**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:

“So much symmetry!

Like the pale *angle* of time

And eternity.

The great shape labored and fell.”

—N. Scott Momaday (b. 1934)

“It is a mistake, to think the same thing affects both sight and touch. If the same *angle* or square, which is the object of touch, be also the object of vision, what should hinder the blind man, at first sight, from knowing it?”

—George Berkeley (1685–1753)

“From whichever *angle* one looks at it, the application of racial theories remains a striking proof of the lowered demands of public opinion upon the purity of critical judgment.”

—Johan Huizinga (1872–1945)