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Researchers in Switzerland Calculate the Value of Pi to a Record of 62.8 Trillion Digits

Posted by Guy Pirro   08/19/2021 03:52AM

Researchers in Switzerland Calculate the Value of Pi to a Record of 62.8 Trillion Digits

In applied mathematics, Pi describes the ratio of a circle’s circumference to its diameter. The origin of Pi goes back thousands of years to some of the world’s most ancient civilizations. Although the values attributed to Pi back then were not exactly the ones we use today, it’s remarkable just how close ancient mathematicians came to workable values of the number. If we were to write down the most accurate value of Pi today, we’d have to jot down a number that contains trillions of digits. But since it is an irrational number, the mathematical constant actually goes on forever. But while accuracy in mathematics is important, so is sanity. For this reason, we typically just shorten the value of Pi to 3.14159. (Content Credit: University of Applied Sciences in Graubunden, Exploratorium – San Francisco) (Image Credit: Post University - Waterbury, Connecticut)

 


Researchers in Switzerland Calculate the Value of Pi to a Record of 6.28 Trillion Digits

By early Saturday morning, August 14th, it was clear -- The world record calculation for the number Pi had fallen to a Swiss team at the University of Applied Sciences in Graubunden.

The record is now back in Switzerland after two previous American world records. The high performance computer at the Center for Data Analytics, Visualization, and Simulation (DAViS) exceeded the old world record of 50 trillion digits by adding 12.8 trillion new, previously unknown digits to the back-end of  the irrational number known the world over as Pi. The last ten known digits of Pi are now 3.1415926535…7817924264.

The calculation of the new pi-digit world record by the Swiss team took 108 days and 9 hours. It was therefore almost twice as fast as the record that Google set in its cloud computing attempt in 2019, and around 3.5 times as fast as the last world record from 2020. The record team from Graubunden is extremely satisfied with the calculation process. "We wanted to achieve several goals with the record attempt," said Dr. Heiko Rolke, head of the DAViS team. “In the course of preparing and performing the calculations, we were able to build up a lot of know-how and optimize our processes. This is now of particular benefit to our research partners, with whom we jointly carry out computationally intensive projects in data analysis and simulation."

Thomas Keller, the project manager entrusted with performing the calculations, added “The calculation showed us that we are prepared for data and computing power-intensive use in research and development. The calculation also made us aware of weak points in the infrastructure, such as insufficient backup capacities. "

The expertise gained by the DAViS team, as demonstrated by the world record, as well as the hardware used are in demand in areas of research such as RNA analyzes, flow simulations, and text analyses. The University of Applied Sciences team supports project partners in these and other areas. With the achieved calculation of 62.8 trillion digits, the DAViS team will have the achievement officially registered with the Guinness Book of World Records. The number itself will then be made publicly available.

 

 

 

Mathematical constants have fixed values, and more often than not, they appear again and again across a range of mathematical equations. Pi is one such mathematical constant. Its value will always be 3.14159, and it will always appear in equations where circles are a calculation. Regardless of the size of the circle, Pi will always describe the relationship between its diameter and circumference. Mathematical constants are not calculated by physical measurements, which is why they don’t differ from equation to equation. There are many, many constants that appear repeatedly throughout mathematics, with the value of Pi being one of the better known and more frequently used.

If we were to write down the most accurate value of Pi today, we’d have to jot down a number that contains trillions of digits. But since it is an irrational number, the mathematical constant known as Pi actually goes on forever. But while accuracy in mathematics is important, so is sanity. For this reason, we typically just shorten the value of Pi to 3.14159.

In applied mathematics, Pi describes the ratio of a circle’s circumference to its diameter. The origin of Pi goes back thousands of years to some of the world’s most ancient civilizations. Although the values attributed to Pi back then were not exactly the ones we use today, it’s remarkable just how close ancient mathematicians came to workable values of the number. The origin of Pi makes for a fascinating story.

The number Pi has been known for almost 4000 years. But even if we totaled the number of seconds in those 4000 years and calculated Pi to that number of places, we would still only be approximating its actual value.

The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for Pi, which is a closer approximation.

The Rhind Papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for Pi.

The first actual calculation of Pi was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world. Archimedes approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons -- The polygon inscribed within the circle and the polygon within which the circle was circumscribed. Since the actual area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave upper and lower bounds for the area of the circle. Archimedes knew that he had not found the value of Pi but only an approximation within those limits. In this way, Archimedes showed that Pi is between 3-1/7 and 3-10/71.

A similar approach was used by Zu Chongzhi (429–501), a brilliant Chinese mathematician and astronomer. Zu Chongzhi would not have been familiar with Archimedes’ method, but because his book has been lost, little is known of his work. He calculated the value of the ratio of the circumference of a circle to its diameter to be 355/113. To compute this accuracy for Pi, he must have started with an inscribed regular 24,576-gon and performed lengthy calculations involving hundreds of square roots carried out to 9 decimal places.

Mathematicians began using the Greek letter Pi in the 1700s. Introduced by William Jones in 1706, use of the symbol was popularized by Leonhard Euler, who adopted it in 1737.

The University of Applied Sciences in Graubunden is an innovative and entrepreneurial university of applied sciences with over 2000 students. It trains people to become responsible and skilled professionals and managers. As a university of applied sciences with strong regional roots, it attracts students from beyond the region and even from outside Switzerland. The University of Applied Sciences in Graubunden offers a range of bachelor’s, master’s, and further education programs in Architecture, Civil Engineering, Digital Science, Management, Mobile Robotics, Multimedia Production, Photonics, Service Design, and Tourism. It also performs applied research in these disciplines and in doing so contributes to the development of innovations, knowledge, and solutions for society.

 

 

For more information:

 

https://www.fhgr.ch/news/newsdetail/die-fh-graubuenden-kennt-pi-am-genauesten-weltrekord/

 

https://www.exploratorium.edu/pi/history-of-pi

 

https://post.edu/blog/origin-of-pi/

 

https://www.theguardian.com/science/2021/aug/17/new-mathematical-record-whats-the-point-of-calculating-pi

 

https://www.theguardian.com/science/2021/aug/16/swiss-researchers-calculate-pi-to-new-record-of-628tn-figures?utm_source=join1440&utm_medium=email&utm_placement=newsletter

 

https://astromart.com/news/show/sixty-symbols-unravelling-the-secret-language-of-physics-and-astronomy

 

https://astromart.com/news/show/happy-pi-day

 

 

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