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The ‘Value’ of Pi Symbol

By Shreyanjana, published on 15/09/2019 We Love Prof - IN > Academia > Maths > The True Value of the Mathematical Pi in Everyday Life

This statement is both literal as well as figurative. While it connotes the actual numerical value of the mathematical concept of Pi, it also denotes the real-world applications of the formula, which enhances it figurative value in our lives. Pi is one of the more enduring as well as endearing concepts that make mathematics fun to learn!

First, a bit of history.

The symbol of Pi, “π” has been derived from two Greek words, viz. “περιφέρεια” (meaning periphery) and “περίμετρος” (meaning perimeter). The Welsh mathematician William Outright is the first documented user of the symbol in the year 1647. However, it only gained popularity in 1748 with the publication of Leonhard Euler’s “Introduction to Analysis of the Infinite.”

In mathematical terms, the formula Pi translates to the ratio between the circumference of a circle and its diameter. Pi is an irrational number and its approximation stands at 3.14 or 22/7.

“If it is merely another formula, why does Pi hold a unique place in mathematics?”

Read on to find out the fascinating story of this unassuming mathematical formula that, as you will discover, is essentially at the core of most things in our everyday life.

Tracing Origins and Evolution

  • Going by historical and archaeological inquiries and records, it was the Babylonians who can be credited with the discovery of the value of Pi ( 2000 BCE). They achieved this feat by calculating the perimeter of a hexagon within a circle and then assuming that the ratio of this hexagonal perimeter to the circle’s circumference was 24/25.
  • The Rhind Papyrus ( 1650 BCE), discovered in 1855 also indicates that ancient Egyptians studied and used Pi. We find mention of the value of Pi in the early historical Indian text, Shatapatha Brahmana (c. 700 BCE) as 25/8 (3,125).
  • In 250 BCE, the celebrated mathematician Archimedes devised a method to accurately determine the value of Pi and published his findings in the essay, ‘Measurement of a Circle’. This mathematical genius astutely figured out ways to estimate the perimeters for polygons with twice as many sides, to arrive at the approximate value of 220/71 <Pi <22/7.

“Archimedes’ principles outlived him by two thousand years!”

Who discovered Pi? The perimeter of the circle (blue) is between the perimeter of the green hexagon and that of the purple hexagon according to Archimedes’ method. (Source: math.psu.edu)

Challenge yourself to find out how many of these mind-boggling mathematical paradoxes you know of!

Life after Archimedes

If you thought that scientific inquiry was a leisurely activity in the old world, you are grossly mistaken. Following Archimedes’ approximation of the value of Pi, there started a positive competition among contemporary mathematicians as well as those of posterity to determine more and more digits of Pi.

Without looking it up, how many digits of Pi can you recite? Who will find the most decimal places of Pi? Source: visualhunt

  • 5 decimal places: Liu Hui adapted Archimedes’ approximation in the 3rd century CE to expand Pi decimals to the nearest one hundred-thousandth.
  • 6 decimal places: Tsu Chung Chih followed it up by expanding Pi decimal to the nearest millionth (3.141592) in the 5th century CE.
  • 14 decimal places: A further ten centuries down the line, Persian astronomer Jemshid al Kashi expanded Pi decimal to 14 decimal places.

“The race to expand the Pi decimal system did not affect the West until the 17th century CE when Leonardo da Pisa Fibonacci added an interesting twist to the enigmatic story of Pi.”

  • 20 to 32 decimal places: German mathematician Ludolph Van Ceulen is credited with the determination of the first 20 decimals of Pi in 1596, using a whopping 480 billion sides of polygons (60 * 233). He then moved on to devise the first 32 decimals in the year 1615. To honour his contributions, the number Pi is also referred to as Number of Van Ceulen.

Heated Competition and a Matter of Prestige

The discovery of analysis and differential calculus proved to be a defining moment in the long evolutionary history of Pi. This led celebrated mathematicians such as John Wallis, James Stirling and Isaac Newton to deduce that Pi was not only geometrically perceived but also be found in the form of a series.

