Calculating Pi: Archimedes

Archimedes, a pioneer in applied mathematics, focused on the circle to approximate π, the ratio of a circle's circumference to its diameter. While ancient civilizations like the Egyptians had rough estimates of π, Archimedes developed a more precise method by inscribing and circumscribing polygons around a circle. By increasing the number of polygon sides, he achieved a highly accurate approximation of π, realizing its infinite decimal nature. His work laid the foundation for future mathematical discoveries.

What was the primary focus of Archimedes' mathematical work?

• The circle

• The rectangle

• The triangle

• The square

How did the Egyptians approximate the value of π?

• As 22/7

• As 3.14159

• As 4 thirds to the power 4

• As 3.14

What method did Archimedes use to calculate a more accurate value of π?

• Using straightedge shapes

• Using algebraic equations

• Using a compass

• Using a protractor

What was the number of sides Archimedes used in his shapes to approximate π?

• 120

• 96

• 72

• 48

What did Archimedes realize about the nature of π's decimal expansion?

• It is finite

• It is irrational

• It is a whole number

• It is infinite