is taught in elementary and high school which for some reason teaches memorization and a mechanical way of doing things at the cost of understanding)
Pythagoras was killed by Illuminati/Masons who accused him of not "respecting Greeks Gods" who asked eating of animal sacrifeces. Pythagoras ate only RAW VEGAN DIET and healed people for FREE through this diet! He gave knowledge for FREE in a Serbian way bcs he was a SERB. He never spoke a word of Greek. Now, people who killed him, continue to destroy his image and his deeds out of hate. They destroy everything what is good and they rule the world by satanism.
That is probably the best presentation of Pythagorean theorem (and history of) I have ever heard, and that saying a lot. Been engineering for 40 years. Again, kudos to you young lady, very well done, you will accomplish a great deal
"There's totally a ratio! You can make this with whole numbers!" "Is not!" "Is too!" "Is not!" "Is too!" "Fine! Have is your way! So there's a whole number ratio in simplest form where this square plus this square equals this square?" "Yea, that's the Pythagorean theorem! I made it." "Yea, but for this triangle, you dont even need the full theorem. Its easy to see that its the same area by cutting it into four triangles." "But I dont wanna divide the squares up into triangles! I want unit squares!" "So, you mean, kinda like this, where this square is divided into units and so is this one and they all fit perfectly into this one and vice versa but NOT like this. It almost works but when you divide the squares evenly to fill up the two equal other squares, you've got this odd one out. There's an odd number of squares to begin with, so you cant divide them evenly between the two squares." "*That's not even a right triangle!* What's your point‽" "Just so you know, an odd number like seven isn't gonna be it, without even trying. An odd number times itself gives an odd number of squares, so whatever this number is, it can't be seven. It has to be _even_." "Okay, so the hypotenuse is even, that's fine." "So what if I proved the leg is even too?" "Then it's not in simplest form. Any ratio where both are even, you divide by two until you can't anymore because one of them is odd, and then that ratio is the best. I thought we were talking about simplest form ratio." "We are. If there's a ratio in simplest form, at least one of the numbers is odd, and since the hypotenuse has to be literally divisible by two, so the leg has to be the odd one. But what if I proved the leg had to be even?" "You just proved it's not. It cant be both!" "UNLESS IT DOESN'T EXIST! What you forget, Pythagoras, is that if this is a square, then the two sides have to be the same, and if it's divisible right down the center, so too is it divisible the other way! And the number of squares on this side, which is the number of squares in just one leg, is an even number! And for a number of squares to be even, what does that mean, Pythagoras, oh my brother?" "If leg squared is even, then it can't be even, because it's already odd..." "UNLESS IT DOESN'T EXIST!" "But if they're both even, you can divide by two and start again, but this still has to be even, which means that _this_ still has to be even, which means you can divide it by two and start again, but this still has to be even, and everything has to be even forever and you'll never find the perfect ratio and *aww, beans!*"
Painting Kitteh i used to be like you when i watched these videos for the first time, but now when i come back and watch them again after having learnt all this in school. Suddenly they make sense and give a deeper meaning to all the stupid shit i had to remember, it's amazing really!
With the triangle and squares thing: You have the numbers in the squares that is squared. Work out what the 2 squared numbers are. Add them together and that is the bigger square number. Now all you gotta do is find the square root
Ancient Greek "algebra" was a really interesting topic, (the term and concept of algebra as we know it didn't really exist until Al-Khwarizmi in the ninth century) with solutions to what we'd today call equations using compass and straightedge constructions. It's incredible what they did without arithmetic.
The thing about Pythagoras thinking of numbers as separate beings reminded me that my for my mom each number always had its own personality, gender, and character traits. I really should turn on a tape recorder and have her describe them all to me. I'm not sure how high her number people go but I'm pretty sure it's into the teens and maybe higher.
it makes you wonder, if the Greeks of Pythagoras' time couldn't even conceptualize our modern understanding of numbers then what will future perceptions of numbers and mathematics entail? Will their concept of math be so sophisticated that we could not even begin to understand it because for our whole lives we have been conditioned to believe math, as we understand it, is the perfect most absolute expression of quantitative reasoning?? Its crazy to think that in a thousand years people will look back and be like "wow, people in 2016 had no concept for the number asdkfjaslfkajhfk" the same way we think its crazy Pythagoras had no concept of 0 as a number.
Let's get real here for a second. Zero is not a number, it does not behave like one. (Three number-puns achievement unlocked) Pythagoras did not miss a number, he missed an instrument. We surely miss a lot that will be there in the future, but my opinion is that it's safe to say we got the basics alright.
+Batrax Well I think zero is a number. We use it as a digit on its own to show that an amount has no value but also use it other ways. Zero isn't the lack of a number. If you have 1.7 then that seven is showing the amount of that unit in the same way that 1.75 shows this. With that logic if you had 1.0 It shows the amount of that unit however could continue as 1.05. However you define a number, zero is used in the same way as other numbers. Half of zero maybe zero but then again if you double one you get one, but one is still classed as a number.
