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Diameter
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 (geometry), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diameter Of A Set
In mathematics, the diameter of a set of points in a metric space is the largest distance between points in the set. As an important special case, the diameter of a metric space is the largest distance between any two points in the space. This generalizes the diameter of a circle, the largest distance between two points on the circle. This usage of diameter also occurs in medical terminology concerning a lesion or in geology concerning a rock. A bounded set is a set whose diameter is finite. Within a bounded set, all distances are at most the diameter. Formal definition The diameter of an object is the least upper bound (denoted "sup") of the set of all distances between pairs of points in the object. Explicitly, if S is a set of points with distances measured by a Metric (mathematics), metric \rho, the diameter is \operatorname(S) = \sup_ \rho(x, y). Of the empty set The diameter of the empty set is a matter of convention. It can be defined to be zero, -\infty, or undefined. ... [...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] |
Circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a Disk (mathematics), disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Terminology * Annulus (mathematics), Annulus: a ring-shaped object, the region bounded by two concentric circles. * Circular arc, Arc: any Connected ... [...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] |
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] |
Sphere
A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the center (geometry), ''center'' of the sphere, and the distance is the sphere's ''radius''. The earliest known mentions of spheres appear in the work of the Greek mathematics, ancient Greek mathematicians. The sphere is a fundamental surface in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubble (physics), Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is spherical Earth, often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres rolling, roll smoothly in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sauter Mean Diameter
In fluid dynamics, Sauter mean diameter (SMD) is an average measure of particle size. It was originally developed by German scientist Josef Sauter in the late 1920s. It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. Several methods have been devised to obtain a good estimate of the SMD. Definition The Sauter diameter (''SD'', also denoted ''D'' ,2or ''d''32) for a given particle is defined as: :SD = \frac where ''d''''s'' is the so-called ''surface diameter'' and ''d''''v'' is the ''volume diameter'', defined as: :d_s = \sqrt :d_v = \left(\frac\right)^, The quantities ''A''''p'' and ''V''''p'' are the ordinary surface area and volume of the particle, respectively. The equation may be simplified further as: :SD = 6\frac. This is usually taken as the mean of several measurements ''n'', to obtain the Sauter mean diameter (SMD): :SMD = \sum_i^n SD_i / n This provides intrinsic data that help determine the part ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius
In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is the line segment or distance from its center to any of its Vertex (geometry), vertices. The name comes from the Latin ''radius'', meaning ray but also the spoke of a chariot wheel.Definition of Radius at dictionary.reference.com. Accessed on 2009-08-08. The typical abbreviation and mathematical symbol for radius is ''R'' or ''r''. By extension, the diameter ''D'' is defined as twice the radius:Definition of radius at mathwords.com. ... [...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] |
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] |
Line Segment
In geometry, a line segment is a part of a line (mathematics), straight line that is bounded by two distinct endpoints (its extreme points), and contains every Point (geometry), point on the line that is between its endpoints. It is a special case of an ''arc (geometry), arc'', with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is often denoted using an overline (vinculum (symbol), vinculum) above the symbols for the two endpoints, such as in . Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (geometry), edge (of that polygon or polyhedron) if they are adjacent vertices, or a diagonal. Wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
