"Central angle Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). The central angle is also known as the arc's angular distance. The size of a central angle is or (radians). When defining or drawing a central angle, in addition to specifying the points and , one must specify whether the angle being defined is the convex angle (<180°) or the reflex angle (>180°). Equivalently, one must specify whether the movement from point to point is clockwise or counterclockwise. If the"
"36, 40, 45, 60, 72, 90, 120, 180, 360}. 360-gon In geometry, a 360-gon (triacosihexacontagon or triacosihexecontagon) is a polygon with 360 sides. The sum of any 360-gon's interior angles is 64440 degrees. A ""regular 360-gon"" is represented by Schläfli symbol {360} and also can be constructed as a truncated 180-gon, t{180}, or a twice-truncated enneacontagon, tt{90}, or a thrice-truncated tetracontapentagon, ttt{45}. One interior angle in a regular 360-gon is 179°, meaning that one exterior angle would be 1°. The area of a regular 360-gon is (with ) and its inradius is The circumradius of a regular 120-gon is Since"
"Degree (angle) A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of angular measure is the radian, but it is mentioned in the SI brochure as an accepted unit. Because a full rotation equals 2 radians, one degree is equivalent to radians. The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is"
"360-gon In geometry, a 360-gon (triacosihexacontagon or triacosihexecontagon) is a polygon with 360 sides. The sum of any 360-gon's interior angles is 64440 degrees. A ""regular 360-gon"" is represented by Schläfli symbol {360} and also can be constructed as a truncated 180-gon, t{180}, or a twice-truncated enneacontagon, tt{90}, or a thrice-truncated tetracontapentagon, ttt{45}. One interior angle in a regular 360-gon is 179°, meaning that one exterior angle would be 1°. The area of a regular 360-gon is (with ) and its inradius is The circumradius of a regular 120-gon is Since 360 = 2 × 3 × 5, a regular"
"this system. In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more ""natural"" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number 360. One complete turn (360°) is equal to 2"""" radians, so 180° is equal to radians, or equivalently, the degree is a mathematical constant: 1° = . The turn (or revolution, full circle, full rotation, cycle) is used in technology and science. One turn is equal to 360°."
"of thumb approximations only. The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:—""amphicyrtic"" (Gr. , on both sides, κυρτός, convex) or ""cissoidal"" (Gr. κισσός, ivy), biconvex; ""xystroidal"" or ""sistroidal"" (Gr. ξυστρίς, a tool for scraping), concavo-convex; ""amphicoelic"" (Gr. κοίλη, a hollow) or ""angulus lunularis"", biconcave. The ancient Greek mathematicians knew how to bisect an angle (divide it into two angles of equal measure) using only"
"Right angle In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin ""angulus rectus""; here ""rectus"" means ""upright"", referring to the vertical perpendicular to a horizontal base line. Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied"
"Right triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the ""hypotenuse"" (side ""c"" in the figure). The sides adjacent to the right angle are called ""legs"" (or ""catheti"", singular: ""cathetus""). Side ""a"" may be identified as the side ""adjacent to angle B"" and ""opposed to"" (or ""opposite"") ""angle A"", while side ""b"" is the side ""adjacent to"
"Right triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the ""hypotenuse"" (side ""c"" in the figure). The sides adjacent to the right angle are called ""legs"" (or ""catheti"", singular: ""cathetus""). Side ""a"" may be identified as the side ""adjacent to angle B"" and ""opposed to"" (or ""opposite"") ""angle A"", while side ""b"" is the side ""adjacent to"
"Gradian The gradian is a unit of measurement of an angle, equivalent to formula_1 of a turn, formula_2 of a degree, or formula_3 of a radian. The gradian is defined as formula_4 of the right angle (in other words, there are 100 gradians in the right angle), which implies a full turn being 400 gradians. It is also known as gon (from Greek /""gōnía"" for angle), grad, or grade. In continental Europe, the French term ""centigrade"" was in use for one hundredth of a grad. This was one reason for the adoption of the term Celsius to replace centigrade as"
"with an inclination between 0 and 90 degrees is orbiting or revolving in the same direction as the primary is rotating. An object with an inclination of exactly 90 degrees has a perpendicular orbit that is neither prograde nor retrograde. An object with an inclination between 90 degrees and 180 degrees is in a retrograde orbit. A celestial object's axial tilt indicates whether the object's ""rotation"" is prograde or retrograde. Axial tilt is the angle between an object's rotation axis and a line perpendicular to its orbital plane passing through the object's centre. An object with an axial tilt up"
"on the need for detail and personal preferences. The traditional major aspects are sometimes called ""Ptolemaic aspects"" since they were defined and used by Ptolemy in the 1st Century, AD. These aspects are the conjunction (0°), sextile (60°), square (90°), trine (120°), and opposition (180°). It is important to note that different astrologers and separate astrological systems/traditional utilize differing ""orbs"" (the degree of separation between exactitude) when calculating and using the aspects, though almost all use a larger orb for a conjunction when compared to the other aspects. The major aspects are those that can be used to divide 360"