Craft It Note that the only "zero" greeks lacked is the one with nothing else after or before. They had fractions (for rationals) and they could write 100 alright (there is no real reason to use the zero there), they could write 203 by simply not stating the tens, in short they could use nearly anything for which a zero is needed in maths. And by the way, Pythagoras and his contemporary were fucking brilliant, on the same class of the mathematicians of today. I doubt they lacked the concept of "no number", they simply lacked the structure of mathematical relations connected to that concept.
+Sam Lee Maybe you eat the beans and fart the souls of the deceased? Or, no, you fart out your own soul which is then replaced by the souls of the deceased which you just consumed? That's kind of scary. I see why he was scared of beans now.
One tiny problem: I always heard that Pythagoras wasn't afraid of beans he worshiped them. "He would rather die than trample on something holy" makes more sense to me than "he would rather be killed by an angry mob than by beans." It also seems to be more consistent with what we see from people throughout history. Also I wanted you to talk about him believing a dog was his reincarnated friend because of the twinkle in its eye.
Thank you, Ms Hart. I could listen to you all day, even though you talk so fast that you lose me at about the two minute mark. It isn't what you say, it's how you say it. You have style, character and a great sense of humour. And I'm sure you will already have deduced from the missing Oxford comma and the addition of a 'u' that I'm English. Oh, and I very much like your drawings. I'll be back.
+nick jack Well he definitely didn't use Arabic numerals. Roman numerals are the closest things to Greek numerals that her viewers are likely to understand.
+Thuperman well they used letters, alpha beta gamma delta and so on, but it wasn't a=1, b=2,c=3, it was A=1,B=2, but then after a little while it changed so that they could have bigger numbers. There's a numberphile video if you like that kind of thing.
Hi Vi, awesome stuff, going to use it in my work as a Math teacher. Small gripe with this video: The ratios you use from 4:12 to 4:27 are inverted, 1.4 is 14:10 not 10:14, etc. Ah, well. Nobody seems to have noticed (sorry if it was in older comments, I didn't go back more than a month). Still AWESOME video, keep them coming!
This is one of my favourite videos. It combines history and maths and REALLY AWESOME THINKERS who had super-smart ideas long before the framework of what we know as mathematics even existed. I mean wut.
We watched this in my GEM class and we loved it!! We watch your videos all the time and I’m just like “I’ve watched this one!” Or “let’s watch this one next!” It just makes me happy and makes school a little better :)
To me, the Pythagorean Theorem was an easily formula to easily figure out the sides of a right triangle, easily (irrationality no included).Pythagoras's concept of a relation of numbers with nothing in between, is a great deal more comprehensible than having icky numbers fill up that area. Also, to know that his original formula was talking of (unit) squares somehow makes things more comprehensible. Everything was golden in Pythagoras's perfect little world, until root 2 reared its ugly head. It confused me that the legs had to both be even, yet the rules of how a square works magically filled my head ( after watching it 3 times) and blew my mind. Go irrationality! I liked to see that everything can and was (at some point) broken down to a simpler, nicer way. That helps me take the simple things I know for certain and translate it to anything that maybe challenging. It makes math enjoyable.
In his Present Lifetime, Pythagoras is perfectly Okay with Beans. In fact, he eats beans, pretty much, for Breakfast, Lunch and Dinner, as they are a good source of Protein, they Are Gluten-Free and they are Vegan (not to mention, Cheap and nutritious) So, yeah, I guess you could say that is one relationship that Pythagoras has repaired.
Hey! This is really interesting especially how Phytagoras saw numbers and I like the way you explain with doodling. What i didnt understand was the connection between the odd and even in a^2+b^2=c^2. It was inspiring to understand how all this is connected to to the simple connections between numbers and how by drawing it makes it a lot easier to understand.The amount of history and math was well balanced!
I'm not even a math person (GASP!) and I flipping loved every second of that synaptic fireworks display. Thanks for that! You should sell those notebooks... they're works of art! I totally want one!
You say you suck at math but you take an idiot's false OPINION over number theory that was handed down by men much more intelligent than yourself? This video is literally full of lies.
One of the only videos that have impressed me so much with the amount of time and effort spent on it, that I paused the video around halfway through to make sure I subscribed before losing the channel. Keep crafting!
there's fantastic content: maths, history, storytelling, wit... bravo! But way, way too fast for my old brain! Is there a 20min version? Yes, I know that I could keep pausing and rewinding, but...
sounds like a difficult language to learn ! I think the subject of my sentence was "subject" so it depends on the gender of the word subject, which I don't know. What I'm more interested in is whether most italians give a toss.
Ray Kent (You asked for it so don't complain!) "Subject" cannot be something to which you refer as "bravo", because bravo means "skillful", or "good at doing something", or "I agree with what you just said/did" as a cheer. So you would say "Skillful!" to an opera singer, but not "skillful!" to a subject. English is definitely less complex than Italian, but Spanish and French are basically the same, so you can maybe guess from that. About the giving a toss, picture if someone put an extra s at the end of singular nouns or after every verb. "They does sound sincere." It's not like anyone would cry or shout at you, it's just mildly grating to hear.
