Pi day: what it is and why it is important also in computer science

Pi day: what it is and why it is important also in computer science

Il pi greco (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is an irrational number: which means it cannot be expressed as a fraction of whole numbers and has an infinite number of non-periodic decimal digits. In other words, there is no repetition or periodic sequence in its decimal digits.

This constant, widely used in many disciplines, is celebrated on March 14th every year. The pi greco dayin fact, derives from data 3/14 structured in the Anglo-Saxon format (14 March, in fact), to remember the integer and the first two decimal figures which form the constant (π = 3.14).

Why the constant pi is so important, even in the computer science field

In geometry, pi is critical for calculating the circumference, area, and volume of circles, spheres, and other circular shapes. In computer calculations, the constant is therefore essential for the computer graphics3D modeling and the calculation of areas and volumes in algorithms and software involving the construction, use and manipulation of geometric figures.

In many scientific and engineering simulations, the accuracy of the constant pi is crucial. For example, in computational fluid dynamics simulations or structural behavior simulations, using pi ensures accurate results.

The importance of pi lies in its ubiquity in mathematical formulas, especially in geometry and trigonometry, but also in many other fields of mathematics, science and engineering. Pi also boasts surprising connections to other areas of mathematics and science, such as probability theory and the study of the behavior of DNA molecules.

Il golden ratio is a mathematical constant that appears in many areas of nature and art and is represented by the Greek letter phi (Φ). Pi and the golden ratio are connected through the Fibonacci sequence: The ratio between consecutive Fibonacci numbers approaches the golden ratio. As the Fibonacci sequence becomes larger, the ratio of consecutive terms gets closer and closer to Pi.

The problem of calculating the value of pi: a challenge that continues over the years

Per calculate new decimal places of pi, various algorithms and computational methods are available. One of the best known is the algorithm of Gauss-Legendre, which uses a convergent series to approximate the value of the constant. This algorithm and others like it can be implemented on computers to calculate multiple decimal places. However, obtaining a large number of decimal places requires considerable computational resources and a lot of time.

On March 14, 2019, Google announced that it had discovered 31,000 billion decimal digits of pi: to accomplish the feat, Emma Haruka Iwao (an employee of the Mountain View company) used 96 virtual CPUs supported by 1.4 Terabytes of RAM within a specific “robust” instance created on Google Cloud. The cloud nodes worked tirelessly for 112 days to reach the milestone.

The record was “taken away” in 2021 by academics from the University of Applied Sciences of Grisons (Switzerland) who managed to calculate over 37,000 billion digits after the decimal point in the constant pi.

Google holds the record: 100,000 billion decimals of pi correctly calculated

The Guinness Book then returned to Google in 2022: on 14 March of the same year, in fact, Iwao announced that it had once again used the Google Cloud infrastructure to discover 100,000 billion decimal places of pi.

Iwao explained that he designed the use of cluster formed by a computational node (made up of 128 vCPU, 864 GB of memory, 100 Gbps of bandwidth and Debian Linux 11) and 32 storage nodes, for a total of 64 iSCSI blocks for data storage. Each server di storage it based its operation on two 10,359 GB disk drives. The script published on GitHub, which has remained unchanged since then, made it possible to optimize the generation of the pi digits, reducing the time to “just” 157 days of work.

At the moment the record of 100 trillion decimal places calculated seems to remain undefeated: those wishing to limit themselves to knowing the first 10,000 can refer to the page set up by the University of Utah in 1996.

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