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Oval
An oval (from Latin ovum, "egg") is a closed curve in a plane which "loosely" resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or two axes of symmetry. In common English, the term is used in a broader sense: any shape which reminds one of an egg. The three-dimensional version of an oval is called an ovoid.Contents1 Oval
Oval
in geometry 2 Projective geometry 3 Egg shape 4 Technical drawing 5 In common speech 6 See also 7 Notes Oval
Oval
in geometry[edit]This oval, with only one axis of symmetry, resembles a chicken egg.The term oval when used to describe curves in geometry is not well-defined, except in the context of projective geometry. Many distinct curves are commonly called ovals or are said to have an "oval shape"
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Oxford English Dictionary
The Oxford
Oxford
English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University
Oxford University
Press. It traces the historical development of the English language, providing a comprehensive resource to scholars and academic researchers, as well as describing usage in its many variations throughout the world.[2][3] The second edition came to 21,728 pages in 20 volumes, published in 1989. Work began on the dictionary in 1857, but it was not until 1884 that it began to be published in unbound fascicles as work continued on the project, under the name of A New English Dictionary on Historical Principles; Founded Mainly on the Materials Collected by The Philological Society
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Superellipse
A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape. In the Cartesian coordinate system, the set of all points (x, y) on the curve satisfy the equation x a n + y b n = 1 , displaystyle left frac x a right^ n !+left frac y b right^ n !=1, where n, a and b are positive numbers, and the vertical bars   around a number indicate the absolute value of the number.Contents1 Specific cases 2 Mathematical properties 3 Generalizations 4 History 5 See also 6 References 7 External linksSpecific cases[edit] This formula defines a closed c
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Vesica Piscis
The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other.[1] In Latin, "vesica piscis" literally means "bladder of a fish", reflecting the shape's resemblance to the conjoined dual air bladders ("swim bladder") found in most fish. In Italian, the shape's name is mandorla ("almond").The vesica piscis in Euclid's ElementsThis figure appears in the first proposition of Euclid's Elements, where it forms the first step in constructing an equilateral triangle using a compass and straightedge
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Athletics Track
An all-weather running track is a rubberized artificial running surface for track and field athletics. It provides a consistent surface for competitors to test their athletic ability unencumbered by adverse weather conditions. Historically, various forms of dirt, grass, sand and crushed cinders were used. Many examples of these varieties of track still exist worldwide.Contents1 Measurement of a track1.1 Lane measurement2 History 3 See also 4 References 5 External linksMeasurement of a track[edit] The proper length of the 1st lane of a competitive running track is 400 m (1,312.3 ft). Some tracks are not built to this specification, instead some are legacy to imperial distances like 440 yd (402.3 m). Prior to rule changes in 1979, distances in Imperial units
Imperial units
were still used in the United States. Some facilities build tracks to fit the available space
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Tangential
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz
Leibniz
defined it as the line through a pair of infinitely close points on the curve.[1] More precisely, a straight line is said to be a tangent of a curve y = f (x) at a point x = c on the curve if the line passes through the point (c, f (c)) on the curve and has slope f '(c) where f ' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space. As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point
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Radius
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin
Latin
radius, meaning ray but also the spoke of a chariot wheel.[1] The plural of radius can be either radii (from the Latin
Latin
plural) or the conventional English plural radiuses.[2] The typical abbreviation and mathematical variable name for radius is r. By extension, the diameter d is defined as twice the radius:[3] d ≐ 2 r ⇒ r = d 2 . displaystyle ddoteq 2rquad Rightarrow quad r= frac d 2 . If an object does not have a center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere
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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 widest points of the perimeter. The semi-major axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter
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Reflection Symmetry
Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric
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Rotational Symmetry
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks the same.Contents1 Formal treatment1.1 Discrete rotational symmetry 1.2 Examples 1.3 Multiple symmetry axes through the same point 1.4 Rotational symmetry
Rotational symmetry
with respect to any angle 1.5 Rotational symmetry
Rotational symmetry
with translational symmetry2 See also 3 References 4 External linksFormal treatment[edit] See also: Rotational invariance Formally the rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation
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Principal Axis Theorem
In the mathematical fields of geometry and linear algebra, a principal axis is a certain line in a Euclidean space
Euclidean space
associated with an ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular, and gives a constructive procedure for finding them. Mathematically, the principal axis theorem is a generalization of the method of completing the square from elementary algebra. In linear algebra and functional analysis, the principal axis theorem is a geometrical counterpart of the spectral theorem. It has applications to the statistics of principal components analysis and the singular value decomposition
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Ellipsoid
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface, that is a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse like"). It is bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular axes of symmetry which intersect at a center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the principal axes, or simply axes of the ellipsoid
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Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth. Lines are an idealization of such objects. Until the 17th century, lines were defined in this manner: "The [straight or curved] line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width
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Closed Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that its curvature need not be zero.[a] Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However, many of these meanings are special instances of the definition which follows. A curve is a topological space which is locally homeomorphic to a line. In everyday language, this means that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola, shown to the right
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Special
Special
Special
or specials may refer to:Contents1 Music 2 Film and television 3 Other uses 4 See alsoMusic[edit] Special
Special
(album), a 1992
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Synonym
A synonym is a word or phrase that means exactly or nearly the same as another word or phrase in the same language. Words that are synonyms are said to be synonymous, and the state of being a synonym is called synonymy. For example, the words begin, start, commence, and initiate are all synonyms of one another. Words are typically synonymous in one particular sense: for example, long and extended in the context long time or extended time are synonymous, but long cannot be used in the phrase extended family. Synonyms with the exact same meaning share a seme or denotational sememe, whereas those with inexactly similar meanings share a broader denotational or connotational sememe and thus overlap within a semantic field
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