Batrax I'm native anglophone living in france. My elderly neighbour uses the masculine plural for chickens despite all of them being female! I think that language follows usage.
I finally understood what she was talking about when the guy was explaining to Pythagorus that the ratio for the right triangle was irrational. Didn't get it until now but I briefly understand :3
The hypotenuse of the triangle, if you were to multiply it by some integer so as to make it become an integer, which is impossible since it's irrational. I think it's a bit like asking if infinity is odd or even!
Greeks thought that beans contained the spirit of the dead so were forbidden to eat them. They weren't allowed to touch white cockatrices. They believed that left was bad (sorry left handed ones). They said to help people load but not to unload. They wouldn't allow themselves to etc...
This is fascinating! I love how you explain how he explored math when there was really no serious math at his time period. My question is: How did he use his cultural influences to prosper in math? Did it have to do with peer pressure?
Pythagoras and his cult was heavily influenced by the poems of Orpheus (of which, there is no surviving manuscript) Pythagoras' hatred of beans and lentils goes back further to the allegorical stories of the Orphics (who scholars claim never existed as a religious community, but rather prevailed through literary tradition)
Advances in math. Addition. Negatives and zero invented to make subtraction meaningful every time, not just when the result yielded a positive integer. Square root of 2 was needed to make all Pythagorean Theorem results have values even when irrational. A length that cannot be represented by any ratio. We'd like every equation to be solvable and another strange square root without an answer appeared in some. No square can yield a negative, and yet we'd like math to be complete... the square root of negative one filled the gap. Now quaternions with i^2, j^2 and k^2 all -1, and i*j*k=-1. There are four parameters in every quaternion. a + b*i +c*j +d*k. These numbers are not commutative, ij = -ji.
@@78anurag i dropped out for a lot of reasons but mostly because i was working full time to support myself when i was 16-17 and didn't see a purpose in continuing school, things are pretty bad at the moment but that's standard, i hope you're doing well though kind internet stranger
There's a huge difference between how we think of numbers and how the ancient Greeks did. For one, they didn't have a concept of infinity, as illustrated by Zeno's paradox and the fact that Archimedes, despite his obsession, never quite completed the task of creating calculus and resolving pi. He came extremely close, but didn't quite cross the threshold, so to speak. For another, they had no zero - the concept of nothingness as a thing unto itself basically originated in central Asia, and the idea of nothingness as a quantity came about in medieval India. Third, they didn't conceptualize numbers in the same way we do. Like Vi said, they didn't think of them as having an existence unto themselves, but as an attribute - as an amount of things. That might be why they freaked out about irrational numbers - how can such an amount even exist? Fourth, and probably most important overall, it isn't the numbers themselves they were interested in - they were interested in geometry, and how different shapes relate to each other.
I never really thought of the theorem visually. The fact that squares are made off of the legs to see if the two sides equal the hypotenuse's square blew my mind!
I love this video to death, but Pythagoras was greek, so at 0:09 he would have claimed to be the son of Hermes, not Mercury. I'm sorry I'm nitpicking but its all the fun that you get to have with a classics major.
Beans were anciently used in casting votes by swallowing them, the white beans for affirmative and the black ones negative. When Pythagoras said to his disciples, "Abstain from beans," he had no reference to them as an article of diet, for he ate them himself. What he did mean, and what his immediate followers already understood, was that they should abstain from the intrigues of politics as being antagonistic to a philosopher's pursuits.
+Isabelle Henson Well,making puns are my FAVa. If you can spit straight fire,urad. I've Pinto to the deepest part of hell to bring you these shite... I mean puns......save me
It's basically a proof of contradiction. We know that both of the legs are odd. We then assume thr sqr root of 2 is irrational, meaning it can be written as a ration in simplest form. We then prove that it can never be written in simplet form since ine of the legs neeeds to be even, which contradicts the fact that both legs are odd.
I'm supposed to be doing Algebra 2 right now, I'm not because Algebra 2 bores me. Yet I find myself watching a video about math. I don't know how, but Vi Hart makes math actually cool.
I mean she was a busy, self-indulgent little snot that went on and on trying to impress (but not) everyone while disrupting the professor with prattle disrupting valuable class time with our professor. I hope that is clear enough, good people of the WWW.
Douglas Moseley uh... what? a busy, self-indulgent little snot trying to impress people? how do you know that? All I see before me is a girl who has taken interest in the history of pythagoras and his theorem, and she wanted to share what she knew/thought through a humorous and entertaining video.
TenshiRockin My comment was only to speak about a girl I knew in MY classroom and how this girl, gifted or not, reminded me of her. There were/are many brilliant people with social oddities. What is your deal? Why are you running to the defend this little snot?
Vi Harts video was really enjoyable because she made so many entertaining drawings to keep you interested. The video was really informational and funny. A piece of information that intrigued me was that Pythagoras didn't think about numbers as a line but as each being their own separate being. What I don't understand is why Pythagoras was so obsessed with finding the perfect proportion and why it mattered so much to him. The thing that was quite inspiring was how long ago Pythagoras lived and how abstractly he was thinking for his time.
