Super computing PI to trillion digits

Pi (π) is one of the most fascinating and mysterious mathematical constants in the world. Pi is the fascination, admiration and cult of millions of people worldwide, engineers, physicists, mathematicians, artists, musicians, administrators, economists lawyers, painters, soldiers, politicians, businessmen. The world's youth in universities greatly enjoy the challenges that the number Pi represents in their lives and the careers that are about to begin. Without a doubt, it is one of the most popular numbers in the world. Who does not mention pi without intuiting or knowing all the power and mysteries that are hidden behind this number.

The origin of π Its conception arises from ancient Babylon (1900 BC), where the experts of that era unequivocally analyzed the relationship between polygons and circles, reaching an approximation of 3.125.

The Rhind papyrus, around 1650 BC, is also considered as the continuation of his study. The document shows a calculation of 256/81, around 3.1604. The value of this number is also written between the Biblical passages. In the Book of the First Kings, around the 6th century BC, it speaks of a sea of molten metal with a circumference of 30 cubits and a diameter of 10 cubits, which would give a value of pi equal to 3.

However, it would be in 250 BC, when the Greek polymath Archimedes would have an exact approximation of this curious number. Using an algorithm based on the Pythagorean theorem, the physicist calculated his upper and lower limits, 3/7 and 310/71, which predicted a mean value of 3.1418. In turn, he observed that this result was related to the operation between the area of a circle divided by its radius.

And that is precisely the current definition we have of this rational number, with one that has notably more decimals and to which we constantly continue to get closer.

The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed,but no proof of this conjecture has been found.

For thousands of years, mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians made a five-digit approximation, both using geometrical techniques. The first computational formula for π, based on infinite series, was discovered a millennium later. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by the Welsh mathematician William Jones in 1706.

Did the Chinese mathematician Zu Chongzhi calculate Pi to seven decimal places in the 5th century? His groundbreaking contribution to #mathematics remains a testament to the ingenuity and brilliance of ancient Chinese mathematicians.

The invention of calculus soon led to the calculation of hundreds of digits of π, enough for all practical scientific computations. Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have pursued new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits. These computations are motivated by the development of efficient algorithms to calculate numeric series, as well as the human quest to break records. The extensive computations involved have also been used to test supercomputers.

Swiss researchers at the University of Applied Sciences Graubünden this week claimed a new world record for calculating the number of digits of pi – a staggering 62.8 trillion figures. By my estimate, if these digits were printed out they would fill every book in the British Library ten times over. The researchers’ feat of arithmetic took 108 days and 9 hours to complete, and dwarfs the previous record of 50 trillion figures set in January 2020.

Because calculating pi has become a way for computers to flex their computational abilities, as programmers look toward extremely resource-intensive tasks, like modeling the universe or even making high-performance imagined worlds in video games. Scientists can also use powerful supercomputers for practical tasks like mapping the human genome, or crunching all of the world’s known chemical compounds in order to find candidates for new medicines.

SUPER COMPUTING WITH RASPBERRY PI

Three years after Seattle software developer Emma Haruka Iwao and her teammates at Google set the world record for calculating pi precisely, they’ve done it again. Thanks to Iwao and Google Cloud, we now know what pi equals to an incredible precision of 100 trillion digits.

Pi calculated to '62.8 trillion digits' with a pair of 32-core AMD Epyc chips, 1TB RAM, 510TB disk space

155 comment bubble on white Swiss uni challenges world record after 108 days and 9 hours of divisive effort.

Switzerland's University of Applied Sciences Graubünden has challenged the world record for calculating Pi, claiming it has computed the mathematical constant to 62.8 trillion digits.

The university yesterday claimed it had broken the record, asserting it beat the previous record of 50 trillion digits, set by Timothy Mullican last year, by 12.8 trillion digits, and completed the task in just over 108 days versus Mullican's 303.

Helpfully, the uni has also published details of the hardware used for its feat.

A pair of 32-core AMD Epyc 7542 processors powered the uni's rig. AMD states the CPU cores spend most of their time at 2.9GHz, can burst to 3.4GHz, have 128MB L3 cache and happily run 64 threads apiece. A server with 1TB of RAM was also employed, with Ubuntu Linux 20.04 installed on a pair of solid-state disks of unspecified size.

A JBOD housed 38 7200RPM hard disks, each with 16TB capacity.

Thirty-four of those disks were used to store values swapped from RAM – a design chosen because memory is very expensive. Hard disks were chosen over SSDs because SSD performance degrades over time and the university's designers feared their intensive calculations could cause problems. In all, the uni said 510TB of disk space was used.

Google has put its cloud to work calculating the value of Pi all the way out to 100 trillion digits, and claimed that's a world record for Pi-crunching.

The ad giant and cloud contender has detailed the feat, revealing that the job ran for 157 days, 23 hours, 31 minutes and 7.651 seconds.

A program called y-cruncher by Alexander J. Yee did the heavy lifting, running on a n2-highmem-128 instance running Debian Linux and employing 128 vCPUs, 864GB of memory, and accessing 100Gbit/sec egress bandwidth. Google created a networked storage cluster, because the n2-highmem-128 maxes out at 257TB of attached storage for a single VM and the job needed at least 554TB of temporary storage.

32 storage nodes, using the n2-high CPU-16 instance, and a single compute node were assembled into a cluster that offered 64 iSCSI block storage targets.

The constant π helps us understand our universe with greater clarity. The definition of π inspired a new notion of the measurement of angles, a new unit of measurement. This important angle measure is known as “radian measure” and gave rise to many important insights in our physical world.

Now you are probably wondering how Pi appears in biological processes. The answer to this question lies in the interdisciplinary field of biophysics: biology + physics. Biology studies life and living organisms. Biologists investigate how organisms grow, get food, communicate, sense and response to the environment, reproduce, and evolve. On the other hand, physics studies the nature and properties of matter and energy. Physicists search for the mathematical laws of nature and the universe. Biophysicists look for patterns in life and analyze them with mathematics to gain novel insights about how organisms work.

Let’s now consider one of the patterns observed in the life sciences. The appearance of an organism’s body plan – a process called morphogenesis – is one of the most striking features of living creatures. In animals, the embryo grows from an almost uniform group of cells into a patterned structure with a brain, backbone, and limbs. In 1952, the mathematician and father of computer science, Alan Turing, proposed a mathematical model describing the simple biophysical principles of pattern formation during morphogenesis. He proposed that an embryo becomes patterned into different anatomical features by chemicals (termed morphogens by Turing), which diffuse through tissues. In the simplest case, the formation of the pattern results from the reaction of two morphogens, an activator and inhibitor. 40 digits of Pi (π) can measure entire observable universe

Back in 2015, scientists found something amazing - a classic formula for pi hidden in the world of quantum physics.

Pi is the ratio between a circle's circumference and its diameter, and is incredibly important in pure mathematics. But this was the first time scientists had found it "lurking" in the world of physics, when using quantum mechanics to compare the energy levels of a hydrogen atom.

Pi (π) is a mathematical constant defined as the ratio of a circle's circumference to its diameter. The diameter of the observable universe is known to be about 93 billion light-years. To calculate the circumference of a circle with such a diameter to an accuracy equal to width of a hydrogen atom, only 39 post-decimal places of pi are needed.

Fernando Jiménez Motte Ph.D (c) EE, MSEE, BSEE

CEO of NEUROMORPHIC TECHNOLOGIES NT Robotics, Control Systems, Artificial Intelligence AI

https://fernandojimenezmotte.com/

https://neuromorphic-technologies.com/

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