who tried to legislate a value for pi
amateur mathematician Edward J. Goodwin
title: Pi text: reach 71 digits. In ancient China, values for included 3.1547 (around 1 AD), (100 AD, approximately 3.1623), and (3rd century, approximately 3.1556). Around 265 AD, the Wei Kingdom mathematician Liu Hui created a polygon-based iterative algorithm and used it with a 3,072-sided polygon to obtain a value of of 3.1416. Liu later invented a faster method of calculating and obtained a value of 3.14 with a 96-sided polygon, by taking advantage of the fact that the differences in area of successive polygons form a geometric series with a factor of 4. The Chinese mathematician Zu Chongzhi, around 480 AD, calculated title: Pi text: a formula for the area of a circle that treats as () ≈ 3.1605. Astronomical calculations in the "Shatapatha Brahmana" (ca. 4th century BC) use a fractional approximation of ≈ 3.139 (an accuracy of 9×10). Other Indian sources by about 150 BC treat as ≈ 3.1622. The first recorded algorithm for rigorously calculating the value of was a geometrical approach using polygons, devised around 250 BC by the Greek mathematician Archimedes. This polygonal algorithm dominated for over 1,000 years, and as a result is sometimes referred to as "Archimedes' constant". Archimedes computed upper and lower bounds of by drawing a title: Sophistic works of Antiphon text: consolation to the bereaved. In his championship of the natural liberty and equality of all men, Antiphon anticipates the natural rights doctrine of Locke, and the Declaration of Independence. Antiphon was also a capable mathematician. Antiphon, alongside his companion Bryson of Heraclea, was the first to give an upper and lower bound for the value of pi by inscribing and then circumscribing a polygon around a circle and finally proceeding to calculate the polygons' areas. This method was applied to the problem of squaring the circle. Iamblichus' "Protrepticus" contains a lengthy excerpt from an important early author (studied by scholars title: Pi text: regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he proved that (that is ). Archimedes' upper bound of may have led to a widespread popular belief that is equal to . Around 150 AD, Greek-Roman scientist Ptolemy, in his "Almagest", gave a value for of 3.1416, which he may have obtained from Archimedes or from Apollonius of Perga. Mathematicians using polygonal algorithms reached 39 digits of in 1630, a record only broken in 1699 when infinite series were used to title: Pi text: that (a fraction that goes by the name "Milü" in Chinese), using Liu Hui's algorithm applied to a 12,288-sided polygon. With a correct value for its seven first decimal digits, this value of 3.141592920 remained the most accurate approximation of available for the next 800 years. The Indian astronomer Aryabhata used a value of 3.1416 in his "Āryabhaṭīya" (499 AD). Fibonacci in c. 1220 computed 3.1418 using a polygonal method, independent of Archimedes. Italian author Dante apparently employed the value . The Persian astronomer Jamshīd al-Kāshī produced 9 sexagesimal digits, roughly the equivalent of 16 decimal digits, in 1424 using