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How Archimedes Found the Volume of a Sphere without Calculus

Audience:

Tags: calculusvolume-of-a-sphere

Content: This video shows how Archimedes in Ancient Greece derived the formula for the volume of a sphere. It uses only the knowledge Archimedes himself had, so the audience can appreciate the brilliance of his method. By the end of the video, the limitations of this method will be revealed, along with the significance of calculus. Audience: High school students who know the formula for the volume of a sphere but do not know how to derive it without calculus. College students who are just beginning to learn calculus. This video demonstrates the importance of calculus by contrast. People who are interested in mathematics and the history of mathematics.

Analytics

6.87 Overall score*

32 Rank

22 Votes

11 Comments

Comments

7.5

It was a very interesting video, however, I have no clue how he did it without Carthesian plane. It would be great if you have also explain on that! And maybe even showing a bit of old texts to add some WOW :)

This was wonderful! I loved seeing how everything fit together in the end, and it was a beautiful argument throughout. Excellent visuals, too. Great job!

Motivation: 6 Novelty: 6 Clarity: 8 Memorability: 7

8.6

Wow, this is beautifully animated and explained. Bravo!

6.5

Proof for the other volumes and areas in the video

Awesome

7.5

Clear exposition with good graphics

5.7

I was not familiar with this approach, but there are others within reach of early high-school students. However, the topic, although well presented, seems clearly beyond the reach of students. An analytical approach would be better. This video may be useful for those who want to delve into the history of mathematics.

7.2

Awesome video! It’s always fun to find out that people from more than 2000 years ago were solving math problems smarter than I am today.

This video is short (in a good way), clear and with an understandable motivation. The topic isn’t outright novel, but too few channels cover it—especially in this clean style. And thanks to the smooth animations and story telling the video is quite memorable.

I’m always amazed by the brilliance of ancient mathematicians and I always will be.

It’s always interesting to know how important results were derived without all the knowledge we have today (e.g., on calculus).

That was cool and new for me! I’m glad to have seen it.