Search results
Results from the WOW.Com Content Network
The quotients formed by the area of these polygons divided by the square of the circle radius can be made arbitrarily close to π as the number of polygon sides becomes large, proving that the area inside the circle of radius r is πr 2, π being defined as the ratio of the circumference to the diameter (C/d).
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 ...
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. ...
This page was last edited on 17 December 2024, at 15:13 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
Ancient Greek mathematicians are known to have solved specific instances of polynomial equations with the use of straightedge and compass constructions, which simultaneously gave a geometric proof of the solution's correctness. Once a construction was completed, the answer could be found by measuring the length of a certain line segment (or ...
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]
Eratosthenes (c. 276 – c. 194/195 BC), a Greek mathematician who calculated the circumference of the Earth and also the distance from the Earth to the Sun. Hipparchus (c. 190 – c. 120 BC), a Greek mathematician who measured the radii of the Sun and the Moon as well as their distances from the Earth. On the Sizes and Distances