**Angle** is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of an angle (figure), the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.

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 Greek ἀγκύλος *(ankylοs)*, meaning "crooked, curved," and the English word "ankle". Both are connected with the Proto-Indo-European root **ank-*, meaning "to bend" or "bow".

Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.

Read more about Angle: Measuring Angles, Identifying Angles, Types of Angles, Angles Between Curves, Dot Product and Generalisation, Inner Product, Angles Between Subspaces, Angles in Riemannian Geometry, Angles in Geography and Astronomy

### Famous quotes containing the word angle:

“The good lawyer is not the man who has an eye to every side and *angle* of contingency, and qualifies all his qualifications, but who throws himself on your part so heartily, that he can get you out of a scrape.”

—Ralph Waldo Emerson (1803–1882)

“I fly in dreams, I know it is my privilege, I do not recall a single situation in dreams when I was unable to fly. To execute every sort of curve and *angle* with a light impulse, a flying mathematics—that is so distinct a happiness that it has permanently suffused my basic sense of happiness.”

—Friedrich Nietzsche (1844–1900)

“Modesty is the only sure bait when you *angle* for praise.”

—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)