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
Other articles related to "angle, angles":
... There are 3 angles The superior angle is covered by trapezius ... The inferior angle is covered by latissimus dorsi ... The lateral or glenoid angle is broad and bears the glenoid cavity or fossa, which is directed forward, laterally and slightly upwards ...
... border is the shortest and thinnest it is concave, and extends from the medial angle to the base of the coracoid process ... glenoid cavity, and inclines obliquely downward and backward to the inferior angle ... three, and extends from the medial to the inferior angle ...
... allowing the transmission of an image through a right angle without inverting it (that is, without changing the image's handedness) as an ordinary right-angle prism or mirror would ... inside the prism are not caused by total internal reflection, since the beams are incident at an angle less than the critical angle (the minimum angle for total ... but truncates what would otherwise be an awkward angle joining the two mirrored faces ...
... specifies the latitude and longitude of any location in terms of angles subtended at the centre of the Earth, using the equator and (usually) the Greenwich meridian as references ... The angle between those lines can be measured, and is the angular separation between the two stars ... One could say, "The Moon's diameter subtends an angle of half a degree." The small-angle formula can be used to convert such an angular measurement into a distance/size ratio ...
... These two angles combine to define sunrise to occur when the Sun's center is 50 arcminutes below the horizon, or 90.83° from the zenith ...
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 (18031882)
“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 mathematicsthat is so distinct a happiness that it has permanently suffused my basic sense of happiness.”
—Friedrich Nietzsche (18441900)
“Modesty is the only sure bait when you angle for praise.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (16941773)