The History of Non-Euclidean Geometry - Sacred Geometry - Part 1 - Extra History

Подписаться 3,6 млн

Просмотров 1,7 млн

50% 1

📜 Before we get into non-Euclidean geometry, we have to know: what even is geometry? What's up with the Pythagorean math cult? Who was Euclid, for that matter? And what the heck is the 5th Postulate?
* Watch Extra History ad-free & get 1-week early access on NEBULA go.nebula.tv/extrahistory
* Suggest & Vote on our next episodes, get exclusive content & 24-hour early access on PATREON bit.ly/EHPatreon
* Show off your fandom with MERCH from our store! extracredits.store/
* Interested in sponsoring an episode?* Email us: extracredits@standard.tv
TWITTER: bit.ly/ECTweet I FACEBOOK: bit.ly/ECFBPage
INSTAGRAM: bit.ly/ECisonInstagram I TIKTOK: bit.ly/ECtiktokz
BLUESKY: bit.ly/ECBlueSky I TWITCH: bit.ly/ECtwitch
GAMING: / @extracredits
Miss an episode in our Non-Euclidean Geometry Series?
Part 1 - • The History of Non-Euc...
Part 2 - • The History of Non-Euc...
Part 3 - • The History of Non-Euc...
Part 4 - • The History of Non-Euc...
Part 5 - • The History of Non-Euc...
Series Wrap-up & Recommended Reading / Lies Episode - • History of Non-Euclide...
♪ "Postulate S" by Sean & Dean Kiner - • ♫ "Postulate 5" by Sea...
Thanks for the high-quality conversations & for following our community guidelines here: bit.ly/ECFansRNice
Artist: Nick DeWitt I Writer: James Portnow I Voice: Daniel Floyd I Editor: Carrie Floyd I ♪ Music by Demetori: bit.ly/1EQA5N7 I
#ExtraHistory #WorldHistory #History

Опубликовано:

25 май 2018

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 1,8 тыс.

@extrahistory 6 лет назад

Hi everyone! Sorry for how often we repeated prop 5, but understanding how it's both weirdly simple and yet super complex is important for the rest of the series. There will be math in the rest of these episodes but not as heavy handedly done ; ) -JP

@rngwrldngnr 6 лет назад

darthmunck I think that's required to gain an understanding if you aren't already familiar with Euclidean geometry (and the history is interesting).

@refreshdaemon 6 лет назад

Everyone, vote for Prop 5! Parallel lines must be maintained!

@ahmedmuawia2447 6 лет назад

Extra History.Is a great example of Fun Education also I am a huge I like your way of telling stories of the past wich encourge me to look for more detail by myself.

@Yes-hd5ku 6 лет назад

I'm confused; what exact complexity do you imply?

@andrew-paulclements1502 6 лет назад

Yeah, it seems kinda common knowledge now-a-days. I find it interest that apparently that was a supper big thing.

@njord3582 6 лет назад

I knew people who liked math were cultists

@qallincha 6 лет назад

Look at Pythagoreanism and how it tragically ended

@kevinami5585 6 лет назад

Ya mean all Asians are cultists ?

@pyrocancer8581 6 лет назад

pecu alex You know it's a mystery cult when the cultists themselves don't know they're cultists.

@robertwalpole360 6 лет назад

This is what happens when you herd the nerds.

@Anergyne 6 лет назад

Mathemagicians. *nods*

@letstrithisagain7156 5 лет назад

Non-euclidean geometry explained! *H.P Lovecraft sweats nervously*

@thechickenman3713 4 года назад

Overly sarcastic productions?

@ericoliver1603 4 года назад

Basically why I clicked on this video lol

@TORchic1 4 года назад

I feel like even this simplified explanation series will be too much for Lovecraft.

@masterzoroark6664 4 года назад

Yeah

@samirseedat1274 4 года назад

Just what i was thinking.

@jackmyers8687 3 года назад

"What are you watching?" "A video on Non- Euclidean geometry." "Ha ha, no really, what are you watching."

@yellowstarproductions6743 Год назад

"A actual video on geometry"

@hypeflexington7081 2 месяца назад

Just say porn. You'll get less weird looks and questioning glances XD

@geoffreyaughtman6917 2 месяца назад

and here i am drinking while searching Euclidean and here i am 3 years later.

@evelyngravatt3198 6 лет назад

Me: "I don't care about geometry" *Extra History uploads a video about it* Me: "I care about geometry"

@sk8rdman 4 года назад

Me: "I don't care about history" Sees video on Euclidean Geometry Me: "I care about history"

@Gospel-xm7vd 4 года назад

How RU-vid manages to suddenly catch my attention, it's basically mind control at this point.

