Know your pi and eat it too!

Sundaram S

The world of mathematics is mysterious, strange and magical. One often comes across interesting and strange numbers. One such number is the π. This number has been known for over 5,000 years. In fact, it is the first of such interesting numbers discovered by humans. It was discovered independently by many civilizations in China, India, Greece, Egypt and Sumeria.

It was given the name “π” from the 18th century. It is written like the Greek letter π & pronounced as “pi” or “pie”.

Drawing a circle
Humans in all civilizations discovered that the world is made of different kinds of shapes, like circle, cylinder, cone, etc. They saw that the Sun and the Moon were circular in shape. They also realized that the circle was one of the easiest shapes to draw perfectly.

Discovery of π
All civilizations discovered interesting facts about the circle. They found that when you divide the length of the circumference of any circle by its diameter, the answer was almost the same! This was true for “any” circle of any diameter! So, they knew it was a “constant”.

They also discovered that the formula for the area of a circle also involved the same constant.

Estimating the value of π
An accurate value of π was also important for the government and kings. Every government levied tax on the size of the land owned by farmers. An accurate value of π would determine the area and circumference of circular fields and wells correctly so that tax was not underestimated.

Another reason was that the human mind is always curious. Once they discovered this special number (which we now call π), they also wanted to find its exact value.

One of the first estimates was 3. Another was √10(square root of 10, which is a number which when multiplied by itself will give 10) or approximately 3.162278.

Various civilizations estimated the value of π to 6 or 7 decimal places. Archimedes estimated π to be between 223/71 and 22/7 which in decimal form means it is between 3.140845 and 3.142857.

Attempts to discover the exact value of π also revealed that it was actually a “strange and interesting” number.

The strange number π
It was discovered that π can never be exactly written as a fraction of the form a/b. The commonly used value 22/7, is an approximation.

It is a number whose decimal part consists of a continuous series of digits which literally “never ends”. It means that π can never be written down in full. All the paper in the universe will never be sufficient to write down π! It would be a good idea to print out the value of π to 10,000 digits (available on the Internet) and string it like a ribbon around the corridors of the school. This will bring the idea of infinity understandable to even primary school children in a very real manner!

π contains all other numbers!
Another strange fact is that any number that you can think of, like your date of birth or your salary or your mobile number can be found somewhere in the decimal part of π. The only issue is that we will not know where to look for them!

In 2010 a mathematician worked out that the two-quadrillionth digit of π is a 0! But he did not calculate the in between digits. He does not even know the digits on either side of this 0!

Accurate value of π
Today the accepted value of π to 7 decimal places is 3.1415927.

In schools we take π as 22/7 which works out to be 3.142857. This is close to the actual value of π. It can be used in place of π, for our normal day to day purposes (like estimating the length of fence required for a circular garden). Even for calculating space travel distances, 15 decimal places of π is sufficient!

But every year more and more digits of π are being calculated. In the last few decades, the development of computing has enabled the calculation of unimaginable number of digits of π. On 14th March 2019, Emma HarukaIwao, a Google employee from Japan, calculated 31 trillion digits of π using Google’s cloud computing service.

Why is there this craze about finding more digits of the π? There are several reasons.

Calculating the unending digits of π
One is the ever-present human urge to discover the unknown.

Another reason is related to computing the power of computers. The time taken to calculate the digits of π can be used to compare the “computing power” of different supercomputers.

Yet another reason is related to the science of computing. Trying to calculate more and more digits accurately is also a technical and computing challenge. The discovery of new computing methods leads to further developments in science and technology.

World π (Pie) Day
The world started celebrating “π Day”, starting from 1988. Why was 14th March chosen as the π Day? In the US, 14th March is written as 3/14 which is the value of π to two decimals.

Americans have a knack of converting anything into business opportunities. So, the idea of π Day was converted to Pie Day. Many schools celebrate it by ordering and eating pies which is good business for restaurants! But in that process the real π is many times forgotten.

22nd of July (22/7) could also have been named the Pie Day if India had taken the initiative in such matters. In fact, 22/7 is a better approximation of π compared to 3.14.

π moment
American mathematician, Steven Strogatz noted that the “π moment” happened in the year 2015, exactly on 3.14.15 at 9:26:53!

The lighter side of π
There are many jokes related to π. Two of them – “Too much pie increases the circumference” and “Pi’s driving license was cancelled as it did not know when to stop”.

There is also a not too difficult puzzle connecting Pi & pie; √PI + E = √PIE, where P, I & E stand for different numerals! (see fun puzzle below).

π has company now
π is called an irrational number in mathematics. It also belongs to a set of numbers within irrational numbers, which are called “transcendental” numbers.

After the discovery of π, a few other “irrational and transcendental” numbers like e and ϕ have been discovered. Though only a few of these numbers have been discovered, mathematicians have proved that their total number is far more than fractions and whole numbers which we are familiar with.

π and nature
π is intimately connected to the circle. And through the circle, it is related to anything which repeats periodically, which is almost everything in this universe! Hence equations describing many natural phenomena contain π. Scientists and mathematicians are still trying to figure out the exact role played by π in the various processes happening in the universe.

π in primary school
At the same time, it is a number which can be understood by primary school students as it appears in some of the earliest formulae which they come across in the math curriculum. They deserve to know more about this wonderful number to realize the beauty of mathematics.

Fun puzzle: Answer to the problem √16+9=√169.

The author started his school career, lasting 24 years, with the Rishi Valley School. He has worked as a principal, teacher, teacher trainer and educational consultant in several schools in India. He can be reached at [email protected].

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