Understanding Archimedes' Method for Approximating Pi

The video explains Archimedes' method for approximating pi using simple trigonometry. It starts with a circle of diameter 1 and explores the relationship between the circle's circumference and the perimeters of circumscribed and inscribed squares. By calculating side lengths using trigonometry, the video demonstrates how pi is bounded between 2.828 and 4. Further approximation is achieved by increasing the number of sides in the polygons, with Archimedes reaching a 96-sided polygon to approximate pi between 3 1/7 and 3 10/71.

What geometric shape did Archimedes use to initially approximate pi?

• Square

• Triangle

• Pentagon

• Hexagon

When a square is inscribed inside a circle, how does its perimeter compare to the circle's circumference?

• The perimeter is twice the circumference

• The perimeter is greater than the circumference

• The perimeter is equal to the circumference

• The perimeter is less than the circumference

What is the approximate perimeter of the inscribed square calculated using trigonometry?

• 3.5

• 2.828

• 3.14

• 4.0

How did Archimedes improve his approximation of pi?

• By using a smaller circle

• By increasing the number of sides of the polygons

• By using a larger circle

• By decreasing the number of sides of the polygons

What was the range of pi that Archimedes calculated using a 96-sided polygon?

• Less than 3 1/6 but greater than 3 1/5

• Less than 3 1/3 but greater than 3 1/4

• Less than 3 1/7 but greater than 3 10/71

• Less than 3 1/2 but greater than 3 1/3