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Exploring Pi Day: Revealing the Secrets of a Mathematical Icon

StoriesExploring Pi Day: Revealing the Secrets of a Mathematical Icon

Pi Day is observed globally on March 14, or 3/14 according to American custom, in honor of the most well-known estimate (3.14) of the mathematical constant Pi.

Initiated in 1988 by physicist Larry Shaw of the Exploratorium museum in San Francisco, the practice has gained worldwide recognition. Mathematicians attempt to increase general public awareness of their field on this day by holding lectures, museum exhibits, and pie-eating contests.

Pi Day was declared the International Day of Mathematics in 2019 by the 40th General Conference of UNESCO.

What is Pi?

The most well-known of all mathematical constants is pi, which is frequently symbolized by the Greek letter π. It is the ratio of a circle’s diameter (a straight line that passes through the center of the circle) to its circumference (its boundary). This ratio is constant regardless of the size of the circle.

Pi is an irrational number that is best approximated as 3.14 or the fraction 22/7. It is a decimal with no end and no repeating pattern.

How is Pi calculated?

Pi’s significance has been understood for at least 4,000 years. “By 2,000 BC, men had grasped the significance of the constant that is today denoted by π, and that they had found a rough approximation of its value,” according to Petr Beckman in his 1970 book A History of Pi.

The methods used by the ancient Babylonians and Egyptians to determine circumference were likely drawing a circle of a certain diameter and measuring the length of a rope that would have allowed for that diameter. The value of Pi was determined by the Babylonians to be 25/8 (3.125), whereas the ancient Egyptians determined it to be (16/9)^2 (around 3.16).

The formula for calculating Pi was developed by the Greek polymath Archimedes (c. 287–212 BCE), and it was in use until the 17th century. He realized that whereas the perimeter of a comparable polygon circumscribed around the circle is greater than its circumference, the perimeter of a regular polygon of ‘n’ sides inscribed in a circle is smaller than the circle’s diameter. Using this, he was able to determine the bounds on the value of Pi.

Currently, this polygon approaches the shape of a circle as more and more sides are added to it. After arriving to 96-sided polygons, Archimedes demonstrated that 223/71 < Pi < 22/7 (or 3.14084 < π < 3.142858 in decimal notation).

In order to calculate Pi to ever-larger decimal places, mathematicians continued to increase the number of sides of the polygon after Archimedes. By 1630, Austrian astronomer Christoph Grienberger used polygons with 10^40 sides to calculate Pi to 38 digits.

The main disadvantage of this approach, though, is how labor-intensive it is. For instance, it took the Dutch mathematician Ludolph van Ceulen (1540-1610) an astounding thirty years to calculate Pi to thirty decimal places.

It would be none other than Isaac Newton (1643–1727), who greatly streamlined the Pi calculation procedure. In 1666, he used calculus, which he and mathematician Gottfried Wilhelm Leibniz (1646–1713) discovered, to compute Pi to sixteen decimal places. It would now only take a few days to calculate what had taken years for mathematicians in the past.

Pi was originally determined by French mathematician Thomas Fantet de Lagny (1660–1734) to 112 accurate decimal places by 1719. This approach can now determine Pi’s value to 31 trillion (1012) decimal places thanks to contemporary computers.

But make all this effort?

There are circles all over the place. Thus, too, are three-dimensional forms with the Pi proportion, such as spheres, cones, and cylinders. Therefore, understanding Pi’s value has several very useful applications in the domains of engineering, design, and architecture. Pi is essential in a variety of fields, from building water storage tanks to designing sophisticated satellite equipment.

Furthermore, Pi appears to be woven into explanations of the universe’s most profound operations, such as figuring out how big space is or comprehending how DNA spirals. “Pi is frequently a crucial component in the resolution of numerous issues motivated by actual occurrences in the real world. Prof. Dorina Mitrea, chair of the mathematics department at Baylor University in Texas, told Newswise in 2023 that “[it] will only increase its relevance as we continue to further our understanding of the world we live in.”

It is less evidently “useful” to calculate Pi 31 trillion digits, though. Although Pi could have been calculated to around 39 decimal places to do all calculations in the observable universe with almost little mistake in Archimedes’ day, Pi is now required to be calculated to about 39 decimal places. Then why the fixation on the number among mathematicians?

Of course, there is the rather esoteric claim that knowledge is useful in and of itself, independent of the benefits it may have in real life. Pi is seductive for additional reasons, though. In a 2015 article for The New Yorker, mathematician Steven Strogatz—author of the acclaimed The Joy of X: A Guided Tour of Math, from One to Infinity (2012)—wrote: “One of the things that makes Pi so beautiful is that it makes infinity accessible.” Little ones understand this even. Pi’s digits are infinite and never follow a pattern. They appear to continue on indefinitely at random, but they are unable to be random since they represent the order that permeates a perfect circle.


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