answers: Archimedes
context: and Moon could be deduced using a form of trigonometry. From the diagram and trigonometry, we can calculate that The diagram is greatly exaggerated, because in reality, "S = 390 L", and "φ" is extremely close to 90°. Aristarchus determined "φ" to be a thirtieth of a quadrant (in modern terms, 3°) less than a right angle: in current terminology, 87°. Trigonometric functions had not yet been invented, but using geometrical analysis in the style of Euclid, Aristarchus determined that In other words, the distance to the Sun was somewhere between 18 and 20 times greater than the distance to </s> in his book "Measurement of a Circle". (The circumference is 2"r", and the area of a triangle is half the base times the height, yielding the area "r" for the disk.) Archimedes approximated the value of π (and hence the area of a unit-radius circle) with his doubling method, in which he inscribed a regular triangle in a circle and noted its area, then doubled the number of sides to give a regular hexagon, then repeatedly doubled the number of sides as the polygon's area got closer and closer to that of the circle (and did the same with circumscribed </s> to Heron's was discovered by the Chinese independently of the Greeks. It was published in 1247 in "Shushu Jiuzhang" ("Mathematical Treatise in Nine Sections"), written by Qin Jiushao. In the 7th century CE, Brahmagupta developed a formula, now known as Brahmagupta's formula, for the area of a cyclic quadrilateral (a quadrilateral inscribed in a circle) in terms of its sides. In 1842 the German mathematicians Carl Anton Bretschneider and Karl Georg Christian von Staudt independently found a formula, known as Bretschneider's formula, for the area of any quadrilateral. The development of Cartesian coordinates by René Descartes in the 17th century
question: who discovered formula for area of a circle