Finding the area of the shadow part is one of the important problems in the circle. This lesson introduces the common methods of this kind of problem with examples. In addition, there are equation method, superposition method and so on. There are many methods to calculate the shadow area, which are very skillful and should be chosen flexibly according to the problem.
Area of circle:
1. In the 5th century BC, Hippocrates of Hiosburg was the first person to show that the area of a disk was proportional to the square of its diameter, which was part of his orthogonality in Hippocrates' time, 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.
2. Subsequently, the first volume of Euclid's Elements of Geometry involves 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. ?
3. Archimedes' approximate value is π and his multiple method, that is, a regular triangle circle is instantly marked with its area, and then the number of sides is doubled to obtain a regular hexagon, and then the number of sides is repeatedly doubled as the area of the polygon approaches the number of sides of the circle.
4. 176 1 year, Swiss scientist johann heinrich lambert proved that the ratio of the area of a circle to its square radius is unreasonable, that is, π is not equal to the quotient of any two integers.
5. 1794, the French mathematician Adrian-Marie Legendre proved that π 2 was unreasonable; This also proves the irrationality of π. 1882, the German mathematician Ferdinand von Lin Deman proved that π is transcendental, which confirmed the speculation of Legendre and Euler.