Arch is a mathematical term, which means that when a circle rolls on a fixed straight line, the trajectory of a fixed point on the circumference is an arched figure with periodicity, and one period is called an arch, also known as cycloid, cylindrical line and hypocycloid line.

Starting from a book published by C. Powell in 150 1 year, in17th century, a large number of outstanding mathematicians, such as Galileo, Pascal and Torricelli, were keen to study the properties of an arch.

One arch equation: x = r * (t-Sint); Y=r*( 1-cost)r is the radius of the circle, and t is the radian rolling angle through which the radius of the circle passes. When t changes from 0 to 2π, the moving point draws a branch of the cycloid, which is called an arch.

The nature of the arch: its length is equal to 4 times the diameter of the circle of revolution. Its length is a rational number that does not depend on π. The area under the arc is three times that of the circle of revolution.

History of One Arch: The study of cycloid first began with Nicholas in Kusa, and later Malan Mei Sen also studied cycloid. Galileo named the cycloid in 1599. 1634 giles rod Beva le pointed out that the area under the cycloid is three times the area of the circle that produced it.