Who determined pi by approximating it between 223/71 and 22/7?

Who determined pi by approximating it between 223/71 and 22/7?

• A. Euclid
• B. Archimedes
• C. Ptolemy
• D. Fibonacci

Answer: (B)

Archimedes determined pi by bounding its value through inscribed and circumscribed polygons around a circle. By starting with simple polygons and then doubling the number of sides (going up to 96 sides), he calculated perimeters that tighten the circle’s circumference from both inside and outside. The resulting bounds are 223/71 and 22/7, which sit on either side of pi, with pi ≈ 3.14159 falling between them. This polygon-based bounding method is what links pi to those two fractions. Euclid laid foundational geometry, Ptolemy worked with astronomy and geometric models, and Fibonacci is known for sequences and number theory, but Archimedes is the one who used this polygon approach to pin pi between those specific values.

Archimedes determined pi by bounding its value through inscribed and circumscribed polygons around a circle. By starting with simple polygons and then doubling the number of sides (going up to 96 sides), he calculated perimeters that tighten the circle’s circumference from both inside and outside. The resulting bounds are 223/71 and 22/7, which sit on either side of pi, with pi ≈ 3.14159 falling between them. This polygon-based bounding method is what links pi to those two fractions.

Euclid laid foundational geometry, Ptolemy worked with astronomy and geometric models, and Fibonacci is known for sequences and number theory, but Archimedes is the one who used this polygon approach to pin pi between those specific values.