Una "breve" historia del número Pi | Feliz día de 𝜋

The History and Significance of Pi

Introduction to Pi

• Pi is a well-known mathematical constant, yet many are unaware of its history and significance.

• The term "pi" was popularized by Euler in 1748, derived from the Greek words for circumference and perimeter.

Early Approximations of Pi

• Ancient Egyptians approximated the area of a circle using a square with sides equal to eight-ninths of the diameter.

• Archimedes inscribed polygons within a circle to approximate pi, starting with hexagons and stopping at 96-sided polygons due to calculation limitations.

Contributions from Various Cultures

• Roman engineer Vitruvius approximated pi as 25/8 around 20 BC; later, Chinese astronomer Liu used a polygon with 3,072 sides for better accuracy.

• By the end of the 5th century, Chinese mathematician Zu Chongzhi accurately calculated pi to six decimal places (3.141592).

Advancements in India and Persia

• Indian mathematicians made significant contributions but were often dismissed; Brahmagupta defended √10 as an approximation.

• Persian mathematician Al-Khwarizmi calculated pi with nine digits using sexagesimal base systems.

European Developments in Calculating Pi

• Fibonacci utilized Archimedes' method in Europe during the 12th century; later mathematicians like François Viète improved calculations significantly.

• John Wallis developed series approximations for pi in 1655; Newton followed suit with his own series ten years later.

Formal Recognition of Irrationality

• William Jones first used the Greek letter π officially in mathematics; Euler further popularized it in 1737.

• Johann Heinrich Lambert proved that pi is irrational in the 1760s; Karl Ludwig Ferdinand von Lindemann demonstrated its transcendental nature in 1882.

Final Calculations Before Computers

Calculating Pi: A Journey Through Decimal Precision

The Evolution of Pi Calculation

• The quest for calculating pi has advanced significantly, with electronic calculators enabling computations up to 808 decimal places. Early mathematicians faced challenges in achieving high precision.

• In 1949, Jacques broke the record by calculating 2,037 decimal places in just 70 hours. This marked a significant milestone in the history of pi calculations.

• Over the years, various computers have surpassed previous records; notably, an IBM computer calculated 250,000 decimals in only 8 hours and 23 minutes in 1966.

• By 2009, a supercomputer from Tsukuba System achieved over 2.5 trillion decimal places within approximately 73.5 hours using a network of 640 computers operating at a speed of 95 teraflops.

• The current record was set on March 14, 2019, when Emma Haruka Iwao calculated over 31 trillion digits with Google's help. This number aligns with the first thirteen digits of pi (3.1415926535897).

Significance and Implications

• Many question the practical utility of calculating such extensive digits of pi; writing them out at one digit per second would take nearly a thousand years.

• However, exploring infinite decimal representations like that of pi aids mathematicians in developing theories about random distributions and serves as a benchmark for testing modern computational power.