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An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation...

the angle formed between the vector perpendicular (or normal) to the ellipsoidal surface from the point, and the plane of the equator. Two levels of abstraction...

the motion of its inertia ellipsoid, which is rigidly fixed to the rigid body like a coordinate frame. Its inertia ellipsoid rolls, without slipping, on...

An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's shape and size, used as part of a reference frame for coordinates...

Erdmessung (Central Bureau of International Geodesy), and a series of global ellipsoids of the Earth were derived (e.g., Helmert 1906, Hayford 1910 and 1924)...

surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of about...

the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates a sequence of ellipsoids whose...

celestial body is called a reference ellipsoid. The reference ellipsoid for Earth is called an Earth ellipsoid. An ellipsoid of revolution is uniquely defined...

A Jacobi ellipsoid is a triaxial (i.e. scalene) ellipsoid under hydrostatic equilibrium which arises when a self-gravitating, fluid body of uniform density...

giving us a varying ellipsoid of constant energy. This is shown in the animation as a fixed orange ellipsoid and increasing blue ellipsoid. For concreteness...

A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal...

In geometry, ellipsoid packing is the problem of arranging identical ellipsoid throughout three-dimensional space to fill the maximum possible fraction...

Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system ( λ , μ , ν ) {\displaystyle (\lambda ,\mu ,\nu )} that generalizes the two-dimensional...

In geodesy, the Hayford ellipsoid is a reference ellipsoid named after the American geodesist John Fillmore Hayford (1868–1925), which was introduced in...

ellipse. There are two types of ellipsoidal domes: prolate ellipsoidal domes and oblate ellipsoidal domes. A prolate ellipsoidal dome is derived by rotating...

The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth...

standards, also includes a choice of geodetic datum (including an Earth ellipsoid), as different datums will yield different latitude and longitude values...

line) tangent line and the normal vector to the surface of the reference ellipsoid (chosen to approximate the Earth's sea-level surface). VDs are caused...

5 mm (0.020 in) on the Earth ellipsoid. Vincenty's goal was to express existing algorithms for geodesics on an ellipsoid in a form that minimized the...

In robot kinematics, the manipulability ellipsoid represents the manipulability of a robotic system in a graphical form. Here, the manipulability of a...

The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic...

axes of that special ellipsoid. The dimensions of a minor planet can be uni-, bi- or tri-axial, depending on what kind of ellipsoid is used to model it...

geodesy based on a reference ellipsoid. They include geodetic latitude (north/south) ϕ, longitude (east/west) λ, and ellipsoidal height h (also known as geodetic...

A condyloid joint (also called condylar, ellipsoidal, or bicondylar) is an ovoid articular surface, or condyle that is received into an elliptical cavity...

reference ellipsoid is called geoidal undulation, and it varies globally between ±110 m based on the GRS 80 ellipsoid. A reference ellipsoid, customarily...

In mathematics, the John ellipsoid or Löwner–John ellipsoid E(K) associated to a convex body K in n-dimensional Euclidean space ⁠ R n {\displaystyle \mathbb...

an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia. In the early 19th century, the flattening of the earth ellipsoid was...

In crystal optics, the index ellipsoid (also known as the optical indicatrix or sometimes as the dielectric ellipsoid) is a geometric construction which...

The n-vector representation (also called geodetic normal or ellipsoid normal vector) is a three-parameter non-singular representation well-suited for...

The reference surfaces for some planets (such as Earth and Mars) are ellipsoids of revolution for which the equatorial radius is larger than the polar...

mapped even if they are too irregular to be modeled well with a sphere or ellipsoid. The most well-known map projection is the Mercator projection. This map...

expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattened sphere whose equatorial bulge is caused...

the geocentric radius, R0, not restricted to points on the reference ellipsoid surface. The geocentric altitude is a type of altitude defined as the...

The Airy spheroid or Airy ellipsoid is a mathematical model of the Earth, an Earth ellipsoid, designed to fit the well for the British Isles. It is named...

as an ellipsoid whose semi-axes are equal to the eigenvalues and directed along their corresponding eigenvectors. In particular, if the ellipsoid is stretched...

calculations from its light curve are consistent with it being a Jacobi ellipsoid (the shape it would be if it were a dwarf planet), with its major axis...

crystallography, thermal ellipsoids, more formally termed atomic displacement parameters or anisotropic displacement parameters, are ellipsoids used to indicate...

stress ellipsoid is an alternative to Mohr's circle for the graphical representation of the stress state at a point. The surface of the ellipsoid represents...

scientists defined ellipsoids of revolution, more closely emulating the shape of Earth, modified for a particular zone; a published ellipsoid would be a good...

triaxial ellipsoid maps Earth or some other astronomical body modeled as a triaxial ellipsoid to the plane. Such a model is called the reference ellipsoid. In...

which means it ignores altitude and treats the earth surface as an oblate ellipsoid. The system divides Earth into 60 zones and projects each to the plane...

planetary datums. Since the rise of the global positioning system (GPS), the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications...

h} data points, but the Minimum Volume Ellipsoid estimates multivariate location and scatter from the ellipsoid of minimal volume that encapsulates the...

measurements on a reference ellipsoid approximating the entire Earth, which is what systems such as GPS do. In aviation, the reference ellipsoid known as WGS84 is...

between two geographic points are: Flat surface; Spherical surface; Ellipsoidal surface. All abstractions above ignore changes in elevation. Calculation...

assembly for the government of the French Revolution should be a triaxial ellipsoidal dome. The lines of curvature are the guiding curves for the workers to...

beobachteter Eigenbewegungen" [On the determination, according to the ellipsoid hypothesis, of the vertex and apex from a small number of observed proper...

Geodetic Reference System 1980 (GRS80) consists of a global reference ellipsoid and a normal gravity model. The GRS80 gravity model has been followed...

parabolas, and hyperbolas). In three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids. More generally, a quadric hypersurface...

Earth, the reference ellipsoid is the International Reference Ellipsoid, and the value of gravity predicted for points on the ellipsoid is the normal gravity...

above inequality defines an ellipsoidal region in the p-dimensional Cartesian parameter space Rp. The centre of the ellipsoid is at the estimate β ^ {\displaystyle...

Clairaut's theorem characterizes the surface gravity on a viscous rotating ellipsoid in hydrostatic equilibrium under the action of its gravitational field...

convex minimization problems (similar to conjugate gradient methods). Ellipsoid method: An iterative method for small problems with quasiconvex objective...

represented by an ellipsoid—if the diffusion values of the six terms of the quadric ellipsoid are placed into the matrix, this generates an ellipsoid angled off...

components such as carbon and nitrogen to cycle. Earth is rounded into an ellipsoid with a circumference of about 40,000 kilometres (24,900 miles). It is...

horizontal datum called the United States Standard Datum, based on the Clarke Ellipsoid of 1866. It was fitted to data previously collected for regional datums...

In mathematics, a superellipsoid (or super-ellipsoid) is a solid whose horizontal sections are superellipses (Lamé curves) with the same squareness parameter...

Practically, they run as fast as the simplex method—in contrast to the ellipsoid method, which has polynomial run-time in theory but is very slow in practice...

geometry of the ellipsoid". The Mercator Projections: The Normal and Transverse Mercator Projections on the Sphere and the Ellipsoid with Full Derivations...