@odysseish5382 6 лет назад

I don't know what Euclid's power level is, but if you tell me his height and what angle he stands at I'm pretty sure I can figure it out.

@dasaggropop1244 6 лет назад

its over 9000

@vicentetemes5793 6 лет назад

That would be 9*10^3, you uneducated nincompoop.

@Jh5kRadio 6 лет назад

He's dead, so he's probably standing at 0 degrees.

@extrams0 6 лет назад

That would be > 9*10^3, you heathen

@void2258 6 лет назад

Where your units?????

@rexrowan6411 6 лет назад

Was it Walpole? *Top 10 questions Science still can’t answer*

@walpol3 6 лет назад

Animootions Man mayyyybe

@Tyleya 6 лет назад

That was hilarious!!

@rexrowan6411 6 лет назад

Ah ha! Are u the one who spread the plague from Egypt to the Sassinid and Byzantine empires?

@walpol3 6 лет назад

Animootions Man I was having a bad day okay?

@Marylandbrony 6 лет назад

Yes it was.

@Beriorn 6 лет назад

"Hey Vsauce, Eucilid here. Where is your proof for the Fifth Postulate?"

@kyle-silver 6 лет назад

Hey Vsauce, Lobachevsky here. What if we assume the fifth postulate... is false [Moon Men by Jake Chudnow plays]

@puddingcupnation1496 6 лет назад

But why do we have 5 postulates?

@Ggdivhjkjl 6 лет назад

Shhh, don't tell the teacher whose homework he copied.

@ffggddss 5 лет назад

Hey, Euclid. It's been proven that the 5th Postulate doesn't follow logically from the others. This has been done by constructing a geometry in which those lines can fail to ever meet (Lobachevsky, Bolyai, et al); and another in which they always meet, even when the sum of interior angles = 180º (Gauss, Riemann, et al). In both cases, all the other postulates hold true, so it follows that P5 can't be a logical consequence of those others. These results were both achieved in the 19th century AD. Finally, in the early 20th century, it was established that all of these systems of geometry are exemplified in our physical universe, in different circumstances, due to gravity (Einstein, Schwazschild, Friedmann, et seq, AD 1915-). Despite all this, what we now call "Euclidean geometry," in which P5 holds, is still of central importance, because it holds to all but imperceptibly high precision, over small enough regions, which are 99.999% of all the cases we have to deal with; and mathematically speaking, it holds true completely, in non-Euclidean geometry, in the limit of small, or "tangent spaces." Fred

@215alessio 5 лет назад

at infinity

@croissantboy1623 4 года назад

>Power Level: ??? >"His work had an nearly indescribable effect on history-" yeah id say hes pretty up there

@DragoniteSpam 6 лет назад

Extra Math when? Screw it, can we just have Extra Credits become the next Crash Course?

@blodsubhistory1334 6 лет назад

Yes.

@taylorhancock5834 6 лет назад

Yes! But they are like the anti-CrashCourse, going over a random and slightly obscure topic in a fairly long form way. Probably two of the best educational series when put in tandem.

@sizanogreen9900 6 лет назад

I'm all for extra credits making more videos like this.

@enlightedjedi 6 лет назад

It is still history :)! But why be in the way of a good Crash Course :)! No worry my friend. EC always have a plan :)!

@midshipman8654 6 лет назад

Taylor Hancock I actually prefer these to crash course most of the time since extra history doesn’t try to produce a moral whenever possible.

@dimitrijejovanovic5939 6 лет назад

Heads up guys, this is the last EH series with Dan Floyd narrating. Let's enjoy it to the fullest extent

@jopersoniusker4268 6 лет назад

Dimitrije Jovanovic The fact that they had to make his last series based around math realy makes that difficult🙃 (But in all seriousness, I'll miss you Dan)

@dimitrijejovanovic5939 6 лет назад

JoGeronimusKer of ebblepub This actually flared up my interest in math again... After 6 years when stupid teachers killed it. I went on to listen to numerous lectures about history of mathematics, even though I am way over my head in the preparations for my finals in Pathology. Well, let's say that it was a nice throwback in time when I was interested in math

@bananalord8575 6 лет назад

what why

@jopersoniusker4268 6 лет назад

Dimitrije Jovanovic I have some bad experiences with mathematics, so I find a bit less interesting. Good thing you like it tho

@dimitrijejovanovic5939 6 лет назад

JoGeronimusKer of ebblepub I actually hated math for the most of there six years, mainly because teachers were incompetent in teaching us the matter. But my pure love and thirst for knowledge pulled me back into research

@espio87 6 лет назад

EH: Basically, Euclidean Geometry is all the Geometry you studied in school. Next week we'll talk about non-Euclidean Geometry. Me: (Nervously) "This is going to be a bumpy ride..."

