8 Questions
What is the approximate value of pi that the ancient Babylonians arrived at?
3
What is the approximate value of pi mentioned in the Egyptian Rhind Papyrus?
3.1605
Who is credited with the first calculation of pi?
Archimedes of Syracuse
What method did Archimedes use to approximate the area of a circle?
Using the Pythagorean Theorem to find the areas of two regular polygons
What were the upper and lower bounds for the area of the circle calculated by Archimedes?
Between 3 1/7 and 3 10/71
Who is the Chinese mathematician and astronomer who calculated the value of pi?
Zu Chongzhi
What is the value of pi calculated by Zu Chongzhi?
355/113
Why is the actual value of pi still not known exactly?
Because even if we calculated pi to a large number of decimal places, we would still only be approximating its actual value
Study Notes
Pi's Ancient History
- Pi has been known for almost 4000 years, but even if calculated to the number of seconds in those 4000 years, it would only be an approximation.
- Ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, giving a value of pi = 3.
- A Babylonian tablet (ca. 1900–1680 BC) indicates a value of pi = 3.125, a closer approximation.
- The Egyptian Rhind Papyrus (ca.1650 BC) shows evidence of calculating the area of a circle, giving an approximate value of pi = 3.1605.
Archimedes' Breakthrough
- Archimedes of Syracuse (287–212 BC) was the first to calculate pi, using the Pythagorean Theorem to find the areas of two regular polygons: one inscribed within the circle and one circumscribing the circle.
- Archimedes showed that pi is between 3 1/7 and 3 10/71, but knew it was only an approximation within those limits.
Later Contributions
- Zu Chongzhi (429–501), a Chinese mathematician and astronomer, calculated the value of the ratio of a circle's circumference to its diameter as 355/113.
- Zu Chongzhi's method is unknown, as his book has been lost to time.
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