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A concretion is a hard and compact mass formed by the precipitation of mineral cement within the spaces between particles, and is found in sedimentary rock or soil. [1] Concretions are often ovoid or spherical in shape, although irregular shapes also occur.
To the definition of an ovoid: t tangent, s secant line. In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension d ≥ 3. Simple examples in a real projective space are hyperspheres . The essential geometric properties of an ovoid are:
This produces a variation on the definition, namely the projective plane is defined as the set of lines in that pass through the origin and the coordinates of a non-zero element (,,) of a line are taken to be homogeneous coordinates of the line. These lines are now interpreted as points in the projective plane.
To the definition of an oval in a projective plane To the definition of an ovoid. In a projective plane a set Ω of points is called an oval, if: Any line l meets Ω in at most two points, and; For any point P ∈ Ω there exists exactly one tangent line t through P, i.e., t ∩ Ω = {P}.
In chemistry, the dispersity is a measure of the heterogeneity of sizes of molecules or particles in a mixture. A collection of objects is called uniform if the objects have the same size, shape, or mass. A sample of objects that have an inconsistent size, shape and mass distribution is called non-uniform.
Homogeneity and heterogeneity; only ' b ' is homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image.A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous ...
An ovoid of () (a symplectic polar space of rank n) would contain + points. However it only has an ovoid if and only n = 2 {\displaystyle n=2} and q is even. In that case, when the polar space is embedded into P G ( 3 , q ) {\displaystyle PG(3,q)} the classical way, it is also an ovoid in the projective geometry sense.
The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction (gravitation) and the centrifugal force of the Earth's rotation.