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Título Original: How Archimedes Almost Broke Math with Circles
Publicado em YT, 22 de Novembro de 2023
Créditos: Ben Syversen
Publicação Original: https://www.youtube.com/watch?v=XfeuCfOUuXg
Descrição Original do Autor:
724.926 visualizações 22 de nov. de 2023
Archimedes proved the area formula for a circle by dividing the shape into infinitesimally small pieces. The concept was behind some of his greatest mathematical achievements, but rested on a paradox that wasn't addressed rigorously for thousands of years. Even Isaac Newton left some key questions unresolved when he wrestled with this paradox 1800 years later.
I skipped the detailed proof in this video - you can find an excellent full explanation of Archimedes' proof of the area formula of the circle by @DanielRubin1 here: • Area of a Circle, the BEST COMPLETE P...
*A few clarifications and comments, based on helpful viewer feedback*
•While Archimedes is often credited with the invention of the screw style water pump, and it bears his name, evidence shows that this invention existed in Egypt before Archimedes, and he was likely the first to "demonstrate and fully explain its properties." https://books.google.com/books?id=5cP...
•Another source, cited in Wikipedia, says that the screw may have been an improvement on a similar pump that existed in the hanging gardens of Babylon: https://muse.jhu.edu/issue/2473 (I have not independently vetted this article since it comprises such a small detail in my video)
•Some have pointed out that Leibniz was given short shrift in my video. Had I known that this video would go viral, I would have held it back for a week or two to fix that problem! As it is, I hope to cover the Newton/Leibniz controversy in a future video.
•It's worth clarifying that parts of the story of Archimedes' death are likely apocryphal, in particular his last words. In the video, I referred to it as a "legend" because there's no question that it's a good story. Some 300 years after Archimedes, Plutarch reported multiple versions of Archimedes' death and his last words. There is probably a version of the truth in there somewhere, but storytelling and myth making surely played a role as well.
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Título Original: How Archimedes Almost Broke Math with Circles
Publicado em YT, 22 de Novembro de 2023
Créditos: Ben Syversen
Publicação Original: https://www.youtube.com/watch?v=XfeuCfOUuXg
Descrição Original do Autor:
724.926 visualizações 22 de nov. de 2023
Archimedes proved the area formula for a circle by dividing the shape into infinitesimally small pieces. The concept was behind some of his greatest mathematical achievements, but rested on a paradox that wasn't addressed rigorously for thousands of years. Even Isaac Newton left some key questions unresolved when he wrestled with this paradox 1800 years later.
I skipped the detailed proof in this video - you can find an excellent full explanation of Archimedes' proof of the area formula of the circle by @DanielRubin1 here: • Area of a Circle, the BEST COMPLETE P...
*A few clarifications and comments, based on helpful viewer feedback*
•While Archimedes is often credited with the invention of the screw style water pump, and it bears his name, evidence shows that this invention existed in Egypt before Archimedes, and he was likely the first to "demonstrate and fully explain its properties." https://books.google.com/books?id=5cP...
•Another source, cited in Wikipedia, says that the screw may have been an improvement on a similar pump that existed in the hanging gardens of Babylon: https://muse.jhu.edu/issue/2473 (I have not independently vetted this article since it comprises such a small detail in my video)
•Some have pointed out that Leibniz was given short shrift in my video. Had I known that this video would go viral, I would have held it back for a week or two to fix that problem! As it is, I hope to cover the Newton/Leibniz controversy in a future video.
•It's worth clarifying that parts of the story of Archimedes' death are likely apocryphal, in particular his last words. In the video, I referred to it as a "legend" because there's no question that it's a good story. Some 300 years after Archimedes, Plutarch reported multiple versions of Archimedes' death and his last words. There is probably a version of the truth in there somewhere, but storytelling and myth making surely played a role as well.
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