Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modernizing Archimedes' Construction of $\pi$   In his famous work, "Measurement of a Circle," Archimedes described a
procedure for measuring both the circumference of a circle and the area it
bounds. Implicit in his work is the idea that his procedure defines these
quantities. Modern approaches for defining $\pi$ eschew his method and instead
use arguments that are easier to justify, but they involve ideas that are not
elementary. This paper makes Archimedes' measurement procedure rigorous from a
modern perspective. In so doing, it brings a rigorous and geometric treatment
of the differential properties of the trigonometric functions into the purview
of an introductory calculus course.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con