@moahammad1mohammad 5 лет назад

Eucilid thought knowing Geometry would make you understand the universe. *Quantum Physics has entered the chat* Quantum Physics: This ain't it chief.

@malcolmthompson6514 3 года назад

**cries in SAM theory**

@lacanm1554 6 лет назад

I’m gonna miss dan, but best of luck to his future.

@Draco-nf7ey 6 лет назад

Valak Dunban At least he will still do stuff in Extra Play! Loved his Dark Souls playthroughs

@megathai 6 лет назад

Which Dan

@BlueZeroThree 6 лет назад

The Dan narrating

@lonathan5653 6 лет назад

We all will miss him

@ironsfamily6 6 лет назад

megathai Dan Prime. The ultimate the Dan. The Dan of all Dans. The Dan who started it all... Dan Floyd.

@Restryouis 6 лет назад

I expected more Lovecraft.

@faizalf119 5 лет назад

Lovecraft is a good writer but a horrible mathematician. He simply read the book about Euclidean and mistaking non euclidean geometry as alien or impossible geometry

@Egoblivion 5 лет назад

Faizal F Lol, you think he really mistook it as literally 'alien' and 'impossible?'

@Egoblivion 5 лет назад

Restryouis Yes, and his allusions to the horror of incorrect geometry.

@adoredpariah 6 лет назад

I can't rate the Extra History series highly enough, you guys do seriously amazing and inspiring work. You really know how to bring life and charm to any topic, and really know how to pick topics for that matter. I can't imagine how many teachers and students teaching/learning experience you have made easier/more accessible, bravo and kudos to all involved.

@pearsetraynor9142 6 лет назад

SIMPLE GEOMETRY!

@lucianodebenedictis6014 6 лет назад

Rip scattur

@pchris 6 лет назад

Pearse Traynor thank goodness that ability is dead

@hartwellcraig7909 6 лет назад

I agreee

@squrtinata 6 лет назад

machine gun Hanzo is worse.

@greyfox4838 6 лет назад

-uploads a video about non-euclidean geometry -talks about euclidean geometry

@JohnJohnson-vq7ze 6 лет назад

I can't tell if you're joking, but just in case you aren't, you really can't talk about the significance of non-euclidean geometry without first talking about euclidean geometry. I mean, it's in the name; the whole big deal about non-euclidean geometry is that it differs that which was, for over a millennium, considered the only geometry.

@RickyCruzMedia 6 лет назад

The series will probably end up being about Non-Euclidean geometry, since this is the first of the set.

@FantasyAddict95 6 лет назад

well, I imagine you would have to have a basic understanding of Euclid in order to understand how noneuclidians built and changed from his stuff. I know nothing of this topic, but I'm sure this is relevant as an introduction.

@NimhLabs 6 лет назад

No mention of the paradox of how can somebody lay dead--but still yet dreaming of strange Aeons where death itself has died.

@scottkrametbauer90 6 лет назад

Exactly, you must fist learn of the beast that is the fifth, before you can learn about all the mathematicians who went insane trying to kill the beast and failed.

@Raz.C 5 лет назад

6:36 "The last, lingering question would be answered." It's my understanding that "The final question" cannot be answered yet, because "There is as yet insufficient data for a meaningful answer." *Aasimov reference

@SMiki55 4 года назад

@ethanekback7670 6 лет назад

I about screamed when I saw this! My favorite channel combining my two favorite subjects is a dream come true! I am so excited!!

@dimitriosvelessiotis6808 6 лет назад

As a Greek and a scientist, I have to thank you, for this episode, and I am truly looming forward for the rest episodes of this subject. I ought to note something more: You always have high standards in your clips, both in presentation and research. Today, was one of your top quality clips, and I have seen the whole Extra History series.

@RivkahSong 2 года назад

I know this was written 3 years ago, but the typo resulting in you "looming forward" to more math rather than "looking forward" is hilarious to me. I just really appreciate the suggestion that scientists express excitement by looming menacingly in the corner like the math they've dedicated their lives to does for the rest of us.

@ardinhelme687 6 лет назад

*Is a Math Major* *Took a class on non-Euclidian geometry last semester* *gets popcorn*

@jhonshephard921 6 лет назад

so comments? Data Scientist here BTW.

