The History of Non-Euclidian Geometry - Squaring the Circle - Extra History - #3
Added 2018-06-08 17:30:02 +0000 UTCEuclidean geometry eventually found its way back into Europe, inspiring RenΓ© Descartes to create the Cartesian coordinate system for maps, and Isaac Newton to invent calculus. Both these tools helped humanity understand the world better.
Comments
"Archimedes' argument has the same basic design as other arguments applying the method of exhaustion "
Hao Sun
2018-07-02 20:08:57 +0000 UTCsquaring the circle referred to constructing with a compass and straight edge which was shown to be impossible (by Galois or someone?)ο»Ώ
Hao Sun
2018-07-02 20:07:14 +0000 UTCI don't think it's fair to say that Newton solved the squaring the circle, since the Greeks also knew how to get a square arbitrarily close to any area via rational approximations Also it should be noted that archimedes calculation of the area of a circle basically is a more rigorous version of Newtons ideas for calculus. see here: <a href="http://www.ams.org/publicoutreach/feature-column/fc-2012-02" rel="nofollow noopener" target="_blank">http://www.ams.org/publicoutreach/feature-column/fc-2012-02</a>ο»Ώ
Hao Sun
2018-07-02 20:06:29 +0000 UTCo_o No, maybe "Offer her the D, after there's a good relationship" Descartes. I've not heard or seen any record of Descartes being a D.
Bill Lemmond
2018-06-11 17:34:19 +0000 UTCHow in god's name did you laugh? Those dancing triangles will haunt me till the day I die!
Pope Urban II
2018-06-09 20:58:55 +0000 UTCNick's art and animations are *really* a great fit for the Extra Credits family of videos. Youtube education videos are always about mixing an entertaining personality and education, and I feel like this style sets the personality so well. I laughed out loud at the living triangle in motion. It's so crisp, but also super concise. Keep up the good work!
Snoopy20111
2018-06-09 18:13:06 +0000 UTCRenΓ© "Give her the D" Descartes
Quinlan Vuong
2018-06-09 17:56:07 +0000 UTCOh. Like you said, I thought an integral was just a Riemann sum to an infinite limit. So, I thought the to were phrases were interchangeable. Thanks for the clearing that up.
Christopher Pitterle
2018-06-09 17:49:14 +0000 UTCIt's not a Riemann sum, it's an integral. Riemann sums have finite number of rectangles. If it help you understand you can see the integral as the limit of a Reinmann sum as the number of rectangles grow to infinity. The Reimann sum itself will never be exactly equal to the area but its limit will.
Marc Langlois
2018-06-09 17:38:56 +0000 UTCGuys. it's not a math video. It's a history video. It's not teaching you math it's teaching you math's history. Stop saying that's the best math class you ever had. If you didn't know how to do an integral before watching it you still don't. Now, don't get me wrong it's a great video. You learn context, history, and a lot of useful things. But no math. And not because it fails but because it does not try. Extra History. It's great at what it does which is teaching history.
Marc Langlois
2018-06-09 09:36:28 +0000 UTCMath = what happens when you quantify the unquantifiable
Darren Loo
2018-06-09 05:59:47 +0000 UTCThe Riemann sum made to an infinite degree should approximately equal the area of the circle, not truly equal it. So, the equal sign should be an about equal sign (I am not sure of its official name). I just thought I should print this out.
Christopher Pitterle
2018-06-09 03:50:17 +0000 UTCwhat will the one off be ?
schuyler
2018-06-08 21:05:29 +0000 UTCNick has definitely been challenged by the unique requirements of this series and he worked really hard! This made him happy to hear :)
Extra History
2018-06-08 19:59:02 +0000 UTCWhen the topic was proposed, I did not know it would be one of the most engrossing subjects you all would cover, yet somehow, it is.
Sientir
2018-06-08 19:02:03 +0000 UTCI am almost unable to handle how much suspense this is leaving me in.
Richard Hardslab
2018-06-08 18:48:26 +0000 UTCIt was Wulpul!
Rossum
2018-06-08 18:15:00 +0000 UTCI have to say, Nick's illustrations and animation styles fit extremely well with this particular series. Geometry's always better to understand when you can see the visualization of the concept. This is already starting to become one of my favorite series you guys have ever done!
Jason Fox
2018-06-08 18:10:04 +0000 UTCNext week - GAUSS!
Joshua Evans-Lowell
2018-06-08 17:58:52 +0000 UTCWish I could have watched this before taking college Calculus. I managed, but it was still annoying how hard it was to relate it to anything I'd done before. I often joke now that learning Calc ruined most of my previous understanding of math.
Alejandro Hall
2018-06-08 17:47:37 +0000 UTCCertainly the most Entertaining Mathematics Class I've ever Attended. I'm Glad to Know it's not only me who Struggles with Understanding that Subject! [and yet at the same Time I am also Aware that Mathematics is the Gateway to Science]
Martin Verran
2018-06-08 17:40:41 +0000 UTC
