L = n (central angle) ×π(π)× r (radius)/180=α (radian of central angle )× r (radius)

The calculation formula of arc length is a mathematical formula, L=n (degree of central angle) × π( 1)× r (radius)/180 (angle system), L=α (radian )× r (radius system). Where n is the degree of central angle, r is the radius, and l is the arc length of central angle.

In a circle with radius r, because the arc length subtended by the central angle 360 is equal to the circumference of the circle C=2πr, the arc length subtended by the central angle n is L = n π r ÷ 180 (L = n X2π r/360).

Example: the radius is 1cm, and the arc length corresponding to the central angle of 45 is l = n π r/180 = 45×π×1180 = 45× 3.14×/kloc.

Arc length is always introduced as a parameter when studying curves, 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.

Settings?

It is a continuous curve (as shown in figure 1). Its endpoints are A and B respectively, and any point between A and B is n- 1: P 1, P2, …Pn- 1. For convenience, write A as P0 and B as Pn. They divided gamma into n segments. Let the parameters corresponding to each point be a=t0, t 1, t2, …, tn- 1, tn=b in turn.

Connect adjacent points with straight line segments to obtain a broken line shape with the length of:

If σn tends to a certain limit that has nothing to do with the choice of bifurcation point when the bifurcation point increases infinitely, this limit is called the arc length of curve segment AB.

Curve?

The necessary and sufficient condition of length is its coordinate function?

It is a bounded variation function. Special, considered in differential geometry?

Class curves (k≥ 1) all have lengths. The length of the curve γ between [t0, t] can be expressed by the following formula:

Express delivery. The arc length is called the natural parameter of the curve.

Extended data:

Various formulas

The surface area of the cone = the side area of the cone+the area of the bottom circle.

Where: the lateral area of the cone =πRL, and the total area of the cone =πRL+πR? π is pi ≈3. 14, r is the radius of the circle at the bottom of the cone and l is the length of the generatrix of the cone. (Note: not the height of the cone) is the side length of the expanded sector. Central angle of n cone = r/l * 360 360r/l.

Solution of the central angle of the side expansion diagram: n=360r/R=πRr or 2π r = nπ r/ 180n = 360r/r If there is a tangent in the topic, the commonly used auxiliary line is to connect the radius of the center and the tangent point to get a right angle, and then solve the problem with relevant knowledge.