Prompt Cast
The History and Calculation of Pi: From Ancient Civilizations to Supercomputers
TLDR Pi, a mathematical constant, has been approximated by civilizations for thousands of years. Ancient civilizations used geometric and physical techniques, while Chinese and Greek mathematicians used polygons to calculate pi. With the development of calculus, infinite series were discovered that converge to pi, leading to more precise calculations. The current record for calculating pi is 66.8 trillion digits.
Timestamped Summary
00:00
Pi is a mathematical constant that has been approximated by civilizations for thousands of years and continues to be studied today with the help of supercomputers.
01:41
Ancient civilizations, such as the Egyptians and Indians, approximated the value of pi using geometric and physical techniques, getting it within 1% accuracy, but further advancements were made by Chinese and Greek mathematicians who discovered that the circumference of a circle could be approximated by creating ever larger polygons inside of it.
03:15
Chinese and Greek mathematicians approximated the value of pi using polygons, with Zhu Shanzhi calculating a 12,288-sided polygon and achieving a value of pi correct to 7 decimals, while later mathematicians like Jamshid Al-Khashi and Ludo von Kulen used even larger polygons to calculate pi to 16 and 35 digits respectively, before the use of infinite series became the next big innovation in pi calculation.
04:50
The development of calculus led to the discovery of infinite series that converge to pi, with one series being able to calculate pi out to 71 digits, and as pi was calculated to more precise values, mathematicians started asking questions about its properties.
06:37
Pi is a transcendental number that was proven to be unsolvable using a compass and straight edge, and calculations of pi continued to improve over time.
08:07
Calculations of pi have improved over time, with the current record set in 2021 at 66.8 trillion digits, and memorizing pi has become a competitive activity, but it's possible that if aliens contacted us, they wouldn't share pi with us.
09:54
Pi may not be the most important number in mathematics, as some argue that the ratio of the circumference to the radius, known as tau, should be used instead, but regardless, pi will continue to be an important mathematical constant.
