Ívhosszszámítás

Ívhosszszámítás refers to the calculation of arc length. An arc is a portion of the circumference of a circle or a curve. The length of an arc can be determined using various mathematical formulas depending on the context. For a circle, if the radius is known and the central angle subtended by the arc is given in radians, the arc length is simply the product of the radius and the angle. If the angle is given in degrees, it must be converted to radians first by multiplying by pi/180. In calculus, the arc length of a curve defined by a function y = f(x) from x=a to x=b can be calculated using an integral. The formula involves integrating the square root of 1 plus the square of the derivative of the function, from the lower limit a to the upper limit b. Similarly, for a curve defined parametrically, specific integral formulas are employed. Understanding ívhosszszámítás is important in fields like geometry, physics (e.g., calculating the path of a projectile), and engineering. It allows for precise measurement of curved paths and surfaces.