In geometry, how many degrees are there in a circle?
"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."
"circle. There are 89 integral (whole degree) circles of latitude between the equator and the Poles in each hemisphere, but these can be divided into more precise measurements of latitude, and are often represented as a decimal degree (e.g. 34.637°N) or with minutes and seconds (e.g. 22°14'26""S). There is no limit to how precisely latitude can be measured, and so there are an infinite number of circles of latitude on Earth. On a map, the circles of latitude may or may not be parallel, and their spacing may vary, depending on which projection is used to map the surface of"
"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°."
"circle) was first used in the mid nineteenth century by Charles-Marc Dapples (1837–1920), a Swiss engineer and professor at the University of Lausanne. Degrees and minutes were the usual units of angular measurement but others were being proposed, with ""grads"" (400 gradians in a circle) under various names having considerable popularity in much of northern Europe. However, Imperial Russia used a different approach, dividing a circle into equilateral triangles (60° per triangle, 6 triangles in a circle) and hence 600 units to a circle. Around the time of the start of World War I, France was experimenting with the use"
"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"
". It is approximately equal to one milliradian ( ). A mil measuring of a revolution originated in the imperial Russian army, where an equilateral chord was divided into tenths to give a circle of 600 units. This may be seen on a lining plane (an early device for aiming indirect fire artillery) dating from about 1900 in the St. Petersburg Museum of Artillery. 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"
"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"
"onto the celestial sphere. Since a complete circle contains 24 of right ascension or 360° (degrees of arc), of a circle is measured as 1 of right ascension, or 15°; of a circle is measured as 1 of right ascension, or 15 minutes of arc (also written as 15′); and of a circle contains 1 of right ascension, or 15 seconds of arc (also written as 15″). A full circle, measured in right-ascension units, contains , or , or 24. Because right ascensions are measured in hours (of rotation of the Earth), they can be used to time the positions"
"degrees), and the other arc, the major arc, will subtend an angle greater than radians. The length (more precisely, arc length), ""L"", of an arc of a circle with radius ""r"" and subtending an angle ""θ"" (measured in radians) with the circle center — i.e., the central angle — equals ""θr"". This is because Substituting in the circumference and, with ""α"" being the same angle measured in degrees, since ""θ"" = , the arc length equals A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the"
"Circle A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. A circle is a simple closed curve that divides the plane into two regions: an interior"
"were 360 rows, portions of which looked as follows: Each number in the first column, labeled , is the number of degrees of arc on a circle. Each number in the second column, labeled , is the length of the corresponding chord of the circle, when the diameter is 120. Thus πδ represents an 84° arc, and the ∠′ after it means one-half, so that πδ∠′ means °. In the next column we see π μα γ, meaning 80 + + . That is the length of the chord corresponding to an arc of ° when the diameter of the"
"around the compass dial. In the 19th century some European nations adopted the ""grad"" (also called grade or gon) system instead, where a right angle is 100 grads to give a circle of 400 grads. Dividing grads into tenths to give a circle of 4000 decigrades has also been used in armies. Most military forces have adopted the French ""millieme"" system. This is an approximation of a milli-radian (6283 per circle), in which the compass dial is spaced into 6400 units or ""mils"" for additional precision when measuring angles, laying artillery, etc. The value to the military is that one"
"of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case that more than one of these factors has come into play. According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be"
"Degree of curvature Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying. The degree of curvature is defined as the central angle to the ends of an arc or chord of agreed length. Various lengths are commonly used in different areas of practice. This angle is also the change in forward direction as that portion of the curve is traveled. Curvature is usually measured in radius of curvature. A small circle can be easily laid out by just using radius of curvature,"
"Āryabhaṭa has chosen the number 3438 as the value of radius of the base circle for the computation of his sine table. The rationale of the choice of this parameter is the idea of measuring the circumference of a circle in angle measures. In astronomical computations distances are measured in degrees, minutes, seconds, etc. In this measure, the circumference of a circle is 360° = (60 × 360) minutes = 21600 minutes. The radius of the circle, the measure of whose circumference is 21600 minutes, is 21600 / 2π minutes. Computing this using the value π = 3.1416 known to"
"Semicircle In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180° (equivalently, radians, or a half-turn). It has only one line of symmetry (reflection symmetry). In non-technical usage, the term ""semicircle"" is sometimes used to refer to a half-disk, which is a two-dimensional geometric shape that also includes the diameter segment from one end of the arc to the other as well as all the interior points. By Thales' theorem, any triangle inscribed in a semicircle with a vertex at each"
"Measurement of a Circle Measurement of a Circle or Dimension of the Circle (Greek: , ""Kuklou metrēsis"") is a treatise that consists of three propositions by Archimedes, ca. 250 BCE. The treatise is only a fraction of what was a longer work. Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle. Any circle with a circumference ""c"" and a radius ""r"" is equal in area with a right triangle with the"
