Pi is a fundamental notion that arises in all areas of mathematics. It is a vital principle that aids in the comprehension of universal truths as well as certain mathematical topics. Pi values are often employed in trigonometry, geometry, and sophisticated concepts such as probability, statistics, and complex numbers. Pi is denoted by the symbol π. If you ask any scientist about pi, they will tell you that the decimal value of pi is 3.14159. However, if you ask a mathematician, they will tell you that pi is a number equal to circle circumference divided by circle diameter. It is a well-known mathematical constant that is utilized all around the globe. So, on Pi Day, let's learn about the mathematical importance of pi while eating a pie.

Moving on from its name to its value, sources state that the Babylonians estimated in base 60 circa 1800 B.C.E. Indeed, they thought that = 25/8, or 3.125—an incredible estimate for so early in human history. Ahmes, an ancient Egyptian scribe linked with the renowned Rhind Papyrus, proposed the estimate 256/81, which works out to 3.16049. Once again, we observe an excellent approximation to this constant. The Bible even has an implied value of provided. A circular bowl with a 30-cubit circumference and a 10-cubit diameter is described in 1 Kings 7:23. As a result, the Bible indirectly indicates that equals 3 (30/10). Unsurprisingly, as humankind's comprehension of numbers grew, so did its capacity to better comprehend and hence assess itself. Liu Hui, a Chinese mathematician, believed that = 3.141014 in the year 263. Around 200 years later, the Indian mathematician and astronomer Aryabhata estimated using the proportion 62,832/20,000, which equals 3.1416. Kashani, a Persian astronomer, calculated properly to 16 digits about 1400 AD.

Figure 2 - Visualization of Pi. Source - Google

What is remarkable is that it occurs in a wide variety of mathematical settings and across all mathematical domains. It turns out that is the ratio of a circle's area to the area of a square constructed on the circle's radius. That seems to be a coincidence since was specified as a different ratio. However, the two ratios are the same. is also the ratio of a sphere's surface area to the area of a square formed on the diameter of the square. What about the ratio of the volume of a sphere to the volume of a cube constructed on the diameter of a sphere? That is π/6.

y=1/(1+x2) is the area under the bell-shaped curve. However, this is not the well-known and ubiquitous bell-shaped curve found in statistics, which has the formula y=e. The area under that curve is the square root of π! If you put a one-centimeter-long pin on a sheet of lined paper with lines spaced at centimeter intervals, the likelihood that the pin will cross one of the lines is 2/π. If you choose two whole numbers at random, the odds of them having no common factor are 6/(π)2.

There are hundreds of formulae of π one kind or another, but it's unclear if any of them will fulfill the urge to know precisely what is. This is one such formula -

 Figure 3 - Formula. Source - Google

where the sigma sign denotes that in the following formula, all whole integers must be substituted for the symbol "k" and the resultant is infinitely many fractions added together. This statement is notable since it was founded by the great Indian genius Srinivasan Ramanujan in 1914 while working alone. Nobody knows how Ramanujan came up with such a brilliant formula. Furthermore, his formula wasn't even shown to be right until 1985—and even proof required high-speed computers, which Ramanujan didn't have access to.

Moving away from the mathematical and scientific world, let us look at the influence of pi in the art world by math artist, John Sims. Sims is an African American conceptual artist whose mathematical background inspires a diverse spectrum of creative work. He has represented pi in a variety of media, including math music, films, drawings, paintings, quilts, apparel, and tales.  Sims is interested in both the practical math part and the symbolic and metaphysical implications of pi. His math art is more than just cerebral or aesthetic—it's also emotional and political, a study of identity.

Figure 4 - John Sims Photograph. Source - Google

The number π  is a mathematical constant that can be found anywhere. In fact, to term, it being "universal" is an understatement, for it exists not just in our reality but in every imaginable universe. It is constant and everlasting.

 Anand Subramanian is a freelance photographer and content writer based out of Tamil Nadu, India. Having a background in Engineering always made him curious about life on the other side of the spectrum. He leapt forward towards the Photography life and never looked back. Specializing in Documentary and  Portrait photography gave him an up-close and personal view into the complexities of human beings and those experiences helped him branch out from visual to words. Today he is mentoring passionate photographers and writing about the different dimensions of the art world.

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