Weird ways to calculate pi manual#

In the 2nd century CE, Ptolemy used the value 377⁄ 120, the first known approximation accurate to three decimal places (accuracy 2♱0 −5).

In the 3rd century BCE, Archimedes proved the sharp inequalities 223⁄ 71 < π < 22⁄ 7, by means of regular 96-gons (accuracies of 2♱0 −4 and 4♱0 −4, respectively). 'verses: 6.12.40-45, Bhishma Parva of the Mahabharata' From that its peripheral circle comes to be equal to thirty thousand yojanas.

The Sun is eight thousand yojanas and another two thousand Its peripheral circle happens to be thirty three thousand yojanas when calculated. The Moon is handed down by memory to be eleven thousand yojanas in diameter. The Mahabharata (500 BCE - 300 CE) offers an approximation of 3, in the ratios offered in Bhishma Parva verses: 6.12.40-45. 6th century BCE) use a fractional approximation of 339⁄ 108 ≈ 3.139. Īstronomical calculations in the Shatapatha Brahmana (c. 1600 BCE, although stated to be a copy of an older, Middle Kingdom text) implies an approximation of π as 256⁄ 81 ≈ 3.16 (accurate to 0.6 percent) by calculating the area of a circle via approximation with the octagon. Īt about the same time, the Egyptian Rhind Mathematical Papyrus (dated to the Second Intermediate Period, c. The Babylonians were aware that this was an approximation, and one Old Babylonian mathematical tablet excavated near Susa in 1936 (dated to between the 19th and 17th centuries BCE) gives a better approximation of π as 25⁄ 8 = 3.125, about 0.528% below the exact value. īabylonian mathematics usually approximated π to 3, sufficient for the architectural projects of the time (notably also reflected in the description of Solomon's Temple in the Hebrew Bible).

Have claimed that the ancient Egyptians used an approximation of π as 22⁄ 7 = 3.142857 (about 0.04% too high) from as early as the Old Kingdom. After this, no further progress was made until the late medieval period. The best known approximations to π dating to before the Common Era were accurate to two decimal places this was improved upon in Chinese mathematics in particular by the mid-first millennium, to an accuracy of seven decimal places. On June 8, 2022, the current record was established by Emma Haruka Iwao with Alexander Yee's y-cruncher with 100 trillion digits. Since the middle of the 20th century, the approximation of π has been the task of electronic digital computers (for a comprehensive account, see Chronology of computation of π).

Weird ways to calculate pi manual#

The record of manual approximation of π is held by William Shanks, who calculated 527 digits correctly in 1853. Early modern mathematicians reached an accuracy of 35 digits by the beginning of the 17th century ( Ludolph van Ceulen), and 126 digits by the 19th century ( Jurij Vega), surpassing the accuracy required for any conceivable application outside of pure mathematics.

In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.įurther progress was not made until the 15th century (through the efforts of Jamshīd al-Kāshī). Approximations for the mathematical constant pi ( π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era.