3.14 Pi Day: A Mathematical Journey

As March 14th rolls around, math enthusiasts and educators around the globe eagerly anticipate the celebration of Pi Day, a day dedicated to honoring one of the most iconic and enigmatic constants in mathematics: π, or pi. This special day serves not only as a tribute to the intrinsic beauty of mathematics but also as an opportunity to delve into the fascinating world of pi, exploring its significance, history, and myriad applications across various domains.

What is Pi?

At its core, pi represents the ratio of a circle's circumference to its diameter. Regardless of the circle's size, this ratio remains constant, making pi a universal constant. Symbolized by the Greek letter π, its approximate value is commonly represented as 3.14, although its decimal expansion extends infinitely without repeating patterns. Pi is an integral component of geometric calculations, enabling the determination of properties such as area, volume, and curvature for circular and spherical objects.

History of Pi

Pi (π) has a rich history spanning nearly 4000 years. The ancient Babylonians, around 1900–1680 BC, approximated π to be 3. The Rhind Papyrus, approximately from 1650 BC, shows the Egyptians calculated it to be around 3.1605.

Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of antiquity, used a geometric method to establish bounds for π, determining it to be between 3 1/7 and 3 10/71.

Zu Chongzhi (429–501), a Chinese mathematician and astronomer, approximated π as 355/113, utilizing an intricate calculation method.

The symbol π was introduced by William Jones in 1706 and popularized by Leonhard Euler in 1737.

Georges Buffon, an 18th-century French mathematician, devised a method to calculate π based on probability.

In 1988, a physicist at the San Francisco Exploratorium held what is thought to be the first official Pi Day celebration, which smartly included the consumption of fruit pies. Math teachers quickly realized the potential benefits of teaching students about pi while they ate pie, and it all caught on so much that in 2009, the U.S. Congress officially declared March 14 National Pi Day.

What is the highest digit of pi discovered?

Using a high-performance computer, a team of Swiss researchers has calculated a new most accurate value of pi. The record-breaking value counts 62,831,853,071,796 digits, as confirmed by project leader Thomas Keller and his team on 19 August 2021, adding 12.8 billion new digits to pi. To imagine this number if it would be seconds, it takes about 1994 years.

Mathematical Significance and Formulas

Pi finds ubiquitous application across various mathematical disciplines, serving as a fundamental constant in geometry, trigonometry, calculus, and beyond. Its role extends beyond simple circle calculations, permeating complex equations and theorems. For instance, pi features prominently in formulas for the area and circumference of a circle, the surface area and volume of spheres, and the calculation of periodic phenomena in trigonometric functions.

Where We Encounter Pi

The influence of pi extends far beyond the realm of mathematics, manifesting in diverse fields such as physics, engineering, and even space exploration. Engineers leverage pi's properties to design structures, machinery, and technologies, while physicists employ it in fundamental theories describing the universe's fabric. Notably, NASA harnesses pi's mathematical precision to navigate spacecraft, analyze celestial bodies, and unravel the mysteries of the cosmos.

Miracle? Pi mentions in Holy books.

Bible. In the News story about scientists' response to creationists, the scientists “comment that the Bible says that π is 3, not 3.14” (Nature 398, 453; 1999). The biblical verse quoted (1 Kings 7:23) reads in part: “⃛measuring 10 cubits from rim to rim⃛ It took a line of of 30 cubits to measure around it”

Torah. It is the sign pi (the Hebrew letter Het) with a simple apostrophe added (the Hebrew letter Yud) to create the Hebrew word “life”. It is how the Jewish culture toasts during celebrations (l'chaim = 'to life')

The Talmudic text of a mishnah in Talmud Tractate Eruvin (page 13b) provides, among other matters, information about circles saying in particular, “Whatever has a circumference of three handbreadths has a width of a handbreadth.” This text also clearly designates the value π =

Quran. As this year's Pi Day coincides with the holy month of Ramadan for Muslims, let's conduct some research to see if there is any mention of Pi in the Quran. Many scientists are aware that there are numerous scientific facts encoded in the Quran that were discovered long after the book was written, making it quite exciting to uncover these codes.

The 22nd Chapter (Surah) of the Quran is called Hajj. And one of the most important rules of Hajj is to circle around the Kaaba for exactly 7 times ( called Tawaf  in arabic). When people perform Tawaf , they perform Tawaf for 7 times, in a circle, keeping Kaaba in the center. 

The 22nd chapter of the Quran is called Hajj. And during Hajj, one has to perform Tawaf 7 times in a circle keeping the Kaaba in the center. Three things are worth noting here–  Value of Pi in Quran. Dividing the number 22 by 7 gives a value of 3.14, which is roughly close to Pi. 

Even more surprising is the word ‘Tawaf’ ( لِلطَّائِفِينَ ) mentioned in verse 26 of Surah Hajj which means ‘to circle around the Kaaba’. And these two numbers 22 and 7 can be found connected with this word “Tawaf”. If you count the letters from the first letter of the word “Tawaf”, the number 7 is found within this word. Again, from the end of the verse, the number 22 is found inside the word “Tawaf”! 

How Pi Makes NASA/JPL Go 'Round

Space is full of circular and spherical features, and to explore them, engineers at NASA build spacecraft that make elliptical orbits and guzzle fuel from cylindrical fuel tanks, and measure distances on circular wheels. Beyond measurements and space travel, pi is used to find out what planets are made of and how deep alien oceans are, and to study newly discovered worlds. In other words, pi goes a long way at NASA.

Why Pi is Unique

Pi's uniqueness lies not only in its mathematical properties but also in its cultural significance and universal appeal. Its transcendence beyond academia into popular culture, literature, and art underscores its timeless allure and intrinsic beauty. Moreover, pi's infinite decimal expansion captivates mathematicians and enthusiasts alike, fueling endeavors to calculate and memorize its digits to record-breaking lengths. As passionate as people are about pi, there are some who believe things would be a whole lot better if we replaced pi with a number called tau, which is equal to 2π or 6.28. Because many formulas call for 2π, tau-enthusiasts say tau would provide a more elegant and efficient way to express those formulas.

Celebrating Pi Day

Pi Day festivities offer a plethora of opportunities for engagement and celebration. From baking and indulging in pies of various flavors to organizing pi-themed contests and educational activities, the possibilities are endless. Educators leverage Pi Day as a platform to instill a love for mathematics among students, fostering curiosity and creativity through interactive lessons and challenges. Across communities, individuals come together to revel in the wonders of pi, reaffirming its status as a symbol of mathematical excellence and intellectual curiosity.

Music of Pi

A musician has composed a piece of music based on the number Pi, assigning numerical values to musical keys, where A is represented by 1 and so forth:

https://www.youtube.com/watch?v=OMq9he-5HUU

Here is the value of pi (π) with 1000 digits after the decimal point:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989...