Dirichlet's ellipsoidal problem, named after Peter Gustav Lejeune Dirichlet, asks under what conditions there can exist an ellipsoidal configuration...

chromaticity diagram above. A more general concept is that of "discrimination ellipsoids" in the entire three-dimensional color space, which would include the...

compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity...

state borders. SK-42 is based on the Krasovsky 1940 ellipsoid, a locally best fitting reference ellipsoid named after Feodosy Krasovsky. It has a semi-major...

parallels is possible for an ellipsoidal model, it would no longer be equidistant because the distance between parallels on an ellipsoid is not constant. More...

Ellipsoidal reflector spot (abbreviated to ERS, or colloquially ellipsoidal or ellipse) is the name for a type of stage lighting instrument, named for...

The MacCullagh ellipsoid is defined by the equation: x 2 A + y 2 B + z 2 C = 2 E , {\displaystyle {\frac {x^{2}}{A}}+{\frac {y^{2}}{B}}+{\frac {z^{2}}{C}}=2E...

formulas at all scales whereas large-scale Mercator maps normally use the ellipsoidal form of the projection.[citation needed] The discrepancy is imperceptible...

American mathematician and computer scientist. He was most famous for his ellipsoid algorithm (1979) for linear programming, which was the first such algorithm...

geocentric frames (see below). OSGB36 is based on the Airy ellipsoid, a reference ellipsoid named after George Biddell Airy. Introduced in 1830, it is...

measurements of meridian arcs can be used to infer the shape of the reference ellipsoid that best approximates the geoid in the region of the measurements. Measurements...

Geodesy Sea Level Datum of 1929 Topographic elevation Topography Reference ellipsoid Geoid US Department of Commerce, National Oceanic and Atmospheric Administration...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

nonlinear programming. It can still be solved in polynomial time by the ellipsoid method if the objective function is convex; otherwise the problem may...

Rotating ellipsoidal variables are a class of close binary variable star systems whose components are ellipsoidal. They are not eclipsing, but fluctuations...

leads to a deformation of electric fields which he called "Heaviside-Ellipsoid" of axial ratio original modern α : 1 : 1 α = 1 − u 2 v 2 | 1 γ : 1 :...

direction and the Earth's axis of rotation. They are also known as local ellipsoidal system, local geodetic coordinate system, local vertical, local horizontal...

surface of Earth is better modelled by an oblate ellipsoid of revolution, for small scale maps the ellipsoid is approximated by a sphere of radius a, where...

geometric model represents the Earth, and comes in the form of a sphere or ellipsoid. Tissot's indicatrices illustrate linear, angular, and areal distortions...

The ellipsoid method is a general method for convex programming, and can be used in particular to solve SDPs. In the context of SDPs, the ellipsoid method...

metal-organic framework thermal ellipsoids - [1] 2009 paper by Korostelev and Noller depicting tRNA thermal ellipsoids - Analysis of Structural Dynamics...

Maclaurin spheroid is considered to be the simplest model of rotating ellipsoidal figures in hydrostatic equilibrium since it assumes uniform density....

opposed to height above mean sea level (AMSL or HAMSL), height above ellipsoid (HAE, as reported by a GPS receiver), or height above average terrain...

single genus, Alphaovalivirus, which contains a single species, Sulfolobus ellipsoid virus 1 (Alphaovalivirus fumarolicaense). The linear genome of dsDNA is...

shape of the object is symmetrically rounded, mostly by rotation, into an ellipsoid, where any irregular surface features are consequent to a relatively thin...

great semicircle on Earth's surface. Adopting instead a spheroidal or ellipsoid model of Earth, the meridian is half of a north-south great ellipse. The...

}}}={\sqrt[{3}]{\frac {3}{4\pi }}}L\approx 0.6204L} Similarly, a tri-axial ellipsoid with axes a {\displaystyle a} , b {\displaystyle b} and c {\displaystyle...

fitting ellipsoid for GB, 1858) These values were of academic value only since Britain continued to define latitude and longitude on the Airy ellipsoid or...

icosahedron cones and cylinders the sphere other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids. Advanced topics include: projective geometry...

most recent models show that Psyche has a shape consistent with a Jacobi ellipsoid and dimensions within a few km of 278 km x 238 km x 171 km. Each shape...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

centers when the ellipsoids are in point contact externally. This distance of closest approach is a function of the shapes of the ellipsoids and their orientation...

geometry, a circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane section of the quadric, as this...

cylinder slices through the model globe. Both exist in spherical and ellipsoidal versions. Both projections are conformal, so that the point scale is...

encompassing some of the best known and most common species. The cuttlebone is ellipsoid in shape. The name of the genus is the Latinised form of the Ancient Greek...

rotates so quickly (once every 3.9 hours) that it is stretched into an ellipsoid. It is part of a collisional family of Kuiper belt objects that share...

projection, and when on a sphere, also a perspective projection. On an ellipsoid, the perspective definition of the stereographic projection is not conformal...

limit, leading it to disintegrate. The Moon is a very slightly scalene ellipsoid due to tidal stretching, with its long axis displaced 30° from facing...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

print is olive-brown to reddish-brown. The spores are 9.5–17 by 4–6 μm, ellipsoid to somewhat ventricose (inflated on one side), smooth, and yellowish....

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

is usually converted to latitude, longitude and height relative to an ellipsoidal Earth model. The height may then be further converted to height relative...

physicist Augustin-Jean Fresnel, is one of a series of confocal prolate ellipsoidal regions of space between and around a transmitter and a receiver. The...

Ball and socket joint 1: Ball and socket joint; 2: Condyloid joint (Ellipsoid); 3: Saddle joint; 4 Hinge joint; 5: Pivot joint Capsule of shoulder-joint...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

The exterior of the NCPA is a steel structural shell. It has a semi-ellipsoidal shape. The length of the long axis in the east-west direction of the...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Geodesy portal History of Science portal Arabic mile Arc measurement Earth ellipsoid Earth's radius Geographical mile International mile Timeline of Earth...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Milky Way would look like a circular nebula viewed from above and like an ellipsoid if viewed from an angle, he concluded that the observed elliptical nebulae...

an earth ellipsoid and a plane (ellipsoid plane sections). Common examples include the great ellipse (containing the center of the ellipsoid) and normal...

found in Spain, North Africa, Armenia, Iran, France, and Italy. The ellipsoidal dome is a surface formed by the rotation around a vertical axis of a...

rotationally symmetric reference ellipsoid of GRS80; in other places, like close to Sri Lanka, it dives under the ellipsoid by nearly the same amount. The...

Simulation of the chaotic rotation of Pluto's moon Nix, modeled as an ellipsoid....

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

{\displaystyle \sigma _{z}} , in the coordinate system of the stress ellipsoid. At any depth in the subsurface, a point subjected to stresses can be...

(250 mi) in diameter, Proteus's shape deviates significantly from an ellipsoid. It is shaped more like an irregular polyhedron with several slightly...

"Universal Transverse Mercator WGS 84 Zone 16N") comprises a choice of Earth ellipsoid, horizontal datum, map projection (except in the geographic coordinate...

slope steepness. Modern growth models utilize a combination of past ellipsoidal descriptions and Huygens' Principle to simulate fire growth as a continuously...

of a long cylinder with a concave modified ellipsoidal bulkhead forward and a convex modified ellipsoidal bulkhead aft. The aft bulkhead is also used...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

r} is the base's radius and h {\textstyle h} is the cylinder's height; Ellipsoid – 4 3 π a b c {\textstyle {\frac {4}{3}}\pi abc} , where a {\textstyle...

rotation. Earth portal Earth Sciences portal History of Science portal Earth ellipsoid Geodesy Spherical Earth Timeline of Earth estimates "10 easy ways you...

efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice...