@JM-us3fr 6 лет назад

I was a math major as well. I'm looking forward to seeing how this series pans out.

@ZlatkoTheGod 6 лет назад

So far I've only heard of the horrors of non-Euclidian geometry. So far I'm having trouble with regular analytic geometry and calc so I think I'm just going to stay as far away from that as I possibly can but I'm still curious to see how this pans out.

@ardinhelme687 6 лет назад

The Red Baron that's a shame, when presented correctly, non-Euclidian geometry can be incredibly fascinating, and I have no doubt Extra Credits will do it justice. It was actually one of my favorite classes last semester (but then again Calc III was right beside in classes I enjoyed, so maybe take that recommendation with a grain of salt) but more then anything I think it's important to remember that we don't live in a Euclidean world, and as such, being able to understand the failings of Euclid's geometry is something I that I think is often undervalued.

@ZlatkoTheGod 6 лет назад

Oh I have no doubt in my mind that it is fascinating, the thing is just that I am a computer science student but the way my school does things we do 60% math and about 40% comp-sci. Calculus is also pretty much the only mathematical subject that interests me (the rest like linear algebra, logic, financial math etc. seems mostly like busy work because it's so easy, everything except for analytic geometry ironically) so don't worry I will take your recommendation. The problem is just that I want to focus more on computer science and calc but the rest doesn't seem like something I would apply too much in the field later on. Heck I might not even use calc but I'm still gonna study that cause it's fun and I wanna be able to come up to a lady in a bar and say "Hey baby are you an exponential function, cause I wanna be your tangent line." or something equally retarded like "The sum of all natural numbers converges to -1/12" ... OK maybe not that retarded but you get the point.

@harleyrussell3018 6 лет назад

I love this video! I've watched it three times for a reason unknown even to myself. It flows so well... It rekindles the hope I've had since childhood of seeing a philosophy reconcile things seen and unseen. And the narrator performed perfectly! Looking foreward to the exciting conclusion

@KampfKeks04 6 лет назад

Very cool idea, focusing on mathematical history. And I like how you're doing it thus far, bringing it down to an elementary level without making dumbing it down. Keep up the good work!

@typhoonzebra 6 лет назад

5:13 That's one fine comb

@Healermain15 6 лет назад

He got it from a Stormtrooper combing the desert.

@Seadalgo 6 лет назад

sander heutink We ain't found shit

@dead_warrior_wae 5 лет назад

I wish I had a comb like that boiii

@TetraTerezi 6 лет назад

im going through therapy for ptsd and i feel like i lack a lot of education due to a rough childhood and then mental illness as a result of a poor home life. So im using Khan academy to get my math skills sorted out because i feel like maybe i just want taught very well, and this here helps me feel really strongly that we could do alot better to teach math to children, This real life story of Euclid who understood it and wrote it down would get so many kids into math! im 27 and this is the FIRST time i've been told anything about who Pythagoras or Euclid were. Thank you so much and i can't wait for my kid to watch all your vids ^.^

@bassemghorab 5 лет назад

Best wishes to you and your child =)

@JimKalaitzis 6 лет назад

In my second year in high school, we had "Euclid's geometry". I remember when our teacher told us in the 1st lesson that the book we're holding was written some years BC, and the only additions are the math problems that we will get as homework.

@antoniojimenezpastor304 6 лет назад

My most sincere congratulations choosing this topic and presenting the greek geometry in this episode. If you do (and I have no doubt of it) a nice job with the other episodes in this serie, the result will be brilliant. If this is the last Extra History serie narrated by Dan, then it is a great topic to say goodbye (to his voice). Congratulations again.

@8bitmagic 6 лет назад

GOD DAMN When I thought extra history couldn't get better

@jacoder23 6 лет назад

One last Extra History with Dan. :( Edit: More details here: www.twitlonger.com/show/n_1sqhrnq

@BlueZeroThree 6 лет назад

Wait what?

@mr.cup6yearsago211 6 лет назад

UK Ball Dan is leaving extra credits, but he said you'll still be hearing him in EH for a while.

@BlueZeroThree 6 лет назад

Who will be replacing him?

@jacoder23 6 лет назад

He announced his departure from the Extra Credits channel in the last video about Choice Paralysis.

@jacoder23 6 лет назад

@UK Ball A guy named Matt.

@EFYletsplays 6 лет назад

I'm going to miss you Dan. Your voice guiding me through so much of history and game design has been a great part of my day. I wish you luck!

@AbsentQuack 5 лет назад

Just found this channel and have been steadily watching every single video. This is awesome stuff man, thank you for the content.

