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Pi Day: Behind the world’s most famous mathematical constant

What is pi? How is it calculated? And why do we care so much about it? March 14, or 3/14 as per the American convention, is celebrated as Pi Day worldwide as an ode to the most well-known approximation (3.14) of the mathematical constant Pi.

The tradition was started by physicist Larry Shaw of the Exploratorium museum in San Francisco in 1988, and has since seen global popularity. On the day, mathematicians try to raise awareness on their subject among lay persons, through lectures, museum exhibitions and pie (sic) eating competitions.

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

What is Pi?

Pi day

Pi, often represented by the Greek letter π, is the most famous of all mathematical constants. It represents the ratio of a circle’s circumference (boundary) to its diameter (a straight line between two points on the circle’s boundary, passing through its centre). Regardless of the circle’s size, this ratio always remains constant.

Pi is an irrational number — it is a decimal with no end and no repeating pattern — which is most often approximated to the 3.14, or the fraction 22/7.

How is Pi calculated?

The importance of Pi has been recognized for at least 4,000 years. Petr Beckman in his classic, A History of Pi (1970), wrote that “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.”

Both ancient Babylonians and ancient Egyptians came up with their own measurements, probably by drawing a circle of some diameter, and then measuring its circumference using a rope of said diameter in length. Babylonians settled at 25/8 (3.125) as the value of Pi, while ancient Egyptians settled at (16/9)^2 (approximately 3.16)-Pi day.

It was Greek polymath Archimedes (circa 287-212 BCE) who came up with the method to calculate Pi that remained in use till the 17th century. He realised that the perimeter of a regular polygon of ‘n’ sides inscribed in a circle is smaller than the circumference of the circle, whereas the perimeter of a similar polygon circumscribed around the circle is greater than its circumference. He used this to calculate the limits within which the value of Pi must lie.

Pi Day 2024

Now, as one keeps adding more and more sides to this polygon, it gets closer and closer to the shape of a circle. Having reached 96-sided polygons, Archimedes proved that 223/71 < Pi < 22/7 (in decimal notation, this is 3.14084 < π < 3.142858).

Following Archimedes, mathematicians constantly increased the number of sides of the polygon to calculate Pi to ever greater decimal places. By 1630, Austrian astronomer Christoph Grienberger calculated 38 digits of Pi using polygons with 10^40 sides.

The problem with this method, however, is that it is extremely labour intensive. For instance, it took Dutch mathematician Ludolph van Ceulen (1540-1610) a staggering three decades to calculate Pi to 35 decimal points-Pi Day.

It would be Isaac Newton (1643-1727) who significantly simplified the process of calculating Pi. In 1666, he calculated Pi up to 16 decimal places using calculus, which he discovered along with mathematician Gottfried Wilhelm Leibniz (1646-1713). What had taken previous mathematicians years to calculate now could be done in a matter of days-Pi Day.

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