C60 has a hollow sphere-like form, but other fullerenes are known with ellipsoid-like shapes. Fullerenes have also been described as "polyhedral closed...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

from Hannay. For surfaces with genus 0 with isolated umbilics, e.g. an ellipsoid, the index of the principal direction vector field must be 2 by the Poincaré–Hopf...

programming that use interior point methods: these include Khachiyan's ellipsoidal algorithm, Karmarkar's projective algorithm, and path-following algorithms...

In the mid-1800s the Bessel ellipsoid of 1841 or the Clarke ellipsoid of 1866 were widely used; the Hayford ellipsoid of 1910 may later have been used...

distances is the following special case of the Vincenty formula for an ellipsoid with equal major and minor axes: Δ σ = atan2 ( ( cos ⁡ ϕ 2 sin ⁡ Δ λ )...

whose bottom cross-section takes the form of an ellipse. Technically, an ellipsoidal dome has a circular cross-section, so is not quite the same. While the...

163.783. A glacier flowing south from Thomas Heights, to the west of Ellipsoid Hill, into Blue Glacier. The name is one of a group in the area associated...

crystal-electrical fields may occur at low-symmetry lattice sites. Significant ellipsoidal deformations have been shown to occur for sulfur ions and chalcogen ions...

lights usually have a Fresnel lens with a spherical reflector or an ellipsoidal reflector with a lens train containing two plano-convex lenses or a single...

diameters (scalene ellipsoids such as Haumea). Unlike bodies such as Haumea, the irregular bodies have a significantly non-ellipsoidal profile, often with...

flattening of the approximative Earth ellipsoid. Gauss developed the universal transverse Mercator projection of the ellipsoidal shaped Earth (what he named conform...

the continuum body lie on the stress ellipsoid surface, i.e., the radius-vector from the center of the ellipsoid, located at the material point in consideration...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

three-dimensional cube on average. Projective algorithm of Karmarkar Ellipsoidal algorithm of Khachiyan More generally, for the simplex algorithm, the...

no deflection of the vertical, "overhead" means perpendicular to the ellipsoid at observer's location, but the perpendicular line does not pass through...

Geodesics on an ellipsoid (blue) from a single point (for flattening f = 1⁄10, latitude φ1 = −30°) form a segment of a circle of latitude; geodesic circles...

angle between two curves that cross each other on Earth (a sphere or an ellipsoid) is preserved in the image of the projection; that is, the projection...

combination of characteristics: the fruit is uniformly ellipsoid, as compared to the symmetrical ellipsoid shape of Cripps Pink; the fruit has a higher percentage...

the index ellipsoids for given directions of the polarization. Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution...

Sphericity is a measure of how closely the shape of a physical object resembles that of a perfect sphere. For example, the sphericity of the balls inside...

an estimate of increased accuracy for the Earth's ellipsoid, nowadays called the Bessel ellipsoid, based on several arc measurements. Honorary doctor...

abbreviated to Leko) is a brand of ellipsoidal reflector spotlight (ERS) used in stage lighting which refers to the half-ellipsoidal dome reflector within which...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

In mathematics, a Lamé function, or ellipsoidal harmonic function, is a solution of Lamé's equation, a second-order ordinary differential equation. It...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Known for Popularizing the character ∂ Jacobi eigenvalue algorithm Jacobi ellipsoid Jacobi elliptic functions Jacobi identity Jacobi method Jacobi operator...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

trigonometric series to compute the meridian arc distance on the surface of an ellipsoid. These have the form m ( θ ) = C 0 θ + C 1 sin ⁡ θ + C 2 sin ⁡ 2 θ + ⋯...

for the simple case of uniform magnetization. For the special case of ellipsoids (including infinite cylinders) the demagnetization field is linearly related...

arc (⁠1/60⁠ degree) along the Earth's equator. For the international ellipsoid 1924 this equalled 1855.4 metres. The American Practical Navigator 2017...

bounded region) bounded by two concentric, similar ellipses (in 2D) or ellipsoids (in 3D). When the thickness of the shell becomes negligible, it is called...

ingredient. Lemon is a small evergreen tree native to Asia, and the tree's ellipsoidal yellow fruit. The fruit is used for culinary and non-culinary purposes...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

The use of a geoid stands in contrast to GeoJSON, which uses direct ellipsoid height. Remembering the example above, geo:37.786971,-122.399677;u=35...

water or erect in shallow water or on land. Leaflets glaucous, sporocarp ellipsoid, on stalks attached to base of petioles. Marsilea crenata is an aquatic...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

earth ellipsoid in toise (a large number), whereas e = 10 8.9054355 − 10 {\displaystyle e=10^{8.9054355-10}} , the eccentricity of the earth ellipsoid (a...

leader in continuous optimization and is best known for his work on the ellipsoid method, modern interior-point methods and robust optimization. Nemirovski...

"Modelling biological macromolecules in solution: The general tri-axial ellipsoid". After completing his doctorate, Harding was a Lister postdoctoral fellow...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

belt, a band of icy planetesimals beyond Neptune. It has a slightly ellipsoidal shape with an average diameter of 1,100 km (680 mi), about half the size...

of the testicle can be estimated by palpating it and comparing it to ellipsoids (an orchidometer) of known sizes. Another method is to use calipers, a...

loci in the k = 2 case are ellipses and in the case of arbitrary k are ellipsoids. Rectified Gaussian distribution a rectified version of normal distribution...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

injury to other players. Australian rules football is played with an ellipsoid ball, between 72 and 73 cm (28 and 29 in) in long circumference, and 54...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

{\displaystyle \mathbf {S} } correspond to the axes of the 1 sd error ellipsoid of the multivariate normal distribution. See Multivariate normal distribution:...

secant plane is a plane containing a nontrivial section of a sphere or an ellipsoid, or such a plane that a sphere is projected onto. Secant planes are similar...

the solution set is an ellipsoid or a hyperboloid.[citation needed] If all the eigenvalues are positive, then it is an ellipsoid; if all the eigenvalues...

one of the sides of a building, or a drawing of this view. ellipsoid See reference ellipsoid. emergence 1.  The rise of the level of a land surface with...

dark olive-brown spore print. The spores are thick-walled, smooth, and ellipsoid to somewhat spindle-shaped, with dimensions of 11.2–16 by 5.2–8 μm. They...

thermal ellipsoid model of [PhBF3]−, as found in the crystal structure of K[PhBF3] space-filling packing diagram of the crystal structure of K[PhBF3]...

Thaspiviridae: spindle- to lemon-shaped Poxviridae and Ovaliviridae: ovoid to ellipsoid Gammaretrovirus and other Retroviridae, such as HIV, roughly round to...

the projection has always been applied to models of the earth as an ellipsoid, which greatly complicates the mathematical development but is suitable...

the constant R 2 {\displaystyle R^{2}} . For an equal-area map of the ellipsoid, the corresponding differential condition that must be met is: ∂ y ∂ φ...

