An arc is the shape of a part of a circle or ellipse. Any deviation or bending of a straight line or level to make it look like an arc or an elliptical arc. The formula of arc area generally refers to an arc, and there are two formulas of arc area. One is related to the length of the arc and the radius of the circle, that is, S= 1/2LR.
One is related to the central angle and radius of the arc, that is, S = n π r 2/360, where L represents the arc length, R represents the radius of the circle, and N represents the degree of the central angle of the arc. The arc length of a curve, also known as the length of a curve, is one of the characteristics of a curve. Not all curves can define the length. Curves that can define the length are called curves that can find the length.
The arc length of the earliest curve is the length of the arc, so it refers to the length of the arc in a narrow sense. In a circle with radius r, the arc length of the arc subtended by the central angle n is nπ r/ 180. Radian, formerly known as "Li". In mathematics and physics, radian is the unit of measurement of angle. It is a unit derived from the international system of units, abbreviated as rad.
When studying curves, we always introduce arc length as a parameter, on the one hand, because the general parameter T of curves has no geometric meaning, and on the other hand, because arc length is an invariant of rigid motion of curves, using arc length as a parameter can greatly simplify the formula and easily derive other invariants.
Source of unit
The Babylonian division of circles influenced ancient Greek astronomy to some extent. In ancient Greece, "geocentric theory" was very popular. People thought that the sun was moving in a circle around the earth, so many problems about the calculation of circular orbit arose.
Furthermore, people want to know how to find the triangle problem of the corresponding chord length when the arc length is known. Therefore, Hippocrates (BC 190- 120) drew the chord table for the first time, and Claudius Ptolemy's book Dacheng also had a similar chord table, which made the idea of chord table widely known, and this was the beginning of trigonometry.