What is Oval (geometry)?

Information about Oval (geometry)

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An oval with two axes of symmetry.


In geometry, an oval or ovoid (from Latin ovum, 'egg') is any curve resembling an egg or an ellipse. Unlike other curves, the term 'oval' is not well-defined and many distinct curves are commonly called ovals. These curves have in common that: The word ovoidal refers to the characteristic of being an ovoid.

Other examples of ovals described elsewhere include: A track is known as a stadium, and is actually not a rounded rectangle.

Egg shape

The shape of an egg is approximately that of half each a prolate (long) and roughly spherical (potentially even minorly 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.

Projective planes

In the theory of projective planes, oval is used to mean a set of q + 1 non-collinear points in PG(2,q), the projective plane over the finite field with q elements. See oval (projective plane).
In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. A simple example is the circle.
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An egg(jamie rolands) is a body consisting of an ovum surrounded by layers of membranes and an outer casing of some type, which acts to nourish and protect a developing embryo.
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ellipse (from the Greek ἔλλειψις, literally absence) is the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant.
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In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. A simple example is the circle.
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In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. A simple example is the circle.
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convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object. For example, a solid cube is convex, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex.
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In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. A simple example is the circle.
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In mathematics, a plane curve is a curve in a Euclidian plane (cf. space curve). The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves.
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Shape (OE. sceap Eng. created thing), refers to the external two-dimensional outline, appearance or configuration of some thing — in contrast to the matter or content or substance of which it is composed.
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circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the centre.

Circles are simple closed curves which divide the plane into an interior and exterior.
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ellipse (from the Greek ἔλλειψις, literally absence) is the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant.
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Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.

It is the most common type of symmetry. In 2D there is an axis of symmetry, in 3D a plane of symmetry.
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Cassini oval is a set (or locus) of points in the plane such that each point p on the oval bears a special relation to two other, fixed points q1 and q2: the product of the distance from p to q1
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In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety—that is, it has a multiplication defined algebraically with respect to which it is an
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superellipse (or Lamé curve) is the geometric figure defined in the cartesian coordinate system as the set of all points (x, y) with
where n > 0 and a and b are the radii of the oval shape.
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An egg(jamie rolands) is a body consisting of an ovum surrounded by layers of membranes and an outer casing of some type, which acts to nourish and protect a developing embryo.
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A prolate spheroid is a spheroid in which the polar diameter is longer than the equatorial diameter.

Prolate spheroids in sport

The prolate spheroid is the shape of the ball in several sports, such as Rugby Football and Australian Rules Football.
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oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it. An M&M's candy (plain) (US) or Smartie (UK and Europe) is an approximate example of an oblate spheroid.
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ellipsoid is a type of quadric surface that is a higher dimensional analogue of an ellipse. The equation of a standard ellipsoid body in an x-y-z Cartesian coordinate system is
where a and b
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principal axes has multiple uses:
  • For physical principal axes of a rigid body, see moment of inertia.
  • For the principal axes of an aircraft, see flight controls or flight dynamics
See also spectral theorem.
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rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag (see opposite) has
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Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.

It is the most common type of symmetry. In 2D there is an axis of symmetry, in 3D a plane of symmetry.
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semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

Ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape.
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projective plane has two possible definitions, one of them coming from linear algebra, and another (which is more general) coming from axiomatic and finite geometry. The first definition quickly produces planes that are homogeneous spaces for some of the classical groups.
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Collinearity may refer to:
  • Line (mathematics)
  • Multicollinearity

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In abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains only finitely many elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and coding theory.
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In PG(2,q), with q a prime power, an oval is a set of points, no three of which are collinear. Indeed, in any finite projective plane of order q, an oval is a set of points, no three collinear.
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