In stage lighting, an ellipsoidal reflector floodlight (sometimes known by the acronym ERF which is often pronounced "erf"), better known as a scoop,...

whispering gallery is usually a circular, hemispherical, elliptical or ellipsoidal enclosure, often beneath a dome or a vault, in which whispers can be...

framework for anisotropic displacement parameters, also known as the thermal ellipsoid, for crystal structure determination in a series of papers published in...

Maindron. The game uses a unique type of ellipsoid graphics to display characters. Each character is made of ellipsoids approximating different parts of the...

equivalent to a particular choice of conjugate axes of an ellipsoid. In detail, let the ellipsoid be defined as y T A y = 1 {\textstyle y^{T}Ay=1} , then...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

system. A choice of geodetic datum, which includes a choice of earth ellipsoid. This binds the coordinate system to actual locations on the Earth by...

mathematical model. The most common theoretical model is a rotating Earth ellipsoid of revolution (i.e., a spheroid). Other representations of gravity can...

main body is similar to a geometric solid obtained from the section of ellipsoid, reminiscent of an upside-down turtle. Nine human-eye-like drawings are...

barrier functions and self-regular barrier functions. Cutting-plane methods Ellipsoid method Subgradient method Dual subgradients and the drift-plus-penalty...

Gravimetric, based on a geoid; or geometric, based on the same Earth ellipsoids that are used in computing a horizontal datum, such as NOAA's planned...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

flowers on a tree. The inflorescences are pedunculated, cylindrical to ellipsoidal or pear-shaped, to about 10–12 cm (4–4+3⁄4 inches) long and 5–7 cm (2–3...

above the tip. Rather than oval as the rest of the trunk, this part was ellipsoidal in cross section, and double the size in diameter. The feature was shown...

greyish, truncate. The spores are white in deposit, smooth, broadly ellipsoid to ellipsoid to elongate, inamyloid, infrequently globose. 8–14 x 6–10 μm. The...

a circle is a special type of ellipse, a sphere is a special type of ellipsoid of revolution. Replacing the circle with an ellipse rotated about its...

conidia and dictyochlamydospores. The conidia are small, unicellular, and ellipsoidal to subglobose. They function as the primary means of rapid dispersal...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

point from the center of the Earth on the Earth's surface because of the ellipsoid shape of the planet. The Andes is the watershed divisor between the Amazon...

global ellipsoid in 1906 with an accuracy of 100 meters (0.002 percent of the Earth's radii). The US geodesist Hayford derived a global ellipsoid in ~1910...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

lengths of three principal axes of an ellipsoid are distinct, but sufficiently close to each other, then the ellipsoid has only three simple closed geodesics...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

\pi (z)={\frac {1}{\Pi (z)}}} ⁠, an entire function. The volume of an n-ellipsoid with radii r1, ..., rn can be expressed as V n ( r 1 , … , r n ) = π n...

surveying in the US, Canada, and Mexico.) ETRS89 is based on the GRS80 ellipsoid. EUREF recommends ETRS89 realisation ETRF2000 for mapping purposes. Although...

Micheli's 1729 work Nova plantarum genera depicted an ascus containing four ellipsoid spores. This is the earliest known published image of ascospores. In 1788...

this long-standing complexity issue in 1979 with the introduction of the ellipsoid method. The convergence analysis has (real-number) predecessors, notably...

a vacuum chamber for his pendulum. This work led in 1901 to the Earth ellipsoid proposed by Friedrich Robert Helmert, whose parameter values were remarkably...

ellipsoid with isophotes (red)...

Thermal ellipsoid model of the molecular cell of dodecahydroxycyclohexane dihydrate...

superellipse into three dimensions, creating shapes that vary between ellipsoids and rectangular solids with rounded edges. The superellipsoid is defined...

Cartesian coordinate grid (for example, a spherical coordinate system or an ellipsoid-based system such as the World Geodetic System) or similar methods. For...

largest among the toothed whales, weighing about 170 g. It is overall ellipsoid in shape, compressed along the visual axis, measuring about 7×7×3 cm....

Geometrically, it is a unit vector which is normal to the reference ellipsoid. The vector is decomposed in an Earth centered earth fixed coordinate...

black as the spores mature. The spores are dark purplish-brown en masse, ellipsoid in shape, and measure 10.5–15 by 6.5–8.5 μm. The mushroom grows in grassland...

which are within 1% of the geodesic length for the WGS84 ellipsoid; see Geodesics on an ellipsoid for details. Detailed evaluation of the optimum direction...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

expeditions confirmed Isaac Newton's belief that the shape of the Earth is an ellipsoid flattened at the poles.[page needed] In 1738, he published the De observationibus...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Although HGRS87 uses the GRS80 ellipsoid, the origin is shifted relative to the GRS80 geocenter, so that the ellipsoidal surface is best for Greece. The...

North America and Oceania. Glaucocystis nostochinearum consists of ellipsoidal colonies up to 40–60 μm. Each colony has typically four to eight (occasionally...

in owls). In all cases, the eye shape diverges significantly from an ellipsoidal shape in the anterior end, and the corneal limbus is usually curved inwards...

non-stellar celestial object. Because of their mass, these moons are large and ellipsoidal (sometimes spherical) in shape due to hydrostatic equilibrium caused...

5.45×39mm and 7.62×39mm) or smokeless powder consisting of spherical ellipsoids which measure from 0.45–0.75mm, resulting in powder density of 0.95g/cm3...

measure 2.7–4.5 millimetres (0.11–0.18 in) in length. They have brown ellipsoidal bodies with a prothorax resembling a monk's cowl. The common furniture...

represent the basis set will no longer correspond to a sphere, but an ellipsoid. This change in the basis set will result in errors in the calculated...

usually in the shape of a sphere, though they may also be spheroid or ellipsoid. Spherical balls include the baseball, basketball, Gaelic ball, cricket...

multiplying density (ρ; kg/m3 units) by ellipsoid volume (V; m3 units): M = ρ V {\displaystyle M=\rho V} . Volume of an ellipsoid with semi-axes 143.8 × 135.2 ×...

Roots single fleshy root expanding to a solitary, napiform to narrow-ellipsoid or narrow-ovoid, annually replaced tuber several fleshy roots, cylindrical...

covariance of the Gaussians can be thought of as configurations of an ellipsoid, which can be mathematically decomposed into a scaling matrix and a rotation...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

the volume of an ellipsoid of 8x4x4km * a density of 0.3 g/cm3 yields a mass of 2.0E+13 kg. 81P/Wild: Using the volume of an ellipsoid of 5.5x4.0x3.3 km...

Retrieved 2016-12-14. Jeremy Tatum (14 April 2017). "2.20: Ellipses and Ellipsoids". phys.libretexts.org. Retrieved 1 May 2023. see e.g. "Moment of Inertia...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

three-dimensional shapes are polyhedra, which are shapes with flat faces; ellipsoids, which are egg-shaped or sphere-shaped objects; cylinders; and cones....

is special case of an earth section path. Assume that the spheroid, an ellipsoid of revolution, has an equatorial radius a {\displaystyle a} and polar...

more than twice the largest deviations of the actual surface from the ellipsoid, including the tallest mountains and deepest oceanic trenches. Earth's...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

geodetic framework that defines the map projection, coordinate system, ellipsoid and geodetic datum. Official topographic maps also adopt a national grid...

