PI - THE CIRCULAR VALUE

By Miraya Kwatra


So, the very first thing you have to do is go to the website of The Scientific Teen. Next, you’ll see an “Articles” dropdown next to the “Home” option. Click the sub option, “Mathematics” and voila! You’ll spot a very big sign, with two legs and a horizontal line for a head. That’s Pi (π)!

The STEM world recently celebrated Pi Day, a day dedicated to pi, the constant that has helped in the development of everything. Everyone, from astronauts to engineers to students, use pi! Now, most of you would be aware of the uses of pi. But have you ever wondered, “What exactly is pi?” You’ll get this and many more answers in the following article.


DISCOVERY AND HISTORY

Everything had a beginning, including pi. Many people, including Chinese and Greek scholars, had worked on the theory of pi for many years. A very long time ago, Babylonians found out a value approximating to three. This was indeed almost coming up to 3.14. It is also said that in 250 BC, Archimedes of Syracuse was the first person to do the calculation of pi in a similar way to what is done today.


FUN WITH PI


The value of pi is known. But do you still sometimes find yourself wondering how it really is what it is? There are a number of ways that can give evidence on this theory. An interesting method is to perform the Pi Toss. It is done by randomly and unevenly throwing toothpicks on a flat surface which has lines ( equally distanced and the distance should be twice the size of the toothpicks) made on it. Some toothpicks will fall in between the lines, while others will fall on the lines, bisecting them and making a cross. We then divide the number of toothpicks that are thrown to the number of crossings that are made. You’ll see that the value that’ll come will be very close to 3.14. As you go on with the procedure by increasing the number of toothpicks, you’ll see that the quotient will keep getting closer to pi. It’s all got to do with the length and also the angle at which the toothpick falls. If your lines are not in the right proportion with the toothpick, you won’t get an approximation to pi.



While we are talking about ratios and proportions , let me also tell you that, the constant, pi, in a circle is the ratio between its circumference and diameter. Check this out. Let’s take a circle of a diameter measuring 4 cm and the circumference being 12.56, now when we divide them, we get….. 12.56 / 4 = 3.24. Wonderful, right?


As the number of toothpicks increase, naturally, the crossings increase too. This graph shows how with more crossings with the corresponding toothpicks, the value comes very near to pi.


ELEMENTS OF A CIRCLE IN RELATION WITH PI


If we can find the circumference ( i.e. the length of the boundary of the circle.) , we’ll be able to calculate its diameter with the help of Pi. Or, it can even be the other way round. For instance there’s a circle with a radius of 4 cm. If we go by the formula, the circumference of a circle is 2πr. That means, the circumference of this circle will be, 2 ✕ 3.14 ✕ 4 = 25.12 cm. No matter how big the circle is and what the constants of the different elements of it are, by hook or by crook pi cannot deceive you by its numericals. You can try it out yourself by dividing the product of the diameter and radius by the circumference. Although it won’t be 3.14, because well, it is an approximation, and so it will be nearing it. According to the values given for the circle above, if we want to look for pi, we’ll get approximately 3.13.


HOW IS PI USED IN PLACES LIKE NASA?


NASA is full of engineers, space scientists, astronauts, and mathematicians. All of them, as I said before, use pi, in almost everything. Some examples and the reason behind them are given here —


An interesting use of pi is measuring the area and other elements of a circular hole or a circular bend, and then determining what would’ve caused it, on a particular planet or any other cosmic body.


It can also be used to compare the size of two moons or planets, for instance. By using the value they can perform complex calculations and make ground breaking discoveries!


Food For a spacecraft ! Yes, NASA also uses pi to calculate the space ( as in area) and the ratios of spherical spacecrafts and that helps them to hit on the right fueling capacity.


In our daily lives for calculations related to circular objects we usually use pi as 3.14. But, here’s the thing: pi is a recurring division, meaning it can never end. That is the reason why we only limit it to 3.14 , to make the calculations easier. But, scientists and engineers also sometimes take more decimal positions in regards to different types of problems. All the answers that we get with pi are not exact but are very sufficient and don’t matter much. The calculation would still be correct. Pi is most certainly used in space agencies and for engineering purposes , but in our day-to-day activities pi can play an integral role too. For example, the pie, professional bakers make, they often measure the size of their food for presenting it in competitions. Gardeners, who want to make their gardens beautiful and proper, may also use pi to measure certain areas.


How captivating was all that? Had you ever imagined that a simple number like pi could have so much to it?!



REFERENCES:

Exploratorium (n.d) A Brief History of Pi (π)

https://www.exploratorium.edu/

https://www.exploratorium.edu/pi/history-of-pi#:~:text=The%20first%20calculation%20of%20%CF%80,mathematicians%20of%20the%20ancient%20world


Exploratorium (n.d) Pi Toss

https://www.exploratorium.edu/

https://www.exploratorium.edu/snacks/pi-toss


NASA (n.d) 18 Ways NASA Uses Pi

https://www.jpl.nasa.gov/

https://www.jpl.nasa.gov/edu/learn/list/oh-the-places-we-go-18-ways-nasa-uses-pi/


IMAGES:


Pillsbury Kitchens ( 2013, March 13) Triple Berry Pi Day Pie https://www.pillsbury.com/ https://www.pillsbury.com/recipes/triple-berry-pi-day-pie/e1a7c76c-cb8e-4a9b-97b7-a0b62aca45ad


Exploratorium (n.d) Pi Toss https://www.exploratorium.edu/

https://www.exploratorium.edu/exhibits/pi-toss