Measuring Angles
The size of an angle is characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are called congruent angles.
In some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing the cumulative rotation of an object in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.
In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The length of the arc s is then divided by the radius of the arc r, and possibly multiplied by a scaling constant k (which depends on the units of measurement that are chosen):
The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered.
Read more about this topic: Angle
Famous quotes containing the word measuring:
“We recognize caste in dogs because we rank ourselves by the familiar dog system, a ladderlike social arrangement wherein one individual outranks all others, the next outranks all but the first, and so on down the hierarchy. But the cat system is more like a wheel, with a high-ranking cat at the hub and the others arranged around the rim, all reluctantly acknowledging the superiority of the despot but not necessarily measuring themselves against one another.”
—Elizabeth Marshall Thomas. “Strong and Sensitive Cats,” Atlantic Monthly (July 1994)