Geodesy portal History of Science portal Earth Figure of the Earth Earth ellipsoid Empirical evidence for the spherical shape of Earth Flat Earth Spherical...

basidia are tremelloid (ellipsoid, with oblique to vertical septa), 10–13 μm × 6.5–10 μm, sometimes stalked. The spores are ellipsoid, smooth, 5–8 μm × 4–6 μm...

to a specific point. DMA Technical Manual 8358.1, Chapter 3. Datums, Ellipsoids, Grids, and Grid Reference Systems NGA Guidance for the Military Grid...

3-dimensional cube, and so on to n dimensions. A quadric, such as a hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to...

which states: Every caustic from any point p {\displaystyle p} on an ellipsoid other than umbilical points has exactly four cusps. Numerical experiments...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

within every convex body there is one unique ellipsoid of maximal volume, now called the John Ellipsoid. From the mid-1950s on, he started working on...

is the radius of the cup, and D is its diameter. If the cup is a hemi-ellipsoid, its volume is given by the formula: V = 2 π a b c 3 ≈ π × c w × c d ×...

[ˈbɔksˌbɔɪ̯tl̩] ) is a type of wine bottle with the form of a flattened ellipsoid. It is commonly used for wines from Franconia in Germany, but is also...

Thermal ellipsoid model of the coordination environment of chlorine in chloryl hexafluoroantimonate, [ClO2][SbF6], showing F–Cl interactions....

quadruped with a small skull, a long neck, a large trunk with a high-ellipsoid cross section, a long, muscular tail and slender, columnar limbs. Large...

the point of view of projective geometry, an elliptic paraboloid is an ellipsoid that is tangent to the plane at infinity. Plane sections The plane sections...

sheathed arteriole of the spleen, and is sometimes referred to as a splenic ellipsoid. It is a spindle-shaped thickening in the walls of the second part of...

explanation needed] The other is that ICS was based on a 19th-century reference ellipsoid (approximation of the shape of the Earth) and this was replaced by a more...

for g as a function of latitude is the WGS (World Geodetic System) 84 Ellipsoidal Gravity Formula: g { ϕ } = G e [ 1 + k sin 2 ⁡ ϕ 1 − e 2 sin 2 ⁡ ϕ ]...

properties Clausius–Mossotti relation Ellipsometry Fermat's principle Index ellipsoid Index-matching material Laser Schlieren deflectometry Optical properties...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

to reflections on an ellipsoid, with the origin of the flash and Earth as its two foci (see animation to the right). This ellipsoid naturally expands over...

Consequently, in contrast with a popular assumption, the toric lens is not an ellipsoid of revolution. Light rays within the (x,y)-plane of the torus (as defined...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Wienerwald tulips. The tulip's fruit is a globose or ellipsoid capsule with a leathery covering and an ellipsoid to globe shape. Each capsule contains numerous...

deliver increasingly precise calculations for the shape of the Earth, an ellipsoid with additional undulations known as the geoid. To generate an accurate...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

a quadratic form that defines a surface in the body called Poinsot's ellipsoid. Let Λ {\displaystyle {\boldsymbol {\Lambda }}} be the inertia matrix...

buried in ovo (in the egg). The outlines of eggs and embryos indicates ellipsoid-shaped eggs in life with dimensions about 12 cm (120 mm) long and 6 cm...

line segments. A different kind of example are axis-aligned ellipsoids, i.e., the ellipsoids with principal axes parallel to the coordinate axes. "3D collision...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Semilanceatae, a grouping of related species characterized by having roughly ellipsoid, usually thick-walled spores, and lacking pleurocystidia. The specific...

Roots single fleshy root expanding to a solitary, napiform to narrow-ellipsoid or narrow-ovoid, annually replaced tuber several fleshy roots, cylindrical...

they emit a pungent odour similar to blue cheese. They are irregularly ellipsoid or ovoid, and may reach up to 9x6 cm. The plants flower and fruit throughout...

with, glabrous, large, elliptic or oblong lanceolate. The fruits are ellipsoid or sub-globose woody capsules. They are green at first, but later turn...

{\text{km}}\approx 6161.6\ {\text{km}}.} By comparison, using a more accurate ellipsoidal model of the earth, the geodesic distance between these landmarks can...

vertically from parent to offspring through infected eggs. Viruses with ellipsoidal to rod-shaped virions, typically non-occluded but some produce occlusion...

Pan American Institute of Geography and History. It uses as reference ellipsoid the Geodetic Reference System 1967 (GRS-67), recommended by the International...

structural explanation of the double refraction of calcite based on ellipsoidal atoms. Huygens discovered the polarization of light by Iceland spar,...

cream to yellow-orange which bloom during June to September. The obovoid-ellipsoid carpels produce 2−4 seeds during September to October. White champak flower...

normally refers to the Bessel ellipsoid. A further datum of interest was ED50 (European Datum 1950) based on the Hayford ellipsoid. ED50 was part of the fundamentals...

4–5 μm in width. The spore shape is described as subglobose to short ellipsoid and the spore surface is smooth to finely roughened. It has been observed...

projection, a circle of latitude is perpendicular to all meridians. On the ellipsoid or on spherical projection, all circles of latitude are rhumb lines, except...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

osmeterium gland of Papilio larvae consists of the following cell types. Ellipsoid gland cells have an extensively infolded basal plasma membrane, abundant...

(4–6 in) long, the individual flowers small and white. The fruit is round to ellipsoid in shape, 1.5–4 cm (0.6–2 in) in diameter. Beneath the outer peel is the...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

potential additional information includes map projection, coordinate systems, ellipsoids, datums, and everything else necessary to establish the exact spatial...

soon become strong, pungent and complex, or "truffly". The spores are ellipsoid to somewhat spindle-shaped with narrowed ends, and light brownish in color...

conditions in the Northern Hemisphere. Ripe grape berries are typically ellipsoid in shape resembling a prolate spheroid. Their flesh has 75-85% water content;...

material. The reservoir in the tower may be spherical, cylindrical, or an ellipsoid, with a minimum height of approximately 6 metres (20 ft) and a minimum...

International Ellipsoid is larger than the GRS 80/WGS 84 ellipsoid, so a given north-south distance will cover more latitude on the new ellipsoid, and a given...

is ornamental. On the other hand, Poco M7 and Poco M7 Plus feature an ellipsoidal camera island with two lenses. On the bottom of smartphones, there is...

conic sections in 3 dimensions, normalized to the unit range. A Diffusion Ellipsoid is completely represented by the Diffusion Tensor, D. FA is calculated...

numerical eccentricity of the ellipsoid. f = 1 − b a {\displaystyle f=1-{\frac {b}{a}}} is the flattening of the ellipsoid. The prime vertical radius of...

and magnetostatic fields generated by uniformly charged or polarized ellipsoidal bodies. The gravitational potential (V) at a location is the gravitational...

ocean tides into a small ellipsoid term which affects the Moon plus a second term which has no effect. The ocean's ellipsoid term also slows the Earth...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

second Floor, has a direct view of center stage. The building features an ellipsoidal dome containing a mural by painter Carlos Cañas and a crystal chandelier;...

having both thickness and parallel faces and with a rounded margin) Ellipsoid Globose – spherical Subglobose (Inflated, but less than spherical) Lenticular...

Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

the two-dimensional shape made by the country (projected to the Airy ellipsoid then flattened using the Transverse Mercator projection), or as the point...

passing object to be contracted (for instance, from a sphere to a flattened ellipsoid), was wrong. A sphere maintains its circular outline since, as the sphere...

generalize the intrinsic viscosity formula from spheroids to arbitrary ellipsoids with semiaxes a {\displaystyle a} , b {\displaystyle b} and c {\displaystyle...

the earliest examples providing such a closed-form solution analyzed a ellipsoidal inclusion of material Ω 0 {\displaystyle \Omega _{0}} with a uniform...

thereof) to create the desired effect. An ellipsoidal reflector has a lamp set at one focus point of an ellipsoid-shaped reflector that bounces the light...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

up to 106 m (348 ft) lower than the global mean sea level (reference ellipsoid), if not for minor effects such as tides and currents in the Indian Ocean...

either insect or self-pollinated. The berries typically grow erect and are ellipsoid-conical to lanceoloid shaped. They are usually very small and pungent...

differently along the horizontal and vertical axes of the lens, becoming ellipsoidal compared to those in a spherical lens. In 2016, Apple Inc. released the...

have relatively low densities, as they are riddled with macroscopic ellipsoidal vesicles (gas bubbles), but in contrast to pumice, most scoriae usually...

expressions for the volume of superellipsoids, such as the superegg. Astroid Ellipsoid Lp spaces Oval Squround Holton, Derek (1990). Creating Problems: Counting;...

orbital radius, it may be represented as a 3-dimensional uncertainty ellipsoid and the orbits (ignoring the interaction) approximated as straight lines...

surface of normal slowness, the surface of wave slowness, etc. The index ellipsoid was called the surface of elasticity, as according to Fresnel, light waves...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

(ZTF) data by Liangliang Ren and colleagues, who had flagged it as an ellipsoidal variable-type binary white dwarf candidate. A 2024 study of Gaia DR3...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

line (a curve, approximated by the ellipsoidal normal, a straight line). The evaluation ranges from the Earth ellipsoid up to the point of interest; the...

interactions are rare. The condensed and spatially organized DNA forms a helical ellipsoid that is radially confined in the cell. The 3D structure of the DNA in...

57 0.70 21.405 – Kepler-56d ≥5.61 – 1002 0.20 Radial vel. 2016 Kepler-91b K3 1.19 6.20 0.81 1.37 6.246 0.07 4385 Transit + Ellipsoidal variation 2013...

entities the size of a man; where a head would be, they have a "convoluted ellipsoid" composed of pyramided, fleshy rings and covered in antennae. They are...

family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by...

material property causes Methone to take the shape of a triaxial ellipsoid, a type of ellipsoid in which all 3 of its principal axes are of different lengths...

which grew almost 4.1 m (13.5 ft) in length Engelman (2023), using an ellipsoid volumetric method, estimated weights of 950–1,200 kilograms (2,090–2,650 lb)...

Like the 7K-OK model, the 7K-LOK was divided into three sections, an ellipsoid Orbital Module, the "headlight"-shaped Descent Module, and a cylindrical...

triangle, one in which no two sides or angles are the same. A scalene ellipsoid, one in which the lengths of all three semi-principal axes are different...

theoretical gravity of an idealized smooth Earth, the so-called earth ellipsoid. Red shows the areas where gravity is stronger than the smooth, standard...

eccentricity of a designated section of it. For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section...

Earth Gravitational Model 1996 (EGM96) geoid, not the WGS84 reference ellipsoid. DTED supports many applications, including line-of-sight analyses, terrain...

merely by using the ellipsoidal isometric latitude. In formulas above on this page, substitute the conformal latitude on the ellipsoid for the latitude on...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

commonly spherical as the name suggests, overhaul balls may also be ellipsoidal or cylindrical. Overhaul balls should be distinguished from wrecking...

Horizons Perihelion. Brown 2013, p. 1. Wolfram Alpha - Ellipsoid Surface Area. Wolfram Alpha - Ellipsoid Volume. Bamberger 2025. Protopapa et al. 2025, p. 8...

fullerenes (the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations). The term allotropy is used for elements only, not for compounds...

not correspondingly massive. It is not spherical but is shaped like an ellipsoid of approximately 380×330×250 km. It was discovered on 4 February 1858...

Structural geology Underlying theory Deformation mechanism Lamé's stress ellipsoid Mohr–Coulomb theory Mohr's circle Overburden pressure Rock mechanics Strain...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

p-dimensional ellipsoid to the data, where each axis of the ellipsoid represents a principal component. If some axis of the ellipsoid is small, then...

astronomical bodies. The shapes of planets and stars are often well described by ellipsoids. A circle viewed from a side angle looks like an ellipse: that is, the...

Fungal. Odor: Fungal. Size: Small to medium. Microscopic features: Spores ellipsoid, 15 - 20 (21) x 10 - 14 x 8 - 10(11) μm. Cheilocystidia cylindrical to...

Blastoconidia (cell buds) are observed. They are unicellular, globose, and ellipsoid to elongate in shape. Multilateral (multipolar) budding is typical. Pseudohyphae...

zero-point energy can be used in violation of conservation of energy. Ellipsoid paradox: This paradox considers a perfectly reflecting cavity with two...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

reflectances in cartographic geometry (combined UTM projection and WGS84 ellipsoid). Level-1C products are tiles of 100 km x 100 km each one with a volume...

can be visualized as any n-dimensional shape (e.g. n-parallelotope, n-ellipsoid); with magnitude (hypervolume), and orientation defined by that of its...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Geoid Mean sea level North American Vertical Datum of 1988 Reference ellipsoid Topography US Department of Commerce, National Oceanic and Atmospheric...

cell with protruding stalks—from which the genus gets its name—and an ellipsoid cell with a single long flagellum and tail. Solarion retains a mitochondrially...

longitudinal section. In fact their shape is a good first approximation to an ellipsoid, with legs and other appendages fitting closely into a streamlined surface...

conditioned primarily by two factors: A closed, planetary-sized and ellipsoidial cavity, consisting of conducting lower and upper boundaries separated...

bounding ellipsoid is an ellipsoid containing the object. Ellipsoids usually provide tighter fitting than a sphere. Intersections with ellipsoids are done...

Ecstatica, with improvements to the game's controls and more detailed ellipsoid graphics. The play area is much larger than the first game and offers...

Conventions. It is also the equatorial radius used for the IERS 2003 ellipsoid. If it were really circular, the length of the equator would then be exactly...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

ω. The curve produced by the angular velocity vector on the inertia ellipsoid, is known as the polhode, coined from Greek meaning "path of the pole"...

Simulation of Nix, modelled as an ellipsoid, showing its chaotic rotation...

programming/semidefinite relaxations (which may themselves invoke the ellipsoid algorithm), complex data structures, or sophisticated algorithmic techniques...

devised a system of using textures with transparencies combined with ellipsoid culling from any Infected character model to simulate the wounds, with...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

whitish-gray, viscous colonies on growth media. Microscopically, cells are ellipsoid in shape. Candida auris can switch between two distinct cell states, called...

distinctive bleach-like odor. The spore print is white. The spores are broadly ellipsoid, amyloid (meaning they will adsorb iodine when stained with Melzer's reagent)...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

small halos merge to form a single virialized dark matter halo with an ellipsoidal shape, which reveals some substructure in the form of dark matter sub-halos...

