Heron (or hero) of Alexander, who has a triangular area, found the so-called heron formula in the triangle, and a proof can be found in his book, Metrica, which he wrote about 60 years ago. Some people think that Archimedes knew this formula two centuries ago.

In 499, aryabhata, a great mathematician and astronomer in the classical times of Indian mathematics and Indian astronomy, expressed the area of a triangle as half the height of Aryabhatiya. China discovered the formula equivalent to heron independently of the Greeks. Published in 1247 "Nine Chapters Publishing" in Shu Qi (referred to as "Nine Chapters Mathematics") by Qin.

Quadrilateral area:

In the 7th century AD, Brahmagupta developed a formula, which is now called Brahmagupta formula, to calculate the area of a circular quadrilateral on its side (the quadrilateral is engraved on a circle). 1842, German mathematicians Karl Anton Bretschneider and Karl Georg Christian von Staudt independently discovered a formula called Bretschneider formula to calculate the area of any quadrilateral.

Area of circle:

In the 5th century BC, Hippocrates in Hiosburg was the first person to show that the area of a disk (the area surrounded by a circle) was directly proportional to the square of its diameter, which was part of the orthogonality in Hippocrates' era, but the proportionality constant was not determined. In the 5th century BC, eudoxus of Cornydos also found that the area of a disk is directly proportional to the square of its radius.

Subsequently, the first volume of Euclid's Elements of Geometry involved the equations between two-dimensional characters. Mathematician Archimedes used the tools of Euclidean geometry to show that in his book Measuring a Circle, the area inside a circle is the same as that of a right triangle, and its diameter triangle has the circumference of a circle and its height is equal to the radius of the circle. ?

The perimeter is 2πr, and the area of the triangle is half of the reference times the height, and the resulting area is πr2. Archimedes approximation method is π (so the area of a circle with unit radius) and his multiple method. Carve a circle with a regular triangle and mark its area, then double the number of sides to get a regular hexagon, and then the area of a polygon is closer to the number of sides of the circle.