"study of dynamical systems. Unit circle In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted ; the generalization to higher dimensions is the unit sphere. If is a point on the unit circle's circumference, then and are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, and satisfy the equation Since for"
"if they take a formal geometry course in secondary school. The levels are as follows: Level 0. Visualization: At this level, the focus of a child's thinking is on individual shapes, which the child is learning to classify by judging their holistic appearance. Children simply say, ""That is a circle,"" usually without further description. Children identify prototypes of basic geometrical figures (triangle, circle, square). These visual prototypes are then used to identify other shapes. A shape is a circle because it looks like a sun; a shape is a rectangle because it looks like a door or a box; and"
"as kilometers plus meters 1+000. Degree of curvature can be converted to radius of curvature by the following formulae: formula_1 where formula_2 is arc length, formula_3 is radius of curvature and formula_4 is degree of curvature, arc definition formula_5 where formula_6 is chord length, formula_3 is radius of curvature and formula_8 is degree of curvature, chord definition ""Note the variation in usage among these samples."" Degree of curvature Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying. The degree of curvature is"
"a degree of a function between cycles, analogous to the degree of a continuous mapping. For example, the natural map from the circle of fifths to the chromatic circle is a map of degree 7. One may also define a rotation number. The set of all cuts is cyclically ordered by the following relation: if and only if there exist such that: A certain subset of this cycle of cuts is the Dedekind completion of the original cycle. Starting from a cyclically ordered set , one may form a linear order by unrolling it along an infinite line. This captures"
"Sailors have traditionally divided a turn into 32 compass points. The ""binary degree"", also known as the ""binary radian"" (or ""brad""), is turn. The binary degree is used in computing so that an angle can be represented to the maximum possible precision in a single byte. Other measures of angle used in computing may be based on dividing one whole turn into 2 equal parts for other values of ""n"". The notion of turn is commonly used for planar rotations. The word turn originates via Latin and French from the Greek word ( – a lathe). In 1697, David Gregory"
"Unit circle In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted ; the generalization to higher dimensions is the unit sphere. If is a point on the unit circle's circumference, then and are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, and satisfy the equation Since for all , and since"
"12 angles of some tetrahedron? Clearly the sum of the angles of any side of the tetrahedron must be 180°. Since there are four such triangles, there are four such constraints on sums of angles, and the number of degrees of freedom is thereby reduced from 12 to 8. The four relations given by this sine law further reduce the number of degrees of freedom, from 8 down to not 4 but 5, since the fourth constraint is not independent of the first three. Thus the space of all shapes of tetrahedra is 5-dimensional. Let be the points of a"
"and this may be used in other places for road work. Other lengths may be used—such as 30 metres or 100 metres where SI is favoured, or a shorter length for sharper curves. Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is , where is degree and is radius. As an example, a curve with an arc length of 600 units that has an overall sweep of 6 degrees is a 1-degree curve: For every 100 feet of arc, the bearing changes by 1 degree. The radius of"
"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"
"Chromatic circle The chromatic circle is a geometrical space that shows relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale on a circle. If one starts on any equal-tempered pitch and repeatedly ascends by the musical interval of a semitone, one will eventually land on a pitch with the same pitch class as the initial one, having passed through all the other equal-tempered chromatic pitch classes in between. Since the space is circular, it is also possible to descend by semitone. The chromatic circle is useful because it represents melodic distance, which is often correlated with"
"Circumference In geometry, the circumference (from Latin ""circumferentia"", meaning ""carrying around"") of a circle is the (linear) distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge (boundary) of a disk, circumference is a special case of perimeter. The perimeter is the length around any closed figure and is the term used for most figures excepting the circle and some circular-like figures such as ellipses. Informally, ""circumference"" may also refer to the edge itself rather than to the"
"degrees to (φ + 0.5) degrees) is about Similarly, the length in meters of a degree of longitude can be calculated as An alternative method to estimate the length of a longitudinal degree at latitude formula_5 is to assume a spherical Earth (to get the width per minute and second, divide by 60 and 3600, respectively): where Earth's average meridional radius formula_7 is . Since the Earth is not spherical that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude formula_5 is where Earth's equatorial radius formula_10 equals ""6,378,137 m"""
"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"
"With the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal ""degrees"" called ""grad"" or ""gon"", where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° = gon). Although that idea was abandoned by Napoleon, grades continued to be used in several fields and many scientific calculators support them. Decigrades () were used with French artillery sights in World War I. An angular mil, which is most used in military applications, has at least three specific variants, ranging from to"
"Circular segment In geometry, a circular segment (symbol: ⌓) is a region of a circle which is ""cut off"" from the rest of the circle by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is bounded by an arc (of less than 180°) of a circle and by the chord connecting the endpoints of the arc. Let ""R"" be the radius of the circle, ""θ"" the central angle in radians, α is the central angle in degrees, ""c"" the chord length, ""s"" the arc length, ""h"" the sagitta (height) of the"