Optical light curves show double-humped profiles due to the companion’s ellipsoidal distortion. LMC X-3 is notable for its persistent yet highly variable...

planets for the largest minor planets—those massive enough to have become ellipsoidal under their own gravity. Only the largest object in the asteroid belt...

these methods was that of the North American Datum 1927 or NAD27, an ellipsoid whose surface best matches mean sea level under the United States. Beginning...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

reference ellipsoid. It is calculated using the orbital parameters of the satellite and various positioning instruments. However, the ellipsoid is not an...

Monge named them "lines of curvature". He would later study those of the ellipsoid in 1795. Let the surfaces be contours of the equation f ( x , y , z )...

vertical deflection, between the local gravity vertical direction and the ellipsoidal normal. The International Hydrographic Organization adopted an early...

as ellipsoids is found in all easily measurable comparators up to a few times of its distance. The alternative explanation is that it is an ellipsoid oriented...

Luo, Yaowen; Wang, Yunbo; Li, Xie (11 April 2026). "Phobos' degree-1 ellipsoidal harmonic gravity field recovery from two Mars Express flybys". Monthly...

fruit. The fruit wall (pericarp) is membranous. The vertical seed is ellipsoid, with yellowish brown, membranous, hairy seed coat. The seed contains...

Like all modern airships, helium is the lifting gas. The AS700 has an ellipsoid hull, with a rigid tail configuration done in an "X" positioning rather...

B.; Miros, A.; Piatkowski, B.; E Søndergård; Holst, B. (2010). "An ellipsoidal mirror for focusing neutral atomic and molecular beams" (PDF). New Journal...

received some cosmetic updates, including new AVUS-style alloy wheels, ellipsoid beam (projector) headlamps, and clear front indicator lenses. This coincided...

field; microscopy is needed to tell the difference, as C. truncorum has ellipsoid spores with a rounded germ pore, compared to the shield-shaped (mitriform)...

consists of small, rounded cells which are spherical, subspherical, or ellipsoidal, and may be surrounded by a layer of mucilage. The cells contain a single...

it acts as if it is in free space. This last restriction requires an ellipsoidal area around the line of sight out to 0.6 of the Fresnel zone be clear...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

the same surface area as the Clarke 1866 ellipsoid. The authalic (equal area) radius of the Clarke 1866 ellipsoid is 6,370,997.2 metres (20,902,222 ft)....

prolate spheroidal coordinates, adapted to boundary conditions on certain ellipsoids of revolution (an ellipse rotated around its long axis, cigar shape)....

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

lines) and longitudinal filaments (dark blue). Recombination nodules (gray ellipsoids) on the central region may help in completing recombination. Chromatin...

has no distinctive dust lanes. Instead, it has an almost featureless, ellipsoidal shape typical of most giant elliptical galaxies, diminishing in luminosity...

represented. Pierre-Simon Laplace originally hoped to figure out the Earth ellipsoid problem from the sole measurement of the arc from Dunkirk to Barcelona...

extended in two ways to the multidimensional case, based on rectangular and ellipsoidal regions. The first way is to define the cdf F ( x ) {\displaystyle F(\mathbf...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

position representation Latitude / Longitude Map projection Reference ellipsoid Satellite geodesy Spatial reference system Spatial relations Vertical...

European Cup, on 29 June 1933. The original design stage consisted of an ellipsoid ring whose major perimeter was about 640 metres. The base consisted of...

Hinge joint 1: Ball and socket joint; 2: Condyloid joint (Ellipsoid); 3: Saddle joint; 4: Hinge joint; 5: Pivot joint Metacarpophalangeal articulation...

plan and a similar length-weight relationship. Engelman (2023), using an ellipsoid volumetric method, estimated weights of 950–1,200 kilograms (2,090–2,650 lb)...

performing azimuthal equidistant projections centered at any point on the ellipsoid. Animated US National Weather Service Wind Data for Azimuthal equidistant...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

partial veil. Panaeolus tropicalis spores are dark violet to jet black, ellipsoid, and 10.5–12.0 x 7–9 μm. The basidia each produce two spores.[citation...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

using 8 satellites, HDOP = 1.02. Altitude = 61.7 meters MSL, geode-to-ellipsoid distance is 55.2 meters. GSA: Device set to 2D/3D automatic mode and is...

famous Bessel ellipsoid (1841). Clarke (1858) combined most of the arc measurements then available to define a new reference ellipsoid. Astrogeodesy Central...

Hilbert's third problem Deltahedron Surface normal 3-sphere, spheroid, ellipsoid Parabolic microphone Parabolic reflector Soddy's hexlet Sphericon Stereographic...

can be visualized as any n-dimensional shape (e.g. n-parallelotope, n-ellipsoid); with magnitude (hypervolume), and orientation defined by that on its...

approximated however by an ellipsoid of revolution called the reference ellipsoid. The currently most widely used reference ellipsoid, that of the Geodetic...

light and brings it to a focus before the secondary mirror (a concave ellipsoid), where it is reflected back through a hole in the centre of the primary...

features. The shape of NGC 1052 is thought to be a triaxial ellipsoid. The longest axis of the ellipsoid is probably aligned at a position angle of −41°, which...

gnuplot 3D rendering of an ellipsoid by gnuplot Initial release 1986; 40 years ago (1986) Stable release 6.0.4 / 18 December 2025; 5 months ago (18 December...

University of British Columbia with thesis An illustrative example of the ellipsoid pendulum. He died at age 24 and had no mathematical publications during...

of a prolate spheroid, joined to a "short" half of a roughly spherical ellipsoid, or even a slightly oblate spheroid. These are joined at the equator and...

Pivot joint 1: Ball and socket joint; 2: Condyloid joint (Ellipsoid); 3: Saddle joint; 4 Hinge joint; 5: Pivot joint; Details Identifiers Latin articulatio...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

circular (or spherical) cross-section becomes distorted into an ellipse (ellipsoid), it is possible for the volume distortion to vanish if the distortions...

long Fruits Berries black (occasionally ultramarine blue), globose to ellipsoid, each berry 6 to 8 mm (0.2 to 0.3 in) long; seeds 2–4 per berry, each...

model accurate to 1 centimeter (0.39 in) to relate orthometric height to ellipsoidal height measured by GPS, eliminating the need for future leveling projects...

shape of the body without any change in volume. The sphere becomes an ellipsoid with two bulges, pointing towards and away from the other body. Larger...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

coordinates there exist ellipsoidal coordinates. In physics confocal ellipsoids appear as equipotential surfaces of a charged ellipsoid. Ivory's theorem (or...

regular polyhedron, cylinder, rectangle, rhombus, circle, sphere, ellipse, ellipsoid, superellipse, superellipsoid, etc.) can be determined by this principle...

exhibiting the properties of overlapping subproblems and optimal substructure Ellipsoid method: is an algorithm for solving convex optimization problems Evolutionary...

John A.; Roman, Nancy G.; Yaplee, Benjamin S.; Eckels, Ann (2013). "Ellipsoid Parameters from Satellite Data". Contemporary Geodesy: Proceedings of...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

Saddle Joint 1: Ball and socket joint; 2: Condyloid joint (Ellipsoid); 3: Saddle joint; 4 Hinge joint; 5: Pivot joint; Ligaments of wrist. Posterior view...

of the Prime Meridian. Any position on or above the Earth's reference ellipsoid can be precisely given with this method. However, when it is inconvenient...

most of the day. Once finished, the female will lay a clutch of 5–7 ellipsoidal eggs that hatch within a period of 8–10 weeks. The sex of common agama...

which the stars reflect from their companion. Second is by observing ellipsoidal light variations which are caused by deformation of the star's shape...

