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6. Archimedes determined that the value of \(\pi\) lies between \(\frac{22}{7}\) and \(\frac{223}{71}\) by comparing a particular circle with two polygons, one larger than the circle and one smaller. Each polygon had how many sides?

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7. Hypatia, commonly considered the earliest known female mathematician, is believed to have written a commentary on which work by Apollonius?

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Final answer:

Archimedes compared circles with polygons to calculate Pi and Hypatia wrote on Apollonius' work on conic sections.


Explanation:

Archimedes determined that the value of Pi lies between 3 and 13 by comparing a particular circle with two polygons, each having 7 sides. Hypatia wrote a commentary on the work by Apollonius that focused on conic sections.


Learn more about Pi value comparison with polygons and Hypatia's commentary on Apollonius here:

https://brainly.com/question/31235970


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