Information AboutAngle |
| CATEGORIES ABOUT ANGLE | |
| elementary geometry | |
| trigonometry | |
| angleelementary geometry | |
| trigonometry | |
| angle | |
| elementary geometry | |
| physical quantity | |
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An angle is the figure formed by two Rays sharing a common Endpoint , called the Vertex of the angle. Angles provide a means of expressing the difference in Slope between two rays meeting at a vertex without the need to explicitly define the slopes of the two rays. Angles are studied in Geometry and Trigonometry . 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. 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 are the Latin ''angere'', meaning "to compress into a bend" or "to strangle", and the Greek ''(angulοs)'', meaning "crooked, curved"; both are connected with the Aryan or Indo-European root ''ank-'', meaning "to bend". UNITS OF MEASURE FOR ANGLES In order to measure an angle, a Circle centered at the vertex is drawn. Since the circumference of a circle is always directly proportional to the length of its radius, the measure of the angle is independent of the size of the circle. Note that angles are dimensionless, since they are defined as the ratio of lengths.
CONVENTIONS ON MEASUREMENT A convention universally adopted in mathematical writing is that angles given a sign are positive angles if measured Counterclockwise , and '''negative angles''' if measured Clockwise , from a given line. If no line is specified, it can be assumed to be the X-axis in the Cartesian Plane . In Navigation , Bearings are measured from north, increasing clockwise, so a bearing of 45 is north-east. Negative bearings are not used in navigation, so north-west is 315. In mathematics radians are assumed unless specified otherwise because this removes the arbitrariness of the number 360 in the degree system and because the Trigonometric Function s can be developed into particularly simple Taylor Series if their arguments are specified in radians. TYPES OF ANGLES An angle of π /2 radians or 90°, one-quarter of the full circle is called a right angle. Two Line Segment s, rays, or lines (or any combination) which form a right angle are said to be either Perpendicular or ''' Orthogonal ''': |
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