Not everything goes on forever. Be it your period of happiness, sadness, success, the supply of your favorite food or your favorite television series. But that is not the case with Pi. Pi goes on forever. Pi is a numerical constant that is the superstar of mathematics and by extension physics. Its importance cannot be overrated. Pi to an approximation of ten digits is 3.141592653. This seemingly random number is so important that for three decades March 14 is celebrated as the International Pi-Day annually. The month March (3) along with the 14th day makes up the first three digits of the number. The mathematician’s craze didn’t stop there on the pi day in the year 2015 at 9:26:53 AM was celebrated as Super Pi-Day. But careful! Don’t confuse this mathematical celebration with the gastronomical celebration called Pie Day celebrated on January 23 every year in which the participants eat a lot of pies. Though that does not mean you cannot eat pies on Pi-day, on the contrary
What’s so special about 3.1415926………. aka Pi ?!
The Universe is a strange, and mathematics stranger. In the most common language, Pi is obtained when the circumference of a perfect circle is divided by its diameter in a plane surface or Euclidean surface. Hence this won’t be true for a circle drawn on a curved surface. This was discovered long ago, since 300 BC or more. This was important for people to make geometrical shapes. Pi is an irrational and transcendental number. Irrational numbers are those that cannot be expressed as fractions and keep going on forever without any repeating pattern of digits. Though Pi is sometimes substituted by 22/7, it should be known that this is just an approximation to the constant. There are many such substitutions for Pi like 223/71 and 339/108. In true sense, pi is infinitely long. Transcendental numbers are numbers which are not the roots or solutions) of any algebraic equation with natural coefficients. Let me explain that in a much easier way. If a number cannot be reduced to 0 by either multiplying, adding, subtracting or raising it to a power using whole numbers, then that number is called a transcendental number.
The importance of Pi can be understood from the fact that it appears in almost every mathematical equation or formula. Some of them are discussed below:
- Volume of a cylinder and a cone: This is equal to Pi times the product of the square of the radius of the cylinder its height. Volume of a cone is 1/3 of the volume of a cylinder of the same height and radius.
- Volume of a sphere: This is equal to the product of pi and 4/3 times the cube of its radius.
- Calculation of electrostatic force and magnetic force: In the calculation of electrostatic and magnetic force the constant pi is used.
- Pi is also used in the calculations concerning the evolution of the Universe as a whole and the galaxies within.
How can you find pi?
Since centuries people have been fascinated y pi, studied it, and have tried their best to remember its digits. As of now, we have calculated pi till a trillion digits using supercomputers. It has now become a trend among the intellectuals to memorize the number to as much length and accuracy as possible. This is made truly difficult because of the fact that the digits in it a truly random and pass all the tests of randomness.
Here are a few ways to calculate pi:
- Archimedes polygon method: In 250 BC Archimedes came up with a creative method to calculate pi. In this method, he took a circle of unit size. Within the circle, he drew a triangle inscribed in it. The vertices of which just touched the circumference. Using the perimeter of the triangle he calculated pi to an approximation. Then he made a polygon with double sides, that is a hexagon, and used it perimeter to do the same. He kept on doubling the sides and calculated pi using a 96-sided polygon. Since these polygons lie inside the circle, the approximation is always less than actual pi and set a lower limit to it. Similarly, drawing polygons circumscribing the circle such that their faces just touch the circumference and using them to calculate the constant pi sets an upper limit to it.
- Using the infinite sum: 4 x (1 – 1/3 + 1/5 – 1/7 + 1/9…… )gives successively more accurate approximations to pi.
- Pi is twice the natural number at which the value of cosine is zero
A dive into the history of international Pi-day
Pi Day started as a celebration of the constant in the San Francisco Exploratorium in the year 1988 by Larry Shaw. He organized a march around the central circular ground and then everyone ate pies and discussed the grandeur of the universal constant. Since then the trend caught over and soon General Assembly of USA passed a non-binding bill that 14th of March every year shall be celebrated as National Pi Day. Henceforth the mathematicians and math fans everywhere around the globe celebrate this day as a tribute to the constant pi. Quizzes are organized, pi is calculated to as much accuracy as possible and much more and people try to spread awareness about the importance of this seemingly random number.
The importance of pi or 3.141592653…… can really never be truly appreciated. It is one of the numbers that control the behavior of the universe and brings out the beauty of geometry. So the next time you relish a cake, a pizza, or the classic pie, do remember that no matter what their size, their boundary divided by their diameter would give the number PI.
-Shantanu Ashima Gaur