"does not contain all other vertices in its edges and interior. The convex hull of the concave polygon's vertices, and that of its edges, contains points that are exterior to the polygon. Concave polygon A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive. Some lines containing interior points of a concave polygon intersect its boundary at more than two points. Some diagonals of a concave polygon lie partly or"
"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"
"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°."
"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"
"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"
"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"
"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"
"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"
"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"
"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"
"an angle of 40° (1/9 of the 360° ecliptic). An orb of 40±1° is allowed. It indicates an energy of perfection and/or idealization. The ""parallel"" and ""antiparallel"" (or ""contraparallel"") are two other aspects which refer to degrees of declination above or below the celestial equator. They are considered moderate influences, though not much research has gone into studying these particular aspects. Astrological aspect In astrology, an aspect is an angle the planets make to each other in the horoscope, also to the ascendant, midheaven, descendant, lower midheaven, and other points of astrological interest. Aspects are measured by the angular distance"
"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."
"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"
"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"
"Angular unit Throughout history, angles have been measured in many different units. The most contemporary units are the degree ( ° ) and radian (rad), but many others have been used throughout history. The purpose of this page is to aggregate other concepts pertaining to the angular unit, where additional explanation can be provided. The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be ""equal"" or ""congruent"" or ""equal in measure"". In some contexts, such"
"the angle is measured as long as each angle is measured in the same unit. One ""radian"" is the angle subtended by an arc of a circle that has the same length as the circle's radius. The radian is the derived quantity of angular measurement in the SI system. By definition, it is dimensionless, though it may be specified as ""rad"" to avoid ambiguity. Angles measured in degrees, are shown with the symbol °. Subdivisions of the degree are minute (symbol ', 1' = 1/60°) and second {symbol "", 1"" = 1/3600°}. An angle of 360° corresponds to the angle"
"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"
"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"
"cosine equals 0, ±1/2, or ±1. The only ones of these giving an angle strictly between 0° and 180° are the cosine value 1/2 with the angle 60°, the cosine value –1/2 with the angle 120°, and the cosine value 0 with the angle 90°. The only combination of three of these, allowing multiple use of any of them and summing to 180°, is three 60° angles. Conditions are known in terms of elliptic curves for an integer triangle to have an integer ratio ""N"" of the circumradius to the inradius. The smallest case, that of the equilateral triangle, has"
"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"
"of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be ""equal"" or ""congruent"" or ""equal in measure"". In some contexts, such as identifying a point on a circle or describing the ""orientation"" of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing the ""cumulative rotation"" of an object in two dimensions relative to a reference orientation, angles that"
"the rays of the angle lie. In navigation, bearings are measured relative to north. By convention, viewed from above, bearing angle are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so a north-west orientation corresponds to a bearing of 315°. There are several alternatives to measuring the size of an angle by the corresponding angle of rotation. The ""grade of a slope"", or ""gradient"" is equal to the tangent of the angle, or sometimes (rarely) the sine. Gradients are often expressed as a percentage. For very small values (less"
"∠BAC might refer to any of four angles: the clockwise angle from B to C, the anticlockwise angle from B to C, the clockwise angle from C to B, or the anticlockwise angle from C to B, where the direction in which the angle is measured determines its sign (see Positive and negative angles). However, in many geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant, and no ambiguity arises. Otherwise, a convention may be adopted so that ∠BAC always refers to the anticlockwise (positive) angle from B to"
"to 90 degrees is rotating in the same direction as its primary. An object with an axial tilt of exactly 90 degrees has a perpendicular rotation that is neither prograde nor retrograde. An object with an axial tilt between 90 degrees and 180 degrees is rotating in the opposite direction to its orbital direction. All eight planets in the Solar System orbit the Sun in the direction of the Sun's rotation, which is counterclockwise when viewed from above the Sun's north pole. Six of the planets also rotate about their axis in this same direction. The exceptions – the planets"
"180 the blind direction. 180 air – Doing and air and spinning a 180 in the air and landing in with a switch stance. 180 shove it – Spinning just the board 180 under your feet and landing with the board “backwards”. 900 spin – Rider spins continuously 2 1/2 times until he is riding switch stance forward. 360 shove it – Same as a 180 but you spin the board a full 360 under your feet. Note: rider does not spin only the board spins. Big Spin – Same as a 360 shove it, only the rider spins a"
"rotate the object at any degree measure, but 90° and 180° are two of the most common. Rotation by a positive angle rotates the object counterclockwise, whereas rotation by a negative angle rotates the object clockwise. Uniform scaling is a linear transformation that enlarges or diminishes objects; the scale factor is the same in all directions; it is also called a homothety or dilation. The result of uniform scaling is similar (in the geometric sense) to the original. More general is scaling with a separate scale factor for each axis direction; a special case is directional scaling (in one direction)."
"carts on a Ferris wheel move along a circle around the center point of that circle. If a cart moves around the wheel once, the angle of rotation is 360 degrees. If the cart was stuck halfway, at the top of the wheel, at that point its angle of rotation was only 180 degrees. This is also referred to as the ""order of symmetry."" Angles are commonly measured in degrees, radians, gons (gradians) and turns, sometimes also in angular mils and binary radians. They are central to polar coordinates and trigonometry. Angle of rotation In mathematics, the angle of rotation"
"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"
"geometry, it is the number of seconds in a minute, and the number of minutes in a degree. In normal space, the three interior angles of an equilateral triangle each measure 60 degrees, adding up to 180 degrees. Because it is divisible by the sum of its digits in base 10, it is a Harshad number. A number system with base 60 is called sexagesimal (the original meaning of ""sexagesimal"" is sixtieth). It is the smallest positive integer that is written with only the smallest and the largest digit of base 2 (binary), base 3 (ternary) and base 4 (quaternary)."
"always a valid angle in the range of −180° degrees (−π radians) to +180° degrees (+π radians). In some cases, it is convenient to use unsigned multiplication (rather than signed multiplication) on a binary angle, which gives the correct angle in the range of 0 to +360° degrees (+2π radians or +1 turn). Compared to storing angles in a binary angle format, storing angles in any other format inevitably results in some bit patterns giving ""angles"" outside that range, requiring extra steps to range-reduce the value to the desired range, or results in some bit patterns that are not valid"
"in a clockwise direction. North is 0°, east is 90°, south is 180°, and west is 270°. Note that, due to wind forces, the direction of movement of the aircraft, or track, is not the same as the heading. The nose of the aircraft may be pointing due west, for example, but a strong northerly wind will change its track south of west. The angle between heading and track is known as the drift angle. Crab angle is the amount of correction an aircraft must be turned into the wind in order to maintain the desired course. It is opposite"
"Reverse perspective Reverse perspective, also called inverse perspective, inverted perspective, divergent perspective, or Byzantine perspective, is a form of perspective drawing in which the objects depicted in a scene are placed between the projective point and the viewing plane. This has the visual effect that objects farther away from the viewing plane are drawn as larger, and closer objects are drawn as smaller, in contrast to the more conventional linear perspective for which closer objects appear larger. Lines that are parallel in three-dimensional space are drawn as diverging against the horizon, rather than converging as they do in linear perspective."