@yaldabaoth2 6 лет назад

Will he ever journey to R'lyeh to find his answer?

@abacussssss 6 лет назад

I just so happen to have a non-Euclidean R’lyeh right here: goo.gl/DWNWoY

@palumbolord7480 6 лет назад

perhaps he would have better luck consulting the Yith

@Gunbladefire 6 лет назад

I'll just pet my cat in Ulthar and wait to find out.

@datfisheboi6519 6 лет назад

Nice! Combining my favorite subject and my least favorite subject!

@assassinxex 6 лет назад

Least we have the answer to the question which bastard made maths

@enlightedjedi 6 лет назад

@assassinxex He wore it like an armor :)!

@only2ndplace 6 лет назад

Yeah, I hate history too. Just kidding ;)

@mathephilia 6 лет назад

Maybe you guys should read Lockhart's Lament, it's a short essay on why math is the worst taught subject in the world. Math is more beautiful and artistic than most art... Any video game is basically a symphony written in the language of mathematics. But if we taught music like we taught math, most people would say things like "I'll never use music in my life, why are we learning this ? Music is useless. I've never been a music person.", or "now we know the bastard who invented music" which admittedly sounds absurd. www.maa.org/external_archive/devlin/LockhartsLament.pdf

@gatgranas4615 6 лет назад

I've been bing watching every EH episodes for the last 3 weeks I can't wait a week for another epiaode 😩😩

@davinweber658 6 лет назад

Great episode! I look forward to the rest of this series.

@Fuzato15 6 лет назад

You missed a great crossover opportunity with numberphile.

@feynstein1004 6 лет назад

Or 3Blue1Brown

@JohnnyElRed 6 лет назад

... It's just a triangle. I mean, you have explained the 5th postulate perfectly, but... I really don't understand the problem. Because the only weirdness I see on it, is the complication in the definition of the postulate. Not the postulate itself. So, can someone explain me what is the problem here?

@extrahistory 6 лет назад

It's not really a problem, but my understanding is that non-Euclidean geometry exists when the 5th postulate *isn't* true. So it's more that we felt the need to explain the basic premise that Euclidean geometry exists on, before moving on to why non-Euclidean geometry is a big deal. I haven't seen all the episodes or the scripts yet but I am pretty sure this is the direction it's moving in --Belinda

@band-o-lear 6 лет назад

My understanding is that Euclidian Geometry only works on a 2 dimensional plane. The 5th postulate requires a perfectly flat plane to always be true, as soon as you start with a non flat plane, then it isn't always true. As an example, look at the lines of longitude on the earth (these ones run from the North Pole to the South Pole). At the equator, they intersect the equator at 90 degrees. Yet they also intersect at the poles.

@paulzagieboylo7315 6 лет назад

This is roughly correct. One of the not-so-obvious results of the 5th postulate is equivalent to saying "the universe is flat". So when you try to do geometry in a universe that isn't flat (like, say, the surface of a sphere), you end up having to replace the 5th postulate with something else that expresses the non-flatness of your new universe. MrCervelo's example of longitude lines is a good one; spherical geometry is equivalent to saying "if a straight line crosses two other straight lines, the other two straight lines always eventually intersect each other on both sides of the first line." Which is clearly not what Euclid's original says.

@brettd2308 6 лет назад

Yep, it's only a triangle if you're working on a 2D plane. Once you add the 3rd dimension, the 5th postulate isn't always true, and that's what leads to the field of non-Euclidean geometry. Even though Euclid's own contemporaries and other early mathematicians were troubled by the 5th postulate, it was so fundamental to early geometry study that mathematicians spent 2000 years trying to prove it to be true before discovering elliptic and hyperbolic geometry.

@Tina-Brune 6 лет назад

I think the other response are just giving you the solution when you asked for what the problem was. The problem with the fifth postulate is that it it doesn't say something as fundamental as "two of the same things are the same", but something that felt like a result that should come from the other 4 postulate. So a lot of very smart people tried to demonstrate the 5th postulate from the other 4 to no success. The reason it 'feels weird' is because the other postulates are definitions about the objects geometry works with within the space while the fifth is aconvoluted way of describing the space the objects are in. Of course, Euclid and co didn't know that, they just noticed it was out of place. And the DID NOT like that.

@JohnDlugosz 5 лет назад

Strange, I've always seen the 5th stated in a different way: Given a line L and a point P that is not on L, there is exactly one line passing through P that is parallel to L. But, I know there are many equivalent postulates; e.g. the interior angles of a triangle will always add up to the same constant.

