Archimedes Area Approximation for x^2

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Discussion Overview

The discussion centers around Archimedes' geometric proof regarding the area under the curve of the function x^2, specifically the claim that this area is equal to x^3/3. Participants seek resources and explanations related to this proof.

Discussion Character

  • Exploratory, Conceptual clarification, Meta-discussion

Main Points Raised

  • One participant expresses interest in Archimedes' proof and requests links or explanations.
  • Another participant suggests reading the introductory chapter of Apostol's Calculus Vol.1 as a resource.
  • A third participant shares a link to a historical overview of the rise of calculus, which may provide context related to the topic.
  • A later reply indicates that the original poster can access Apostol's book, showing engagement with the suggested resource.

Areas of Agreement / Disagreement

Participants do not express disagreement; however, the discussion remains open-ended with no consensus on the proof itself or its details.

Contextual Notes

Limitations: The discussion does not delve into the specifics of Archimedes' proof or the mathematical steps involved, leaving those aspects unresolved.

Feldoh
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I heard that Archimedes proved geometrically that the area under the curve of x^2 is equal to x^3/3. I was just wondering if anyone could give me a link to the proof or try and explain it.

Thanks^^
 
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If you can get hold of a copy, read the intro chapter to Apostol's Calculus Vol.1.
 
neutrino said:
If you can get hold of a copy, read the intro chapter to Apostol's Calculus Vol.1.

Turns out I can get a hold of that.

Thanks guys^^
 

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