Pi is one of the most enigmatic and beguiling numbers in mathematics, embodying its essence: infinity itself. Pi has inspired artists, musicians and mathematicians alike for centuries; today it remains an integral component of mathematics as well as modern technology.

Pi is an iconic example of mathematics as an evolving discipline; more than merely rules and formulae. Instead, mathematics has grown with time as its rules have been stretched out further to include new challenges, discoveries, and understanding.

Archimedes made an indelible mark on the calculation of pi as an ancient Greek mathematician. He took an unconventional approach compared to Antiphon and Bryson. Archimedes devised the first algorithm that helped him calculate pi to several decimal places by drawing an inscribed and circumscribed hexagon, duplicating each side, then duplicating those of two 96-sided polygons; his calculations yielded results equaling pi to three decimal places but proved too time consuming and involved too much measuring.

Later, English mathematician John Wallis devised a formula to simplify calculating pi. In 1656, his formula employed the multiplication of an infinite series of fractions to arrive at its value; later that century, Sir Isaac Newton also utilized this same approach in order to calculate its initial decimal points.

Since the 17th century, Greek letters were assigned to represent numbers, leading to its universally recognized name: pi. William Jones likely used this symbol for its interpretation as representing periphery; later, Swiss mathematician Leonard Euler made its use more prevalent.

Today, mathematicians have calculated pi to an incredible 100 trillionth digit! In order to do so, they have developed computer software capable of breaking it into smaller, more manageable pieces.

Pi is used in numerous areas of mathematics, from calculating circle circumferences and areas to the use in star distance estimation calculations – even as an easy way of estimating their distance from their centers! Simply divide pi by the radius of any star to get its circumference value.

Geometry, used for everything from building buildings to travelling to the moon, often relies on Pi. Trigonometry uses Pi as its base concept – its mathematical foundation allowing scientists to track baby breathing and circadian rhythms that control our sleep and wakefulness patterns – without which measuring length would not be possible! Without Pi, measuring bicycle tires would also not exist.