@NoActuallyGo-KCUF-Yourself 4 года назад

Those two statements are conclusions that follow from the 5th postulate. They are equally true, but not logically equivalent.

@jriver226 6 лет назад

Euclidian geometry and all of this was my favorite class in college. Well done and I look forward to the rest

@MarkSultanaX2 6 лет назад

The most republished book, after the holy book of a rligion which spans roughly a seventh of the world's population, is a book on geometry. Mind Blown!

@cutecommie 5 лет назад

Too bad they didn't tell us the 3rd most republished book.

@ThomCote88 6 лет назад

This is the Extra History series I never knew I wanted so much. I'd love to see a full-fledged Extra Math series at some point!

@TheCreepypro 6 лет назад

when this video was announced I felt like you guys just told me there was new continent that hadn't been discovered till now and you were going to take us there can't imagine non-Euclidean geometry but now it is here and to say I am giddy with excitement would be an understatement can't wait to see the rest of this series

@sombal1999 6 лет назад

Its cool that you decide to make an episode like this, yesterday my professor mentioned this in my electromagnetism class.

@ethan4896 6 лет назад

Dan I don't wanna see you go, but I'm excited for what you'll do next

@katowo6521 6 лет назад

You: Algebra Me, an intellectual: Big Boy Maths

@btdpro752 6 лет назад

o O 0 if you speak the truth you should know that algebra is the base of math.

@Melecie 6 лет назад

Btd Pro i’d rather say modern math since basic calculation (idk what it’s called lol) is more basic than algebra

@martinhorvath4117 5 лет назад

In math everything matters, EH History guy even said in the video too, twice actually!

@silvershet 5 лет назад

@@btdpro752 Abstract Algebra is the basis of mathematics.

@tghuffine6277 5 лет назад

@@silvershet ...Yes, like the study of Quaternions / Octonions.

@phothar93 6 лет назад

I'm so excited for this series! This is my entire mathematical education.

@thepockyx 6 лет назад

love it! very excited for the remainder of this series :D

@spehizle 6 лет назад

Honestly, after all this time, I'm envisioning an Extra Credits animated movie following Walpole as a timetraveling huckster and con-artist, and a ragtag team of cross-millennial heroes that are trying to track him down. Cheng I Sao, Hannibal Barca, Tokugawa Ieyasu, Theodora, John Snow, Jigonsaseh, and Federico da Montefeltro all together running down this financial weasel. Along the way, Walpole puts together a crew of his own: Bohemond and Baldwin from the first crusade, John the Cappadocian, Wilhelm II, and Otto Von Bismark (who eventually betrays Walpole and joins our heroes).

@mobiuscoreindustries 5 лет назад

John blunt, *get the investors*

@salmon1426 4 года назад

make this real. now.

@AbdulGoodLooks 4 года назад

@@salmon1426 Yes!

@hast3110 6 лет назад

I see Pythagoras got my autobiography. Good.

@themightyleek 6 лет назад

Guys, thank you so much for doing a history on something mathematical. It is really rare that I ever see anything like this out there

@ValleyoftheLeaf 6 лет назад

AHHHH!!! This EH covers my exact interests! More so than the Sengoku Jidai, I am sooo interested in Math and the history of it. Honestly I never realized that the ideas of Pythagoras were philiosophical/spiritual, I never knew that Pythagoras was anything more than a scholar of logic and mathematics. To come across this the day after it realized is torture! Now I have to wait to know more!

@beautifulnut5176 6 лет назад

ALL HAIL THE SHAPES WORSHIP THE SHAPES

@braytongoodall4357 6 лет назад

maths major here: really hope you list all 5 axioms next video, or better yet, mention that euclid's contribution was axiomatic thinking; one could bring up ZFC set theory and category theory in passing. Just bc it was hinted at but I think you could trust the EC audience with heavier information!

@tedthisius4778 5 лет назад

Ran across this my accident this morning. Reminded my of a class I took in Projective Geometry many years ago. It was taught by one of my favorite Math instructors. I don't know that it served any practical purpose other than mind games but I enjoyed it. It had several postulates such as all lines meet (those we think of as parallel met in the ideal point). All planes intersect (those we think of as being parallel intersect in the ideal line) etc. I loved it maybe because I got three credits and an "A" in the course

@irvingreis5905 6 лет назад

Guys, it's incredible how you can make a subject that was sooooooooooooooooooooo boring to me at school in something really interesting. You guys are just the best!

