Pi Day – MathQ

March 14th, Pi($\pi$) Day! It’s that special day where math enthusiasts and pie lovers around the world come together to celebrate one of the most fascinating numbers in existence of human history. Pi Day was started in 1988 by a physicist at the Museum of Science in San Francisco. Eating various circular pies is a bonus.

$$ \pi = \frac{C}{d} $$

$\pi$ is a number that is derived from dividing the circumference of a circle by its diameter. It is an infinite decimal that does not repeat. That is why it is called an irrational number. $\pi$ starts with 3.141592…

$\pi$ would have been a natural ratio if you used circular objects. I guess it probably arose when using tools like cartwheels or measuring distances using circles.

The practical use of $\pi$ dates back to around 1900 BC. The Babylonians used $\pi$ as 3 1/8 (3.125). The Egyptians used $\pi$ around 1650 BC, and their approximation was 3.1605. Around 250 BC, Archimedes approximated $\pi$ using geometric methods using inscribed polygons and circumscribed polygons around a circle. His calculations were between 3 10/71 and 3 1/7 with polygons with 96 sides. Around 500 AD, a Chinese mathematician calculated up to seven decimal places, which was close to 355/113.

In the 17th century, a method for calculating $\pi$ using infinite series was introduced. In 1914 an Indian mathematician Srinivasa Ramanujan published several formulae for $\pi$ including

$$ \frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^{\infty} \frac{(4k)!(1103+26390k)}{k!^4(396)^{4k}} $$

The Chudnovsky formula developed in 1987 is

$$ \frac{1}{\pi} = \frac{2\sqrt{10005}}{4270934400} \sum_{k=0}^{\infty} \frac{(6k)!(13591409+545140134k)}{(3k)!k!^3(-640320)^{3k}} $$

Nowadays it is possible to calculate up to trillions of decimal places of $\pi$ with modern computers.

$\pi$ is a very important number used in almost all modern technologies, including GPS. When we send a spacecraft into space, we need to use a more accurate $\pi$ to reduce errors due to long distances and long periods of time.

Interestingly, many of the pies we eat seem to be circular. From pizza pie to pecan pie to pumkin pie, etc. It might be fun to think about $\pi$ every time we eat round pies.