## Π- PI

Introduction

Whenever we hear the word pie, we imagine it to be a chocolate pie. But as we grew up a different meaning of pi was revealed, which cannot be eaten but is the ratio of a circle’s circumference to its diameter approximately equal to 3.14. Pi is denoted by symbol (π).

Origin of pi

• The value was obtained by calculating the perimeter of hexagon inscribed within a circle, reportedly by the Babylonians in 2000 BCE using the approximate value of pi as 3.125. The ratio of the hexagon’s perimeter to the circle’s circumference was assumed as 24/25.
• People in ancient Egypt considered the value of pi to be 256/81 or 3.16045. In 250 CE, Greek scholar Archimedes invented an algorithm for finding the exact value of pi by constructing regular polygons that fit exactly or are enclosed within a circle. Archimedes’ algorithm was extended to polygons having 96 sides.
•  The calculation was further continued by Pythagoras’s theorem which was used to estimate the lower and upper limits of pi to establish the relationship between the lengths of the sides of a regular polygons when the number of sides were doubled.

Squaring the circle

• Squaring the circle was a popular challenge in ancient Greece by the scholars.
•  It involved the construction of squares and circles of the same area just by using compasses and straight edges for construction.
• The Greeks would place a square on a circle and then use their intellect to estimate the area of a square to the approximate area of a circle.
• However, the Greeks didn’t find any success in this due to the irrational nature of pi.

Applying pi

• Application of pi is useful in various fields such as geometry, science, nature, trigonometry etc.
•  Π is used in numerous important formulas in the subjects of statistics, fractals, thermodynamics, mechanics, cosmology, number theory, and electromagnetism.
• It is also used to check the accuracy of a computer, it can definitely detect any issue with the software or hardware.
• Values of functions of trigonometry terms such as sine, cosine, and tangent are derived from pi.
• Circular velocity of things such as truck wheels, motor shafts, engine parts, gears can be measured. It’s not humanly to measure the length of ocean wave but it has been made possible because of pi.
•  Similarly light waves, sound waves, river bends, and radioactive particle distribution can also be measured.
• Pi is used by electrical engineers in their applications. While conducting survey and studying population dynamics, pi is used.
• Even the most important thing in our lives, that is time applies pi. Pendulums of a clock are designed using pi.
• Pi is of utmost importance in calculations done by the space scientists. The lengths of orbits at different altitudes above the surface of the planet can be calculated using the principle; the circumference of a circle can be calculated easily if we know the diameter of the circle.
• In 2015, scientists of NASA used the same method to calculate the duration taken by the spacecraft Dawn to orbit Ceres.
• Again, when the scientists at NASA were wondering about the availability of hydrogen at Europa, one of Jupiter’s moons, they calculated Europa’s surface area by using the formula 4πr2, as per the formula for ensuring the availability of hydrogen in a given unit area.