@PersianMapper 6 лет назад

Best video discussing geometry since Paul barbado's "Geometry Now"

@leovinois4707 6 лет назад

it's so beautifully introduced! geometry is powerful and beautiful! even somehow magic!

@ericshw171 6 лет назад

this is one of the absolute best videos. Ancient math is really inspiring.

@vladimirlagos2688 6 лет назад

As an English major with a love for history I have a natural aversion to numbers, and yet, I now find myself intrigued and engaged on a math conundrum thanks to this video... well played Extra Credits!

@blueroman5538 6 лет назад

This episode is awesome! I'm probably going to learn more here than in math. So yayyy!

@btdpro752 6 лет назад

blueroman55 not really

@btdpro752 6 лет назад

blueroman55 it is impossible to learn more here than in math in school unless you haven't made it to high school or took regular classes in middle school.

@welp2388 6 лет назад

blueroman55 You are learning the history of Math not really the formulas or proceedings for equations.

@blueroman5538 6 лет назад

Yeah I know. I was just trying to be funny

@btdpro752 6 лет назад

Welp this is here I am talking about math as a passion and education not it's history. I find both interesting.

@masterzoroark6664 4 года назад

Euclid Teachers: ok, it's math time Scp fandom: *SPC 173 HAS BROKEN OUT OF THE CONTAINMENT!!*

@lazarjovanovic4388 4 года назад

@@sansirow4595 u stop

@a.h.tvideomapping4293 3 года назад

Sansirow I’m going to make you look at a picture of 096

@ratzeputz6729 5 лет назад

I used your videos on non-euclidean history as inspiration for a presentation at university. I also shamelessly used exclusively pictures from your videos as material. With reference of course. Needless to say: 1.0 was the result. Thanks a lot guys, you are awesome.

@juancarlosalpajora3405 4 месяца назад

Can you explain it on your own words

@feynstein1004 6 лет назад

I am so hyped for this :)

@manuc.260 6 лет назад

I won't lie, having study this subject with some sort of depth, I was a bit scared at first even with the trust I have on extra history. But this episode was impecable. The one thing I often don't see stressed enough is that Euclid did not create classical geometry but made apparently the best synthesis of it, as Euclid's Elements are the only full elements we still have (of what seems to be many composed around that time). This is indeed due to the beautiful and detailed logical evolution of the text. Lewis Carroll, who was also a mathematician, made a beautiful chart showing the logical steps on the first book of Euclid that I couldn't recommend enough. Even without being as familiar with geometry nowadays as then, I still think that the elements, at least the beginning of the first book (and a little bit of the arithmetic books as well), are a wonderful read, and being so self containing, can be tackled with more or less effort by anyone (as long as you have a pencil, a straight edge, a compass and patience).

@manuc.260 6 лет назад

I would have however mention a few of the alternative formulations of the postulate, even if I can imagine they'll appear in later videos, to make sure that people less familiar with it can keep one they understand in mind while going through the series (like, the sum of the internal angles of a triangle is 180º).

@plifal7799 6 лет назад

*scribbles notes* Yes... Yes! History is helping me with Maths. AT LAST!

@btdpro752 6 лет назад

PlifalTV try Khan academy. Taking notes there is much "faster" and it is more organized

@plifal7799 6 лет назад

Haha, it's just part of the joke - I know Khan Academy but I haven't had a Maths class in over a year.

@RoarkeSuibhne 5 лет назад

I love that James has a teacup... spot on, my good man, spot on!

@benjaminmiddaugh2729 6 лет назад

I'm looking forward to this. My great uncle literally finished writing the book on modern Euclidean Geometry, so I have a passing familiarity with some of the difficulty involved in rigorously working these things out. (For those interested, the book is "Euclidean Geometry and its Subgeometries" published by Birkhäuser. I'm biased, of course, but it's an amazing book. I haven't worked through it yet, but my copy is waiting, tempting me...)

@ufa-tw5hy 6 лет назад

What a coincidence, my class visited the grave of Bolyai, a founder of non-euclidian math yesterday.

@emlmm88 6 лет назад

He'll yes! Are we also doing the development of projective, differential, and algebraic geometry? Because their histories are all fascinating. No doubt Poincare will make an appearance.

@familyz9519 6 лет назад

excited for next episode!

@nakata123 6 лет назад

Math yay!!! Thank you guys, my wife and I have been watching your videos, and she hated history, now she's hooked because of you, thank you really!! Please give us some more!!

@Nirakolov 6 лет назад

If people are interested - there's a non-Euclidian Roguelike on Steam called HyperRogue, it's pretty good.