"geometry is that the sum of the interior angles of a triangle is greater than 180 degrees. In the spherical model, for example, a triangle can be constructed with vertices at the locations where the three positive Cartesian coordinate axes intersect the sphere, and all three of its internal angles are 90 degrees, summing to 270 degrees. For sufficiently small triangles, the excess over 180 degrees can be made arbitrarily small. The Pythagorean theorem fails in elliptic geometry. In the 90°–90°–90° triangle described above, all three sides have the same length, and consequently do not satisfy formula_1. The Pythagorean result"
"Vertex (geometry) In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. The ""vertex"" of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight ""sides"" meeting at one place. A vertex is a corner point of a"
"Vertex angle In geometry, a vertex angle is an angle associated with a vertex of an n-dimensional polytope. Often a vertex angle of a polygon is referred to simply as an angle of the polygon. In higher-dimensional polyhedra and polytopes, a vertex angle is an angle formed by two edges of the polyhedron that both belong to a common two-dimensional face of the polyhedron. That is, it is a vertex angle of one of the polygons that form the polyhedron. A vertex angle in a polygon is often measured on the interior side of the vertex. For any simple ""n""-gon,"
"between a planet's orbital plane and another plane of reference. For exoplanets, the inclination is usually stated with respect to an observer on Earth: the angle used is that between the normal to the planet's orbital plane and the line of sight from Earth to the star. Therefore, most planets observed by the transit method are close to 90 degrees. Because the word 'inclination' is used in exoplanet studies for this line-of-sight inclination then the angle between the planet's orbit and the star's rotation must use a different word and is termed the spin–orbit angle or spin–orbit alignment. In most"
"Glenopolar angle The glenopolar angle (GPA) is a measure for the rotational malalignment of the glenoid about an anteroposterior (front-to-back) axis perpendicular to the scapular plane. The glenopolar angle is defined as the angle between the line connecting the most cranial with the most caudal point of the glenoid cavity and the line connecting the most cranial of the glenoid cavity with the most caudal point of the scapular body. A glenopolar angle ranging from 30° to 45° is considered normal. The glenopolar angle is mainly used within the field of scapular surgery (for example, due to a scapular neck"
"Turn (geometry) A turn is a unit of plane angle measurement equal to 2 radians, 360 degrees or 400 gradians. A turn is also referred to as a cycle (abbreviated cyc), revolution (abbreviated rev), complete rotation (abbreviated rot) or full circle. Subdivisions of a turn include half turns, quarter turns, centiturns, milliturns, points, etc. A turn can be divided in 100 centiturns or milliturns, with each milliturn corresponding to an angle of 0.36°, which can also be written as 21′ 36″. A protractor divided in centiturns is normally called a percentage protractor. Binary fractions of a turn are also used."
"common angles of 30° and 60° in geometry must be expressed in fractions ( grad and grad, respectively). Similarly, in one hour ( day), Earth rotates by 15° or gon. These observations are a consequence of the fact that the number 360 has more divisors than the number 400 does. There are eleven factors of 360 less than or equal to its square root: formula_5. However, there are only seven for 400: formula_6 In the 18th century, the metre was defined as the forty-millionth part of a meridian. Thus, one grad of arc along the Earth's surface corresponded to 100"
"Axial tilt In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane. It differs from orbital inclination. At an obliquity of 0 degrees, the two axes point in the same direction; i.e., the rotational axis is perpendicular to the orbital plane. Earth's obliquity oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle; Earth's mean obliquity is currently and decreasing. Over the course of an orbital period, the obliquity usually does not change considerably, and the orientation of the"
"the sum of the interior angles is π(""n"" − 2) radians or 180(""n"" − 2) degrees. Because more than two lines in a polytope can intersect in the same space, the number of vertex angles from any given vertex is not always one. Because of this, it is sometimes necessary to specify not only the vertex, but also the specific line segments that make up the angle. Vertex angle In geometry, a vertex angle is an angle associated with a vertex of an n-dimensional polytope. Often a vertex angle of a polygon is referred to simply as an angle of"
"Angle of rotation In mathematics, the angle of rotation is a measurement of the amount, namely the angle, that a figure is rotated about a fixed point, often the center of a circle. A clockwise rotation is considered a negative rotation, so that, for instance, a rotation of 310° (counterclockwise) can also be called a rotation of –50° (since , a full rotation (turn)). A counterclockwise rotation of more than one complete turn is normally measured modulo 360°, meaning that 360° is subtracted off as many times as possible to leave a non-negative measurement less than 360°. For example, the"
