Angle

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":

Pentaprism
... reflects inside the prism twice, allowing the transmission of an image through a right angle without inverting it (that is, without changing the image's ... by total internal reflection, since the beams are incident at an angle less than the critical angle (the minimum angle for total internal reflection) ... of the prism is not used optically but truncates what would otherwise be an awkward angle joining the two mirrored faces ...
Scapula - Structure - Borders
... and thinnest it is concave, and extends from the medial angle to the base of the coracoid process ... cavity, and inclines obliquely downward and backward to the inferior angle ... the longest of the three, and extends from the medial to the inferior angle ...
Angles in Geography and Astronomy
... 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/si ...
Sunrise - Measurement - Angle
... 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 ...
Scapula - Structure - 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 ...

Famous quotes containing the word angle:

    The inhabitants of earth behold commonly but the dark and shadowy under side of heaven’s pavement; it is only when seen at a favorable angle in the horizon, morning or evening, that some faint streaks of the rich lining of the clouds are revealed.
    Henry David Thoreau (1817–1862)

    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)

    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)