Which Greek mathematician is credited with an early accurate estimate of pi?

Which Greek mathematician is credited with an early accurate estimate of pi?

• A. Archimedes
• B. Euclid
• C. Pythagoras
• D. Aristotle

Answer: (A)

The main idea here is bounding a circle’s circumference by using polygons that fit inside and outside the circle. Archimedes showed how to tighten the estimate of pi by replacing the circle with regular polygons whose sides are doubled each time. Start with a hexagon inside the circle and a hexagon outside it, then move to polygons with 12, 24, 48, and finally 96 sides. Each step gives a smaller difference between the inner and outer perimeters, so the circle’s circumference—and thus pi—can be squeezed more precisely between two numbers. Archimedes found that pi lies between 3 10/71 and 3 1/7 (about 3.1408 to 3.142857), which was the most accurate early bound achieved with purely geometric reasoning. While Euclid, Pythagoras, and Aristotle made foundational contributions to geometry and science, Archimedes is the one credited with this careful, polygon-based estimate of pi.

The main idea here is bounding a circle’s circumference by using polygons that fit inside and outside the circle. Archimedes showed how to tighten the estimate of pi by replacing the circle with regular polygons whose sides are doubled each time. Start with a hexagon inside the circle and a hexagon outside it, then move to polygons with 12, 24, 48, and finally 96 sides. Each step gives a smaller difference between the inner and outer perimeters, so the circle’s circumference—and thus pi—can be squeezed more precisely between two numbers. Archimedes found that pi lies between 3 10/71 and 3 1/7 (about 3.1408 to 3.142857), which was the most accurate early bound achieved with purely geometric reasoning. While Euclid, Pythagoras, and Aristotle made foundational contributions to geometry and science, Archimedes is the one credited with this careful, polygon-based estimate of pi.