![]() Later, in the 5th century A.D, Chinese mathematicians further squeezed the walls on π - they found that it lay somewhere between 3.1415926 and 3.1415927, an unprecedented accuracy that Europe wouldn’t attain until the 16th century. Due to his unflinching diligence, the ratio is also known as the Archimedes constant.Ī more fitting polygon would enable us to calculate the value of π with superior precision. Hearing this, the soldier grew incensed and decapitated him with his sword. In fact, Archimedes was so engrossed with his diagrams that when a Roman soldier tried to arrest him while the city was under siege, he reportedly berated the soldier and asked him not to “disturb my circles”. Archimedes arrived at a window for this constant between 3 10/71 and 3 1/7. This continued until he drew a highly detailed 96-sided polygon that would fit the curved line like an envelope. Then he doubled their sides until the polygons approximated it almost perfectly. He devised a way that allowed him to calculate π’s value to any degree. Archimedes initially inscribed and circumscribed not squares, but hexagons, in and around the circle. This is exactly what Archimedes, arguably one of the greatest scientific and inquisitive minds of antiquity, did. In the above example, a more fitting polygon would enable us to calculate it with superior precision. A few Babylonian texts, however, inferred π to a more precise value of 3.125. ![]() Babylonians believed that the area of a circle is three times the square of its radius, which implied that the value of π is 3. Thus, we have realized that the value of π lies between 3 and 4. What’s more, the area is surely greater than, which also gives us the lower limit. This gives us an upper limit to the value of π. However, discounting the negative space, it is clear that the area of the inscribed circle must be less than. Now, the area of one square is , such that the area of the entire square is. This is nothing but a pizza in a square box. ![]() Because the ratio is so intimately linked to circumference, the Greeks called it π, which is Greek for ‘p’, the starting letter of the word periphery.Ī circle can be circumscribed by a square to approximate its area. The two can therefore only be linked with a constant - the ratio of the two proportional quantities, namely diameter and circumference. One thing is obvious – the circumference or area of a circle is directly proportional to its diameter as the ring expands, logically, so does the area it covers. Even something as trivial as finding the area of a circle is a challenge. However, their nonlinear shape makes studying them quite difficult. (Photo Credit: Remi Jouan / Wikimedia Commons)Ĭircles are some of the most ubiquitous shapes in the Universe. Impatient kids would use the value 3.14 - the quotient of the division 22/7 - and become trapped in the web of arduous decimalized calculations. Back then, multiplications had to be performed manually, without the help of calculators. The indulgent authors of the textbook tested us with problems involving a calculation where an adroit trade of symbols across the equal-to sign would ensure that the ratio is canceled, and the calculation loses its complexity. The chapter claimed its value was equal to the ratio 22/7. All the shapes harboring a curve were described with the help of a constant that appeared to be a miniature pair of diverging swings hanging from an extended metal bar – π. I had never looked at these whimsical shapes so analytically before. The long chapter illuminated the many ways we can gauge aesthetics – the perimeter of a rectangle, the area of a circle and the volume of spheres. I was first introduced to π in middle school, in what seemed to be an interminable chapter called Measurements. It is at the blunt end of a pin and in the heart of magnificent sunflowers. It is in the letter ‘O’ painted so cautiously on my keyboard and the physiognomy of the number ‘9’ just above it. ![]() It is in the outline of capacious domes worn like skull caps by sanctimonious cathedrals. It is in the blinding disk drawn by the Sun and on both sides of my unlit cigarette. The number of digits is currently known to surpass 2 trillion! This implies that the number 3.14 or even 3.145926 is an outrageous approximation. Pi is so important because it is a transcendental, irrational number – the digits occurring after the decimal point are inexhaustible. ![]()
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