"for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. ""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 a geometric angle, 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"
"fracture). Glenopolar angle The glenopolar angle (GPA) is a measure for the rotational malalignment of the glenoid about an anteroposterior (front-to-back) axis perpendicular to the scapular plane. The glenopolar angle is defined as the angle between the line connecting the most cranial with the most caudal point of the glenoid cavity and the line connecting the most cranial of the glenoid cavity with the most caudal point of the scapular body. A glenopolar angle ranging from 30° to 45° is considered normal. The glenopolar angle is mainly used within the field of scapular surgery (for example, due to a scapular"
"hypotenuse measures 90 degrees, with the other two angles adding up to 90 for a total of 180 degrees. Thus, an angle measuring 90 degrees is called a right angle. Ninety is: 90 (number) 90 (ninety) is the natural number preceded by 89 and followed by 91. In the English language, the numbers 90 and 19 are often confused, as sounding very similar. When carefully enunciated, they differ in which syllable is stressed: 19 /naɪnˈtiːn/ vs 90 /ˈnaɪnti/. However, in dates such as 1999, and when contrasting numbers in the teens and when counting, such as 17, 18, 19, the"
"Angle In plane geometry, an angle is the figure formed by two rays, called the ""sides"" of the angle, sharing a common endpoint, called the ""vertex"" of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space,"
"Frank Vigor Morley. The Latin term for ""turn"" is versor, which is a quaternion that can be visualized as an arc of a great circle. The product of two versors can be compared to a spherical triangle where two sides add to the third. For the kinematics of rotation in three dimensions, see quaternions and spatial rotation. Turn (geometry) A turn is a unit of plane angle measurement equal to 2 radians, 360 degrees or 400 gradians. A turn is also referred to as a cycle (abbreviated cyc), revolution (abbreviated rev), complete rotation (abbreviated rot) or full circle. Subdivisions of"
"an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles. The ""exterior"" or ""external bisector"" is the line that divides the supplementary angle (of 180° minus the original angle), formed by one side forming the original angle and the extension of the other side, into two equal angles. To bisect an angle with straightedge and compass, one draws a circle whose center is the vertex. The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of"
"to be made that involves an opportunity cost. It is the smallest major aspect that usually involves houses in different quadrants. A trine (abbrev. Tri) is an angle of 120° (1/3 of the 360° ecliptic), an orb of somewhere between 5° and 10° depending on the planets involved. The trine relates to what is natural and indicates harmony and ease. The trine may involve talent or ability which is innate. The trine has been traditionally assumed to be extremely beneficial. When involved in a transit, the trine appears in situations that emerge a current or past situation in a natural"
"Longitude Longitude (, ), is a geographic coordinate that specifies the east–west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians (lines running from pole to pole) connect points with the same longitude. By convention, one of these, the Prime Meridian, which passes through the Royal Observatory, Greenwich, England, was allocated the position of 0° longitude. The longitude of other places is measured as the angle east or west from the Prime Meridian, ranging from 0° at the Prime Meridian to +180° eastward"
"Latitude In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle (defined below) which ranges from 0° at the Equator to 90° (North or South) at the poles. Lines of constant latitude, or ""parallels"", run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the ""geodetic latitude"" as defined below. Briefly, geodetic latitude at a point is the angle"
"may also conflict with the notation used for three-dimensional cylindrical coordinates. The angles are typically measured in degrees (°) or radians (rad), where 360° = 2 rad. Degrees are most common in geography, astronomy, and engineering, whereas radians are commonly used in mathematics and theoretical physics. The unit for radial distance is usually determined by the context. When the system is used for physical three-space, it is customary to use positive sign for azimuth angles that are measured in the counter-clockwise sense from the reference direction on the reference plane, as seen from the zenith side of the plane. This"
"way and are not surprising. An opposition (abrv. Opp) is an angle of 180° (1/2 of the 360° ecliptic). An orb of somewhere between 5° and 10° is usually allowed depending on the planets. Oppositions are said to be the second most powerful aspect. It resembles the conjunction although the difference between them is that the opposition is fundamentally relational. Some say it is prone to exaggeration as it is not unifying like the conjunction but has a dichotomous quality and an externalizing effect. All important axes in astrology are essentially oppositions. Therefore, at its most basic, it often signifies"