Unraveling Pi: A Journey into the Enigmatic World of Mathematics on Pi Day

Every March 14th, or 3/14 according to the American convention, is celebrated as Pi Day worldwide, paying homage to the most famous approximation (3.14) of the mathematical constant Pi.

The tradition originated with physicist Larry Shaw of the Exploratorium Museum in San Francisco in 1988 and has since gained global popularity. On this day, mathematicians aim to raise awareness of their field among the general public through lectures, museum exhibitions, and pie-eating competitions.

In 2019, UNESCO’s 40th General Conference designated Pi Day as the International Day of Mathematics.

So, What Exactly is Pi?

Pi, often symbolized by the Greek letter π, stands as the most renowned of all mathematical constants. It represents the ratio of a circle’s circumference (the boundary) to its diameter (a straight line between two points on the circle’s boundary, passing through its center). Remarkably, regardless of the circle’s size, this ratio remains constant.

Pi is an irrational number, meaning it is a decimal with no end and no repeating pattern. It is most commonly approximated as 3.14 or by the fraction 22/7.

How is Pi Calculated?

The significance of Pi has been understood for at least 4,000 years. Ancient civilizations such as the Babylonians and Egyptians developed their own approximations. The Babylonians settled on 25/8 (3.125) while the ancient Egyptians settled at approximately (16/9)^2, which is around 3.16.

However, it was the Greek polymath Archimedes (circa 287-212 BCE) who devised a method to calculate Pi that persisted until the 17th century. Archimedes realized that the perimeter of a regular polygon inscribed in a circle is smaller than the circle’s circumference, while the perimeter of a similar polygon circumscribed around the circle is greater than its circumference. Using this insight, he established limits within which the value of Pi must lie.

Archimedes progressively increased the number of sides of the inscribed and circumscribed polygons, ultimately demonstrating that 223/71 < Pi < 22/7. This method, albeit labor-intensive, laid the groundwork for subsequent approximations.

Isaac Newton (1643-1727) revolutionized the calculation of Pi by employing calculus. In 1666, he calculated Pi up to 16 decimal places, significantly simplifying the process compared to previous methods.

Today, with the aid of modern computers, Pi has been calculated to over 31 trillion decimal places.

Why Calculate Pi?

Despite Pi’s extensive calculation, its practical application might seem obscure. However, circles and related shapes abound in architecture, design, engineering, and various scientific fields. Knowing the value of Pi is indispensable for tasks ranging from constructing water storage tanks to designing advanced satellite equipment.

Moreover, Pi appears to be intrinsic to fundamental aspects of the universe, from understanding the structure of DNA to calculating the vastness of space. As Prof. Dorina Mitrea of Baylor University aptly states, Pi’s relevance will only increase as our understanding of the world deepens.

Additionally, there is a certain allure to Pi beyond its practical utility. Its infinite and seemingly random decimal expansion embodies the beauty and order inherent in mathematics, captivating mathematicians and enthusiasts alike.

In essence, Pi represents not only a fundamental constant but also a gateway to the infinite complexities and wonders of the mathematical universe.