1, the formula of the circumference of a circle is C=2πr, where c represents the circumference of a circle, r represents the radius of a circle, and π is a constant, which is about equal to 3. 14 159. By dividing the circle into several equal parts, the formula of the circumference of the circle can be deduced. Suppose we divide the circle into n equal parts, and the arc length of each part is s, then the circumference c of the circle can be expressed as: c = n× s.

2. Since the circle is divided into n equal parts, the arc length s of each segment can be expressed in radians. Radian is the unit of measurement of angle, and the relationship between radian and angle is: 1 radian = 180/π degrees.

3. Therefore, we can rewrite the above formula as: n×s=2πr, where r represents the radius of a circle. Because we know that the circle is divided into n equal parts, the arc length s of each part is equal to the circumference of the circle divided by n, that is, s = c/n. By combining the above two formulas, we can get: C/n=2πr/n, and after simplification, we can get:

4. Through this formula, we can calculate the perimeter c of any circle with radius r .. At the same time, we can also calculate the diameter d and area a of the circle according to the known radius and perimeter. The diameter d is equal to twice the radius, that is, d = 2r, and the area a is equal to π times the square of the radius, that is, A=πr? .

The Concept of Circle and Related Knowledge

1. A circle is a set of all points on a plane that are equidistant from a fixed point (center). The properties of a circle include: the distance from any two points on the circumference to the center of the circle is equal, that is, the radius is equal. The circumferential angle is equal to half of the corresponding central angle. Diagonal complementarity of quadrilateral inscribed in a circle.

2. The ratio of the three sides of the circumscribed circular triangle is 1: 1: √ 2. The formula of circular area is πr? Where r is the radius. The formula for the circumference of a circle is 2πr, where r is the radius.

3. The properties of the circle can be used to solve geometric problems, such as calculating the area, perimeter and arc length of the circle. In mathematics, circle is a very important concept, which is widely used in trigonometric functions, algebra, calculus and other fields. In addition, the circle is also one of the common figures in nature. For example, the orbits of planets in the solar system are circular.