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- The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for π, which is a closer approximation.
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- The Rhind Papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π.
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- The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world. Archimedes approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which the circle was circumscribed.
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- Since the actual area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave upper and lower bounds for the area of the circle. Archimedes knew that he had not found the value of π but only an approximation within those limits. In this way, Archimedes showed that π is between
3 1/7 and 3 10/71. Decimal version Pi is between 3.14285 and 3.140845.
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- A similar approach was used by Zu Chongzhi (429–501), a brilliant Chinese mathematician and astronomer. Zu Chongzhi would not have been familiar with Archimedes’ method, but because his book has been lost, little is known of his work.
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- He calculated the value of the ratio of the circumference of a circle to its diameter to be 355/113. To compute this accuracy for π, he must have started with an inscribed regular 24,576-gon and performed lengthy calculations involving hundreds of square roots carried out to 9 decimal places.
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- Mathematicians began using the Greek letter π in the 1700s. Introduced by William Jones in 1706, use of the symbol was popularized by Leonhard Euler, who adopted it in 1737.
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- An eighteenth-century French mathematician named Georges Buffon devised a way to calculate π based on probability. You can try it yourself at the Exploratorium.
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- The study of numbers is called “number theory” . It date backs to 2000 B.C. When the Babylonians applied the Pythagorean Theorem to approximate the square root of 2.
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- Then in 540 B.C. Pythagoras founded his school and proved the Pythagorean Theorem. The students were confounded by the proof that irrational numbers exist.
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- In 300 B.C. Euclid presented his axiomatic method for geometry. His book “Elements” proved the infinity of prime numbers: And, the irrational number for the square root of 2. And, the fundamental theorem of arithmetic.
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- In 200 B.C. Eratosthenes developed the equation for finding prime numbers up to a given value.
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- In 210 - Diophantus publishes 13 volumes on algebra, “Arithmetica”
- In 1202 - Fibonacci describes his sequence. (See another Review to learn about this).
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- In 1570 - “Arithmetica” translated into Latin.
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- In 1637 - Fermat asserts his last theorem.
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- In 1736 - Euler publishes proof of Fermat’s theorem.
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- In 1737 - Euler establishes analytical number theory.
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- In 1742 - Goldbach conjecture that every number past 4 can be written as the sum of two prime numbers.
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- In 1750 - Euler proves Fermat’s theorem is true for n = 3.
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- In 1770 - Lagrange proves irrational number can be obtained with a periodic fraction expansion.
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- In 1785 - Gauss derives formula to derive sum of “n” natural numbers
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- In 1792 - Legendre and Gauss define the prime number theorem.
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- In 1801 - Gauss introduces modular arithmetic.
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- In 1820 - Germain enhances Fermat’s last theorem
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- In 1837 - Euclid’s theorem extended to infinite of primes.
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- In 1839 - Proof of Fermat’s last theorem is flawed.
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----------------------------- Other Reviews about Pi , available by request:
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- 2308 - Nuclear Reactions and Pi from Breadsticks? Throwing breadsticks on a tile floor is a random process. The probability of a stick touching a line is 63.7%. The ratio of hits to total tosses is 2 / pi = 2 / 3.14 = 63.7%. Georges Buffon figured this out in the 1700’s.
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- 2137 - The history of Pi. By definition, pi is the ratio of the circumference of a circle to its diameter. In other words, pi equals the circumference divided by the diameter (π = c/d). Conversely, the circumference of a circle is equal to pi times the diameter (c = πd). Pi has been known for nearly 4,000 years and was discovered by ancient Babylonians.
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- 1023 - - Our history tells us that the number “Pi” was first approximated in 1,900 years before the birth of Christ. “Pi” was known to be the ratio of the circumference of any circle to its diameter. The calculation was done to the base 60 not to the base 10. To the base 10 their calculation was a little greater than 3.
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- 803 - Transcendental Numbers : “e” and “pi”. Transcendental means “beyond human experience“; but, not beyond human knowledge. Supernatural, but still natural numbers. Numbers are just inventions man created for counting. 0, 1,2,3,4,5, ….. How could numbers be supernatural? We started by simply counting our fingers. We started with positive numbers and it took a while for man to accept negative numbers. For several centuries man could not believe that there could be something less than nothing.
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- March 14, 2020 2667
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