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In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere. In more modern usage, the length d of a diameter is also called the diameter. In this sense one speaks of diameter rather than diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius r. :d = 2r \qquad\text\qquad r = \frac. The word "diameter" is derived from (), "diameter of a circle", from (), "across, through" and (), "measure". It is often abbreviated \text, \text, d, or \varnothing. Constructions With straightedge and compass, a diameter of a given circle can be constructed as the perpendicular bisector of an arbitrary chord. Drawing two diameters in this way can be used to locate the center of a circle, as t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filter Thread
In photography and cinematography, a filter is a camera accessory consisting of an optical filter that can be inserted into the optical path. The filter can be of a square or oblong shape and mounted in a holder accessory, or, more commonly, a glass or plastic disk in a metal or plastic ring frame, which can be screwed into the front of or clipped onto the camera lens. Filters modify the images recorded. Sometimes they are used to make only subtle changes to images; other times the image would simply not be possible without them. In monochrome photography, coloured filters affect the relative brightness of different colours; red lipstick may be rendered as anything from almost white to almost black with different filters. Others change the colour balance of images, so that photographs under incandescent lighting show colours as they are perceived, rather than with a reddish tinge. There are filters that distort the image in a desired way, diffusing an otherwise sharp image, adding ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miscellaneous Technical
Miscellaneous Technical is a Unicode block ranging from U+2300 to U+23FF. It contains various common symbols which are related to and used in the various technical, programming language, and academic professions. For example: * Symbol ⌂ (HTML hexadecimal code is ⌂) represents a house or a home. * Symbol ⌘ (⌘) is a "place of interest" sign. It may be used to represent the '' Command key'' on a Mac keyboard. * Symbol ⌚ (⌚) is a watch (or clock). * Symbol â (⏏) is the "Eject" button symbol found on electronic equipment. * Symbol âš (⏚) is the " Earth Ground" symbol found on electrical or electronic manual, tag and equipment. It also includes most of the uncommon symbols used by the APL programming language. Miscellaneous Technical (2300–23FF) in Unicode In Unicode, ''Miscellaneous Technical'' symbols placed in the hexadecimal range 0x2300–0x23FF, (decimal 8960–9215), as described below. (2300–233F) :1. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydraulic Diameter
The hydraulic diameter, , is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. When the cross-section is uniform along the tube or channel length, it is defined as : D_\text = \frac, where : is the cross-sectional area of the flow, : is the wetted perimeter of the cross-section. More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius , which is defined as the cross-sectional area of the channel divided by the wetted perimeter. Here, the wetted perimeter includes all surfaces acted upon by shear stress from the fluid. : R_\text = \frac, : D_\text = 4R_\text, Note that for the case of a circular pipe, : D_\text =\frac=2R The need for the hydraulic diameter arises due to the use of a single dimension in the case of a dimensionless quantity such as the Reynolds number, which prefers a single variable for flow analysis rather t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalent Diameter
In applied sciences, the equivalent radius (or mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter (or mean diameter) (D) is twice the equivalent radius. Perimeter equivalent The perimeter of a circle of radius ''R'' is 2 \pi R. Given the perimeter of a non-circular object ''P'', one can calculate its perimeter-equivalent radius by setting :P = 2\pi R_\text or, alternatively: :R_\text = \frac For example, a square of side ''L'' has a perimeter of 4L. Setting that perimeter to be equal to that of a circle imply that :R_\text = \frac \approx 0.6366 L Applications: * US hat size is the circumference of the head, measured in inches, divided by pi, rounded to the nearest 1/8 inch. This corresponds to the 1D mean diameter. * Diameter at breast height is the circumference of tree trunk, measured at height of 4.5 feet, divided by pi. This corresponds to the 1D mean diameter. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugate Diameters
In geometry, two diameters of a conic section are said to be conjugate if each chord (geometry), chord parallel (geometry), parallel to one diameter is bisection, bisected by the other diameter. For example, two diameters of a circle are conjugate if and only if they are perpendicular. Of ellipse For an ellipse, two diameters are conjugate if and only if the tangent line to the ellipse at an endpoint of one diameter is parallel to the other diameter. Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram, sometimes called a bounding parallelogram (skewed compared to a bounding rectangle). In his manuscript De motu corporum in gyrum, and in the 'Philosophiæ Naturalis Principia Mathematica, Principia', Isaac Newton cites as a lemma (mathematics), lemma proved by previous authors that all (bounding) parallelograms for a given ellipse have the same area. It is possible to Compass and straightedge constructions, reconstruct an ellipse from any pai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle. The length of the semi-major axis of an ellipse is related to the semi-minor axis's length through the eccentricity and the semi-latus rectum \ell, as follows: The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the cente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity (mathematics), eccentricity e, a number ranging from e = 0 (the Limiting case (mathematics), limiting case of a circle) to e = 1 (the limiting case of infinite elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic solution for its area, but for Perimeter of an ellipse, its perimeter (also known as circumference), Integral, integration is required to obtain an exact solution. The largest and smallest diameters of an ellipse, also known as its width and height, are typically denoted and . An ellipse has four extreme points: two ''Vertex (geometry), vertices'' at the endpoints of the major axis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Center (geometry)
In geometry, a centre (English in the Commonwealth of Nations, Commonwealth English) or center (American English) () of an shape, object is a point (geometry), point in some sense in the middle of the object. According to the specific definition of centre taken into consideration, an object might have no centre. If geometry is regarded as the study of isometry groups, then a centre is a fixed point of all the isometries that move the object onto itself. Circles, spheres, and segments The centre of a circle is the point equidistant from the points on the edge. Similarly the centre of a sphere is the point equidistant from the points on the surface, and the centre of a line segment is the midpoint of the two ends. Symmetric objects For objects with several symmetries, the centre of symmetry is the point left unchanged by the symmetric actions. So the centre of a square (geometry), square, rectangle, rhombus or parallelogram is where the diagonals intersect, this is (among other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord (geometry)
A chord (from the Latin ''chorda'', meaning " bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a ''secant line''. The perpendicular line passing through the chord's midpoint is called '' sagitta'' (Latin for "arrow"). More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's ''diameter''. In circles Among properties of chords of a circle are the following: # Chords are equidistant from the center if and only if their lengths are equal. # Equal chords are subtended by equal angles from the center of the circle. # A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. # If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Section
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set of those points whose distances to some particular point, called a '' focus'', and some particular line, called a ''directrix'', are in a fixed ratio, called the ''eccentricity''. The type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is, as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supremum
In mathematics, the infimum (abbreviated inf; : infima) of a subset S of a partially ordered set P is the greatest element in P that is less than or equal to each element of S, if such an element exists. If the infimum of S exists, it is unique, and if ''b'' is a lower bound of S, then ''b'' is less than or equal to the infimum of S. Consequently, the term ''greatest lower bound'' (abbreviated as ) is also commonly used. The supremum (abbreviated sup; : suprema) of a subset S of a partially ordered set P is the least element in P that is greater than or equal to each element of S, if such an element exists. If the supremum of S exists, it is unique, and if ''b'' is an upper bound of S, then the supremum of S is less than or equal to ''b''. Consequently, the supremum is also referred to as the ''least upper bound'' (or ). The infimum is, in a precise sense, dual to the concept of a supremum. Infima and suprema of real numbers are common special cases that are important in analy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
