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In geometry and trigonometry, an angle (in full, plane angle) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle (Sidorov 2001). The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see "Measuring angles", below). Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity). The word angle comes from the Latin word angulus, meaning "a corner". The word angulus is a diminutive, of which the primitive form, angus, does not occur in Latin. Cognate words are the Latin angere, meaning "to compress into a bend" or "to strangle", the Greek ??????? (ankyl?s), meaning "crooked, curved," and the English word "ankle." All three are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow" (Slocum 2007). In order to measure an angle ?, 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 circle r, and possibly multiplied by a scaling constant k (which depends on the units of measurement that are chosen) The value of ? 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.
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