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.[ref]
The bounds 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.[ref]
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Archimedes (c. 287 – c. 212 BCE) was an ancient Greek mathematician, physicist, engineer, inventor, and astronomer, famously known for his contributions to mathematics and physics. He is often regarded as one of the greatest mathematicians of all time. Some of his most notable achievements and concepts include: 1. **Mathematics**: Archimedes made significant contributions to geometry, particularly in the areas of circles, spheres, and cylinders.