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The idea originated in the late 5th century BC with Antiphon, although it is not entirely clear how well he understood it. [1] The theory was made rigorous a few decades later by Eudoxus of Cnidus, who used it to calculate areas and volumes. It was later reinvented in China by Liu Hui in the 3rd century AD in order to find the area of a circle. [2]
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.
Bryson, along with his contemporary, Antiphon, was the first to inscribe a polygon inside a circle, find the polygon's area, double the number of sides of the polygon, and repeat the process, resulting in a lower bound approximation of the area of a circle. "Sooner or later (they figured), ...[there would be] so many sides that the polygon ...
However, despite this general interest in mathematical harmony, whether the paintings featured in the celebrated 1912 Salon de la Section d'Or exhibition used the golden ratio in any compositions is more difficult to determine. Livio, for example, claims that they did not, [118] and Marcel Duchamp said as much in an interview. [119]
Constantin Carathéodory (1873–1950) - Mathematician who pioneered the Axiomatic Formulation of Thermodynamics. [14] Demetrios Christodoulou (born 1951) - Mathematician-physicist who has contributed in the field of general relativity. [15] Constantine Dafermos (born 1941) - Usually notable for hyperbolic conservation laws and control theory. [16]
Archimedes proved a formula for the area of a circle, according to which < <. [2] In Chinese mathematics , in the third century CE, Liu Hui found even more accurate approximations using a method similar to that of Archimedes, and in the fifth century Zu Chongzhi found π ≈ 355 / 113 ≈ 3.141593 {\displaystyle \pi \approx 355/113\approx 3. ...
– Antiphon: c. 470 BC – 410 BC – Hippocrates: 465 BC – 398 BC – Theodorus: ... Timeline of mathematics; References This page was last edited on 30 March ...
In mathematics, Machin-like formulas are a popular technique for computing π (the ratio of the circumference to the diameter of a circle) to a large number of digits.They are generalizations of John Machin's formula from 1706: