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Assignment 7

Assignment based on Archimedes lecture: law of lever, volume of sphere.

Assignment questions for archimedes lecture:

  1. When Archimedes derives the law of the lever, he provides the derivation first for weights which are commensurable (weight measures expressible as a rational number). You can study and understand this derivation (use Sherman Stein's book and the figures placed on the webpage). How does Archimedes extend this proof/ derivation to incommensurable weights?

  2. Study Archimedes' derivation of the (i) volume of a parallelopiped and (ii) area of a segment of a parabola (reference: Sherman Stein). Write a sketch of the proof in your own words – using prose not just symbols – highlighting the key ideas.

 

Reference: Stein, Sherman (1999) Archimedes, What did he do besides cry Eureka? Mathematical Association of America. (Available in HBCSE library)

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