The origin of Pi (π) dates back some 4000 years to the ancient civilizations. It is a mathematical mystery that has caught the attention of every mathematical enthusiast through the centuries. In Euclidean geometry, Pi is defined as the ratio of a circle’s circumference to its diameter, but it has other equivalent definitions as well. Pi is termed as a mathematical constant that has an approximate value of 3.14159. It is always fun to try to calculate the value of Pi as it can go on forever! As far as calculations go, Pi has been calculated to more than 22 trillion digits. It just took one computer working tirelessly for 105 days with 24 hard drives to calculate it.

The History of the Use of Pi Since Ancient Times

Pi has been in use in several branches of mathematics, statistics, geometry, and others for ages. But the name “Pi” is a relatively recent activity. In 1706, William Jones, a British mathematician, was the first person to call it, Pi, connecting with the Greek letter π.

Let us see how Pi, as we know it today, came into being:

1. In ancient Babylon, the area of a circle was calculated by taking three times the square of its radius, which yielded the value of Pi, which equalled three. The value of Pi was 3.125, as found on a recovered Babylonian tablet.
2. Some examples of Egyptian mathematics can be found in Rhind Papyrus around 1650 BC. The ancient Egyptians used a formula to determine the area of a circle that provided the approximate value of Pi as 3.1605.
3. William Jones introduced the symbol of Pi in 1706, which was later popularized by Leonhard Euler, who adopted it in 1737.
4. George Buffon, a French mathematician, introduced a way to calculate the value of Pi using probability.

Now, let’s try a simple experiment to derive Pi.

On any piece of paper, draw a circle (of any size) using your compass. Place one string on top of the circle and go around it once more, then straighten the string out. Its length will give you the circumference of the circle. The circle’s diameter is two times the radius (the length from any point on the circle to its center). Lastly, divide the circumference by the diameter. Surprisingly, the value will be 3.14⏤no matter the size of your circle! If you have measured and calculated everything correctly, you have derived Pi, which is 3.14.

Modern Applications of Pi in Different Areas of Life

Some might call Pi the most famous number in the world. Pi is so popular amongst people that it has its own dedicated day⏤Pi (π) Day, celebrated on March 14th every year with much pomp worldwide. Though Pi has a strong influence in mathematics and geometry, it also has other significant uses:

1. Sound and Light – Sound and light waves play crucial roles in the functioning of the world, like,
• Pi can be found in sine waves, which are basically used to process signals in sound and light waves.
• Pi also has other uses, like sound waves used for taking an ultrasound of a baby in the womb.
• Pi helps in studying the frequency, wavelength, and amplitude of ocean waves.

Pi also helps to study how springs bounce, strings vibrate, and pendulums swing.

1. Genetics – The most basic structure of the human body is DNA. Guess what? Pi can be found in human DNA. For the lengthy DNA (around 1.8 meters in length) to fit into the small area of the body cell (around 10 microns in diameter), it forms nucleosomes that look like a string of beads, and this string is 1.5 times shorter than our DNA. Pi is also found in the spiral of the double helix in DNA. The structure of the double helix is held together by Pi bonds, which are stacking interactions that help to keep the structure in place.
2. Natural Surroundings – Any circular object with a diameter and circumference in our surroundings can have Pi applied to it⏤from the round pupil of our eyes, the moon, the sun, and even in the rainbow. Pi finds its use in many natural phenomena, like
• It can be found in the pulsing of the heart.
• Pi is also used to measure ripples originating from a central point.
• It is used to measure the sinuosity of rivers.
• Pi can also be found in the solar system.
1. Astronomy and Astrophysics – Since ancient times, Pi has been used to study the universe and our solar system. Let’s see how:
• For searching for new planets and their atmospheres
• Used in the calculation of the number of seconds in a year.
• Many space centers also use Pi to calculate a spacecraft’s trajectory and learn about asteroids and meteors.
1. Pi in Patterns – Did you know that the patterns of animals like zebra or leopard depend on Pi? It’s a wonder how Pi plays such a vital role in the animal kingdom. Alan Turing, an English mathematician, theorized that Pi is the constant that governs the various patterns exhibited by living creatures while still in an embryonic state. He termed this process “morphogenesis.”

Pi is one of the most celebrated numbers in the world and can be found in several branches of mathematics, physics, bioscience, and astronomy. Though it might be difficult to put together all the numerous uses of Pi, we surely cannot deny it. It started its journey in ancient mathematics and astronomy, but nowadays, it can be found in almost all areas of our physical world and even the universe!

What are your thoughts on Pi and its applications? Let us know in the comments section, and check out more such BYJU’S FutureSchool’s blogs.