PI DAY

 INTRODUCTION

Happy PI day everyone, if you dont get why it is pi day today, its just 3/14 , ie the digits of pi.

Pi is a really beautiful number, and one of the most important numbers in mathematics, lets have a tiny look at what pi actually is.

WHAT IS PI?

Pi(π) is a mathematical constant that is a ratio of a circle's circumference to it's diameter.

For example, if there is a circle with the diameter being 1 unit, the circumference of the circle will be 1π unit.

The beauty about pi is that, there is no known exact value of pi, the decimal value goes on forever, and there is no repetitive pattern in the decimal value of pi.

In 2021, there has been more than 62.8 TRILLION decimal values of pi discovered.

HISTORY OF PI

One of the earliest formulae for calculating pi was proposed by English mathematician John Wallis in 1656. While calculating an integral in an attempt to find the area of a circle with a radius of one, he established a formula involving the multiplication of an infinite series of fractions that was based on the value of one-half of pi. Later that century, Sir Isaac Newton — in one of his many achievements — used his binomial theorem to quickly calculate the value of pi up to 16 decimal places.

Next came the Gregory-Leibniz series, which made use of both infinite series and trigonometric functions to develop formulae for values of pi divided by four and six. By the end of the eighteenth century, over one hundred digits of pi had been calculated using this method and others derived from it. 

In this same century, two major developments also occurred concerning the nature of pi: in 1761, Johann Lambert proved that pi was irrational — that is, that it cannot be expressed as the ratio of two numbers — and Ferdinand von Lindemann concluded that it was transcendental soon after. It was also during this period that the use of the Greek letter pi was introduced by William Jones, in 1706, and that it was later popularized by Leonhard Euler, beginning in 1737.

Progress slowed once again for the next few hundred years, as more calculations were made but with little conceptual development. Eventually, though, in the early twentieth century, Indian mathematician Srinivasa Ramanujan developed an incredibly efficient formula for calculating pi based on its reciprocal fraction, which was later incorporated into computer algorithms. 

The subsequent development of more advanced computers meant that pi could be calculated to higher and higher 

decimal places. By 1949, the ENIAC computer could calculate 2,037 digits of pi, and the IBM 704 was able to calculate 16,167 digits a decade later. The IBM 7090 broke the 100,000 digit mark in 1961, and the CDC 7600 was able to reach pi’s millionth decimal place in 1973. 

VISUALIZING PI

How can it even be a svraj blog of we dont visualize anything, there are multiple ways in which we could visualize pi, but the one which I found the most interesting and beautiful was the Daniel Shiffman's ( The Coding Train) processing code.

Here are a few snippets below. 

IT LOOKS LIKE A MOON DOESNT IT