Area of a Circle, the BEST COMPLETE PROOF by Archimedes

Area of a Circle, the BEST COMPLETE PROOF by Archimedes | Tricky Parts of Calculus, Part 3

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Күн бұрын

Пікірлер: 25

@blvckbytes7329 Жыл бұрын

"I'm interested in how we'd establish the area of a circle if we'd had to do it for the first time.", YESSS! That's how *all* proofs should be handled! Maths evolved over time, by people building on top of their predecessors' work. It's great if we can mix and match on the timeline, like how Newton figured out a better way to approximate PI than Archimedes. But I think that it's just plainly wrong and misleading to proof something of a lower level with information gained at a higher level. Each proof should link to all past dependencies and not leave *any* gaps. This is the way to go, your video was such a pleasure to watch. I'm going to try to fully wrap my mind around this approach! :)

@fabriciosebastianrioschave7566 2 жыл бұрын

Wonderful! Simple yet clear and complete explanation, looking foward to watch more of your videos.

@derendohoda3891 2 жыл бұрын

These four videos were fantastic. I know you try to take the simplest path but I think it's understated the level of mathematical sophistication that's required to get this up and running today. Leaning even a little on properties of real numbers is already a scary thought (least upper/lower bounds). Episode 5...? Since we already brought up Eudoxus, maybe the Eudoxus Real Numbers? Hahaha. Thanks a lot sorry this isn't teaming with views.

@DanielRubin1 2 жыл бұрын

Glad you like the math videos! As of now I have posted 8 videos in the Tricky Parts of Calculus series. More math content to come!

@michaelblock9716 3 жыл бұрын

Thoroughly enjoyed your video. I look forward to watching more of your explanations!

@bensyversen Жыл бұрын

I just discovered this video and your channel. This is the best explanation that I've seen on KZbin of Archimedes' proof. Thank you! (I recently made a video about Archimedes that used this proof as a jumping off point for a historical overview of infinitesimals, but I conspicuously avoided a detailed explanation of the intricacies of the proof itself...)

@brandonbennett3082 2 жыл бұрын

"That's the kind of wrong statement only a philosopher could make"-- ouch! you hurt me... great video though :-)

@garfieldnate 9 ай бұрын

At 13:48 I don't understand how you're using DG as the height of the triangle AED. AED is clearly not as tall as AGD.

@christopherallen3353 2 жыл бұрын

Beautiful proof. Bravo!

@DanielRubin1 2 жыл бұрын

Thank you! Cheers!

@shiddy. 2 жыл бұрын

this is really good +sub ... greetings from Minnesota👍

@SummerFrost23 Ай бұрын

13:10 P(2n) < 0.5 P(n) was not proved. You only show P(2n) < P(n). You mentioned " by symmetry" but it is not so apparent.

@robertpezer131 2 жыл бұрын

Brilliant presentation.

@DanielRubin1 2 жыл бұрын

Glad you liked it!

@8obil116 6 ай бұрын

My only question is why Archimedes suspected 1/2Cr could be the area of a circle. Where did 1/2Cr come from before this? Did he just arbitrarily test 1/2Cr and it somehow worked? I feel like I’m missing context.

@AJ-ss3jy 5 күн бұрын

The area of circle Cr/2 was deduced by Antiphon (480BC-411BC) using infinity and infinitesimals. Antiphon used inscribed n-gons and then deduced using infinite sided polygons to get Cr/2. But his reasoning/method was rejected by philosopher Zeno (of Zeno’s paradox fame) and his students because of the absurd outcomes of infinity and infinitesimals. So Archimedes would have learned and known about Cr/2 as the area of circle from the works of Antiphon and his students, but his challenge was to proof Cr/2 was true without using infinity/infinitesimals and this is how this video excellently taught us how Archimedes did it. By the way you should check out Tarek Said channel where I learned what I said above.

@probablyshadman 2 жыл бұрын

Can you do a series like this for real analysis? With the history..the disputes..views like NJ Wildberger's compared with the widely accepted views? It would be awesome

@jf3518 10 ай бұрын

Why not integrate the circumference from the center 0 to the outer side r over r?

@RipRoarLB Жыл бұрын

Would this method be similar to the following: I used the method of stating that (1/2 b * h), the area of a triangle, can equal Pir^2, by breaking down the circle into infinite smaller triangles and summing up the area.