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The History of Non-Euclidian Geometry - Squaring the Circle - Extra History - #3
🕑 Added 2018-06-08 17:30:02 +0000 UTC Euclidean geometry eventually found its way back into Europe, inspiring René 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
Hao Sun
"Archimedes' argument has the same basic design as other arguments applying the method of exhaustion "
Hao Sun
squaring the circle referred to constructing with a compass and straight edge which was shown to be impossible (by Galois or someone?)
Hao Sun
I 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>
Bill Lemmond
o_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.
Pope Urban II
How in god's name did you laugh? Those dancing triangles will haunt me till the day I die!
Snoopy20111
Nick'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!
Quinlan Vuong
René "Give her the D" Descartes
Christopher Pitterle
Oh. 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.
Marc Langlois
It'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
Guys. 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.
Darren Loo
Math = what happens when you quantify the unquantifiable
Christopher Pitterle
The 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.
schuyler
what will the one off be ?
Extra History
Nick has definitely been challenged by the unique requirements of this series and he worked really hard! This made him happy to hear :)
Sientir
When 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.
Richard Hardslab
I am almost unable to handle how much suspense this is leaving me in.
Rossum
It was Wulpul!
Jason Fox
I 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!
Joshua Evans-Lowell
Next week - GAUSS!
Alejandro Hall
Wish 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.
Martin Verran
Certainly 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]