@PoolNoodleGundam 6 лет назад

Would Euclid be Euclid? Or would he be Safe? Keter? Thaumiel?

@HaloInverse 6 лет назад

Euclid himself is Safe/Neutralized, but the contents of Euclid's Elements are Keter/Thaumiel, depending on circumstance - containment cannot be guaranteed due to the inevitability of their independent reinvention. That said, it's unclear whether their non-anomalous appearance is genuine, or the result of an embedded countermeme.

@yonka-cola8792 5 лет назад

Keter squad

@SlowGreyWeasel 5 лет назад

Good work, good quality and easy to understand, i like it

@chrispitterle8831 6 лет назад

How did you just make geometry feel like an epic adventure? It is awesome!

@prycenewberg3976 6 лет назад

-The 5th postulate was broken by Walpole! Search your feelings. You know it to be true. -NOOO!!! THAT'S IMPOSSIBLE!!! i am sorry... couldn't help it

@CrimsonDragon15 6 лет назад

Seems I finally know who to thank for the hell I went through during geometry class!

@alivarfan1009 6 лет назад

Another great video, THANK YOU and please do more videos on history and history of science.

@tedothon7792 6 лет назад

Great video extra credits I love your history videos

@StarSage66 6 лет назад

Math! My old nemesis, we meet again...

@mathephilia 6 лет назад

Your "nemesis" ? On Extra Credits of all places ? Did you know that every video game is literally a symphony written in the language of mathematics ? ^^" Mario can only jump because we imitate the physics of the real world (parabolas, movement/speed/accel, etc) ! You should read the first three pages of Lockhart's Lament, maybe you'll learn to understand your nemesis a bit better, and become curious as to how that nemesis rolls. :)

@winsonwijaya5592 5 лет назад

to extend this idea even more, our entire being as biological creature depends on isomerism of chemistry of life in order to function as well (i.e. same chemical formula of a molecule that have the same pattern of bonds but different geometric positioning of atom could effect how the molecule react with others, which play a significant role in today's drug development) , even geometry plays a very big role in our life on a molecular level

@henryhache5509 5 лет назад

If only the line you were traveling life on crossed another line at 90 degrees, and math crossed the same line at 90 degrees, you and math would never had met again :)

@Goultek 5 лет назад

how mas the meeting?

@rpsgm 5 лет назад

Winson Wijaya n

@braden5831 6 лет назад

Literally the only RU-vid channel to make math fun

@Ilkeyrion 6 лет назад

I think Numberphile does an okay job at that, but you have to have some kind of inherent curiosity about math for it to be fun. I get really curious about mathematical concepts and ideas, but am terrible at it if you look at my math grades

@joshuadarrow 6 лет назад

Extra Math

@ethan6287 6 лет назад

Vihart dude.

@rxy228 6 лет назад

you should take a look at 3Blue1Brown if you want fun math

@rxy228 6 лет назад

3Blue1Brown is IMO the best "explain maths" channel on youtube. mathologer is pretty good as well

@fakechemicals 6 лет назад

Great topic guys! The history of science and knowledge is one too often overlooked I think.

@mwmwmwmwmmdw 6 лет назад

postulate 5 is important with double barrel shotguns since both barrels are slightly pointed toward each other thus if both barrels are fired at once the shot from each shell will intersect each other at some distance. its called barrel regulation in the shooting community but is basically postulate 5's principles at work

@jbklyn 6 лет назад

Congrats you made math interesting to me.

@jbrisby 5 лет назад

"Geometry wasn't the only thing that fascinated him." I'd be worried if it was.

@dannydavi-toe7412 3 года назад

lol

@derchesten 6 лет назад

well. that was taught to me in Basic Mathematics in my university, paraphrasing the 5th postulate is "two coplanar lines that are non-parallel will always meet at some point". that was explained if I remember correctly by newton in his use of vectors, by tracing the rays of said vectors one can resolve the equations for the rays and find the exact point of collision. widely used in games as well.

@Albeit_Jordan 5 лет назад

This is a great little series!

@horsenuggets1018 4 года назад

Pythagoras: the universe is a perfect mechanism Quantum mechanics: helo

@BSOE3058 6 лет назад

Hey there Cthulhu down there in your sunken city...

@merrittanimation7721 6 лет назад

Scream of Shadow Stop confusing obtuse and acute

@DaniEIdiomas 6 лет назад

Fantastic piece of history. Thank you!

@mattkuhn6634 6 лет назад

Oh man, I hope you guys get to Gödel at some point! It's a little bit tangential, but his Incompleteness Theorems were one of the first times that math really blew up my mind.