= Archimedes
{c}
<Archimedes> developed exact methods for geometric measurement. In <Measurement of a Circle by Archimedes>, he proves the relation between a <circle>'s area, <radius> and <circumference> and obtains rational bounds on its circumference-to-diameter ratio.<Measurement of a Circle by Archimedes>[Propositions I and III]{ref}
The bounds $223/71<\pi<22/7$ come from comparing inscribed and circumscribed <polygons>. Increasing the number of sides traps the circular quantity between computable geometric quantities. The argument illustrates the power of a rigorous bound: one need not express a number exactly to establish an accurate approximation with a guaranteed error.<Measurement of a Circle by Archimedes>[Proposition III]{ref}
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