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| | 41 year old Paediatrician Merle from Carp, has many passions that include bird watching, [http://www.rmmonline.com/portfolio/content/new-launches-singapore-property-guides-articles property agents singapore] developers in singapore and sleeping. Likes to visit new places like Historic Centre of Riga. |
| {{Refimprove|date=June 2012}}
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| An '''oval''' (from Latin ''ovum'', "egg") is a [[closed curve]] in a [[plane (geometry)|plane]] which "loosely" resembles the outline of an [[egg (food)|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.
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| In common English, the term is used in a broader sense: any shape which ''reminds'' one of an egg.
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| The 3-dimensional version of an oval is called an '''ovoid'''.
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| ==Oval in geometry==
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| [[File:oval1.svg|thumb|right|This oval, with only one axis of symmetry, resembles a chicken egg.]]
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| The term '''oval''' when used to describe [[curve]]s 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". Generally, to be called an oval, a [[Plane (geometry)|plane]] curve should ''resemble'' the outline of an [[Egg (food)|egg]] or an [[ellipse]]. In particular, the common traits that these curves have are:
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| * they are [[curve|differentiable]] (smooth-looking),<ref>When this property makes sense, i.e. when on a differentiable manifold. In more general settings one might only require that there exist a unique tangent line at each point of the curve.</ref> [[curve|simple]] (not self-intersecting), [[Convex set|convex]], [[curve|closed]], [[plane curve]]s;
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| * their [[shape]] does not depart much from that of an [[ellipse]], and
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| * there is at least one [[axis of symmetry]].
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| Examples of ovals described elsewhere include:
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| *[[Cassini oval]]s
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| *[[elliptic curve]]s
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| *[[superellipse]]
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| *[[Cartesian oval]]
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| An '''ovoid''' is the 3-dimensional surface generated by rotating an oval curve about one of its axes of symmetry.
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| The adjectives '''ovoidal''' and '''ovate''' mean having the characteristic of being an ovoid, and are often used as [[synonym]]s for "egg-shaped".
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| ==Projective geometry==
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| [[File:Chicken egg 2009-06-04.jpg|thumb|200px| A chicken egg is a naturally occurring ovoid]]
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| In the theory of [[projective plane]]s, '''''oval''''' is used to mean a set of ''n'' + 1 points in a projective plane of order ''n'', with no three on a common line (no three points are [[line (geometry)|collinear]]). See [[oval (projective plane)]].
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| An '''[[ovoid (projective geometry)|ovoid]]''' in the finite projective geometry PG(3,q), is a set of ''q''<sup>2</sup> + 1 points such that no three points are collinear. At each point of an ovoid all the tangent lines to the ovoid lie in a single plane.
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| ==Egg shape==
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| The shape of an [[egg (food)|egg]] is approximately half of each of a [[prolate spheroid|prolate]] (long) and a roughly spherical (potentially even slightly [[Oblate spheroid|oblate]]/short) [[ellipsoid]] joined at the equator, sharing a [[principal axis]] of [[rotational symmetry]], as illustrated above. Although the term ''egg-shaped'' usually implies a lack of [[reflection symmetry]] across the equatorial plane, it may also refer to true prolate ellipsoids. It can also be used to describe the 2-dimensional figure that, revolved around its [[major axis]], produces the 3-dimensional surface. Refer to the following equation for an approximation of a 3D egg where the letter "a" represents any positive constant:
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| :<math>x^2 + y^2 + z^2(1.5\cos((z+a/2)/a))^2 = a\!</math>
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| ==Technical drawing==
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| [[File:Owal by Zureks.svg|thumb|An oval with two axes of symmetry constructed from four arcs (top), and comparison of blue oval and red ellipse with the same dimensions of short and long axes (bottom).]]
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| In [[technical drawing]], an '''oval''' is a figure constructed from two pairs of arcs, with two different [[radius|radii]] (see image on the right). The arcs are joined at a point, in which lines [[tangential]] to both joining arcs lie on the same line, thus making the joint smooth. Any point of an oval belongs to an arc with a constant radius (shorter or longer), whereas in an [[ellipse]] the radius is continuously changing.
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| ==In common English==
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| In common speech "oval" means a shape rather like an egg or an ellipse, which may be two-dimensional or three-dimensional. It also often refers to a figure that resembles two semicircles joined by a rectangle, like a [[cricket field|cricket infield]] or [[oval track racing|oval racing track]]. This is more correctly, although archaically, described as [[oblong]].<ref name="OED, Oblong" >{{Cite book
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| |title=[[Oxford English Dictionary]]
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| |chapter=Oblong
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| |edition=
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| |year=1933
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| |quote='''A''' ''adj.'' '''1.''' Elongated in one direction (usually as a deviation from an exact square or circular form): having the chief axis considerably longer than the transverse diameter
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| }}</ref> Sometimes it can even refer to any rectangle with rounded corners.
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| The shape lends its name to many well-known places (see [[Oval (disambiguation)]]).
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| ==See also==
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| *[[Vesica piscis]] – a pointed oval
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| *[[Ellipse]]
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| *[[Stadium (geometry)]]
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| == Notes ==
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| {{Reflist}}
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| [[Category:Curves]]
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| [[Category:Elementary shapes]]
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41 year old Paediatrician Merle from Carp, has many passions that include bird watching, property agents singapore developers in singapore and sleeping. Likes to visit new places like Historic Centre of Riga.