  • From 71 to 100 decimal places: Abraham Sharp got to 71 correct decimal places of Pi in 1699, only to be outdone by John Machin in 1706 who expanded it to a 100 decimals using the arctan function.
  • The advent of the modern-day computer is continuing to push Pi decimal expansion to several thousand billion. The mantle has now been transferred from human to machines. But, the human quest to broaden the horizons of knowledge is never-ending.

“Did you know that there is a group of individuals calling themselves the 1000-club who can recite the first thousand decimal places of Pi? Members include David Thomas (22,500 digits), Mark Aarøe Nissen (22544 digits).”

Still evolving, Pi has provided mathematicians with more mysteries and paradoxes than perhaps the entire gamut of mathematical theories!

The Properties that Make Pi Unique

As already mentioned, Pi is an irrational number. This means that cannot be written as a fraction of two whole numbers (like a rational number). Confused, yet?

Additionally, Pi decimals cannot be predicted. In fact, there exists no mathematical model, not even the mighty computer, on record that can predict Pi decimals. Now, that is unique indeed!

“The discovery of Pi was seen by ancient mathematicians as an affront to God!”

In The Realm of Transcendence

Pi is a transcendental number, which means it cannot be the solution to any polynomial equation with integer coefficients.

However, formulas bind Pi to other mathematical constants such as the Golden Ratio, which corresponds exactly to the construction methods of the Fibonacci sequence.

Is Pi normal?

Mathematicians are still debating whether Pi is a normal number. In other words, it is still a matter of conjecture if Pi can have a finite sequence of decimal places. This has ensured that interest in the concept of Pi has not diminished even after four millennia!

Pi is also an integral part of statistical and probability studies, as exemplified in Buffon’s needle problem.

There is a Pie in Everything!

Yes, you saw that right. Pi is an inescapable part of our everyday life experiences. And, we are not talking geometry classes alone.

Whenever you look at a circle, any circle (such as the Sun, or even a light bulb), you will know that you are looking at Pi.

Pi is everywhere! Oh yes! Pi is all around you! Source: visualhunt

“Even the famous uncertainty principle of Heisenberg has the presence of Pi in it.”

Hey Cheops! Do you rest inside a pyramid or a Pi-ramid?

The golden ratio is to be found in the form of the pyramids What’s the link between Pi and an Egyptian pyramid? Source: visualhunt

Ever wondered how advanced ancient Egyptians truly were in their spirit of inquiry? Just take a look at the magnificent pyramid, err…the Pi-ramid. Calculate the ratio between the perimeter of the base of the pyramid and double the height. Voila! You have your Pi. Was this intentional or a mere coincidence? Perhaps, we will never know.

The Marriage of Mathematics and Literature

For the sceptics who refuse to see the beauty of literature in mathematics or vice versa, here is some food for thought. Our beloved Pi seems to be a peacekeeper between worlds. Don’t believe us? Here is some poetry for inspiration. This is also a fun activity for coding enthusiasts and amateurs!

The following stanza gives thirteen digits of π:

See, I have a rhyme assisting

3    1    4    1     5            9

my feeble brain,

2       6         5

its tasks sometimes resisting.

3      5              9               9

Bet we got your interest piqued!

“Here is a fun fact to make you fall in love with Pi: two math teachers, A. Beveridge and J. Shan, used the mathematical Pi to figure out the lead character in GOT! Even if you are not a GOT fan, you simply cannot ignore the powerhouse that is Pi.”

A Quick Wrap-up

We leave you with a few thoughts to ponder and decide if Pi truly deserves the attention and adulation of a mathematical enigma.

  • Pi has a fascinating history that has kept mathematicians hooked to it for nearly 4000 years, across geographical boundaries.
  • Mathematicians are still unravelling the secrets of Pi. This can only mean that the mystery is far more deep-rooted than originally thought. The symbol of Pi has become a universally celebrated icon.
  • Studies into the concept of Pi have helped restore greatness to the subject of mathematics.
  • A slew of extraordinary properties, unlike any of its mathematical peers, has made Pi a really special phenomenon. Scientists continue to explore and discover the everyday presence of Pi in our lives.

The greatness of Pi has been recognized by scientists and mathematicians the world over. To mark this, March 14th is celebrated as Pi Day. Now, that is what true devotion looks like. We won’t be surprised to find out that the symbol of Pi is worshipped as a God in some corner of the globe!

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