A rugby ball is an elongated ellipsoidal ball used in both codes of rugby football. Its measurements and weight are specified by World Rugby and the Rugby...

Three commonly used model equations are Bhatnagar, Gross, Krook (BGK), Ellipsoidal Statistical (ES-model), and Shakhov (S-model). The computational effort...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

crevices. The photobiont comprises green algal cells that are rounded to ellipsoid and measure about 5 micrometres (μm) in diameter. Apothecia (disc-like...

peak per cycle, astronomers explicitly reject the elongated triaxial ellipsoid shape idea. Instead, the light curve is entirely driven by uneven albedo...

those in dark-toned skin are "packaged into peri-nuclear distributed, ellipsoid" melanosomes while those light-tone skin are "assembled into clustered...

photo etching. Plastic gobos or transparency gobos can be used in LED ellipsoidal spotlights. These "LED-only" plastic gobos can be full-color (like a...

1892 alumnus and rugby football player, posing at Penn in 1891 holding elongated ellipsoidal rugby ball and gestures resembling the famed "Heisman Pose"...

master's thesis, Lawrence built an experimental apparatus that rotated an ellipsoid through a magnetic field. Lawrence followed Swann to the University of...

manufacture than mirrors with a surface described by a paraboloid or ellipsoid. They suffer from spherical aberration and coma, but do not suffer from...

take into account slight departures of the Earth's shape from a simple ellipsoid, or the deflection of the plumb-bob by differences in terrestrial mass...

radioulnar joint One bone rotates about another Condyloid joints (or ellipsoidal joints) wrist joint (radiocarpal joint) A condyloid joint is a modified...

had ellipsoidal shapes. From this testing he observed patterns and was able to determine "line directions" by the longer axes of the ellipsoidal holes...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

of cylinders. There are also known series solutions for scattering by ellipsoidal particles. A list of codes implementing these specialized solutions is...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

Callister Hales. Many other shapes have received attention, including ellipsoids, Platonic and Archimedean solids including tetrahedra, tripods (unions...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

reaction on the cap is negative. The "Spores [are] 5.5-7.5 x 3-3.5 μm, ellipsoid, smooth, inamyloid. Basidia 28-32 x 4-5 μm, 4-spored. Cystidia absent"...

1920 arrived at the picture of a small (diameter about 15 kiloparsecs) ellipsoid galaxy with the Sun close to the center. A different method by Harlow...

three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots. In statistics, the normal distribution...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

true horizon takes into account the fact that the earth is an irregular ellipsoid. When refraction is minimal, the visible sea or ocean horizon is the closest...

slight tidal distortions to their host stars. When a star has a slightly ellipsoidal shape, its apparent brightness varies, depending if the oblate part of...

mechanics – such as the rotation of the earth, and the attraction of ellipsoids – appeared in the second volume. In 1830, he gave a proof of Fermat's...

M\succeq 0} if and only if B 1 ( M ) {\displaystyle B_{1}(M)} is an ellipsoid, or an ellipsoidal cylinder. M ≻ 0 {\displaystyle M\succ 0} if and only if B 1 (...

to citrus canker and citrus scab. The fruit weighs 11–20 grams and is ellipsoid in shape. It has a dark orange rind, which is 4 millimeters thick. The...

surface Boy's surface Sphere Spheroid Oblate spheroid Prolate spheroid Ellipsoid Cone (geometry) Hyperboloid of one sheet Hyperboloid of two sheets Hyperbolic...

representing the Earth as an ellipsoid that approximates the more complex shape of the geoid. Gravity is computed on the ellipsoid surface using the International...

speed between the inner and outer cylinders. The flow tends to orient an ellipsoidal particle (typically, a protein, virus, etc.) in one direction, whereas...

light-years from the Sun. It is a spectroscopic binary star and rotating ellipsoidal variable; a system whose two stars are so close together they are egg-shaped...

level, and has seating for 650 people. The structure is surmounted by an ellipsoidal dome, the interior of which is adorned with a mural painted by Carlos...

the fact that electrostatic fields in motion were deformed ("Heaviside-Ellipsoid" after Oliver Heaviside, who derived this deformation from electromagnetic...

Lighting Methods, Inc. ETC acquired LMI in 1990. The Source Four, an ellipsoidal reflector spotlight, was announced at the Live Design International trade...

environment, overestimates the radiation from floor or ceiling, so an ellipsoid sensor gives a better approximation. There are several other precautions...

whether the Earth is approximated as a perfect sphere or as a reference ellipsoid. In terms of the usual way these geographic coordinates are given, this...

Furthermore Bunchosia argentea has not been cultivated. The fruits are ellipsoidal, almost smooth, slightly hairy and orange to red, briefly tipped berries...

synchronous orbit are expected to asymptotically change shape into rounded ellipsoids under hydrostatic equilibrium, although this may not happen in the age...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

an ellipsoid. Calculated using (1) the known rotation period (5.342 h) and (2) the equatorial radius Req (285 km) of the best-fit biaxial ellipsoid to...

Ediacaria or Cyclomedusa) would remain valid. The type specimens were of the ellipsoid type (they are lost, but a cast remains). Thus, if Aspidella in the loose...

cartography at the time: the Bessel ellipsoid and the Mercator projection. Its measurements used the Bessel ellipsoid as an approximation of the Earth's...

Achlys – a large plutino and possible dwarf planet with an elongated ellipsoid shape (84922) 2003 VS2, a similarly-sized plutino whose shape has been...

5–15 cm (2.0–5.9 in) tall. The basal leaves are thin, with an irregular, ellipsoid shape, smooth-edged, and never starchy. It has fronds the same length...

slim 7 cm high headlamp, which was possible to create using the then new ellipsoid technology developed in conjunction with Hella. The headlamp design was...

short-lived (evanescent), with four to eight sterigmata. The spores are usually ellipsoid or cylindrical in shape, hyaline or pale brown, smooth, more or less smooth-walled...

"Planetary Fact Sheet Notes". Li, Xiong; Götze, Hans-Jürgen (2001). "Ellipsoid, geoid, gravity, geodesy, and geophysics". Geophysics. 66 (6): 1660–1668...

object massive enough to achieve hydrostatic equilibrium and assume an ellipsoid shape, but not enough to sustain core fusion like a star. The purpose...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

(e.g. ⁠ n {\displaystyle n} ⁠-parallelotope, ⁠ n {\displaystyle n} ⁠-ellipsoid); with magnitude (hypervolume), and orientation defined by that on its...

spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid...

continents. A purely geometric quantity is the ellipsoidal height, reckoned from the surface of a reference ellipsoid, see Geodetic system, vertical datum. In...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

(HMI) Hydrargyrum quartz iodide (HQI) Sodium vapor Stationary Reflector Ellipsoidal reflector Multifaceted reflector Parabolic aluminized reflector (PAR)...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

(and planes, and other linear subspaces); parallel lines; ellipses (and ellipsoids). However, it is impossible to define orthogonal (perpendicular) lines...

to remove some debris to check for it. Spores: 7-12 x 6-9 μm. Smooth, ellipsoid, amyloid. The smell has been described as initially faint and honey-sweet...

The stamens are exserted, with filaments 25–30 mm long. The berries are ellipsoid, 10–15 mm long and 0.7–0.9 mm wide. Chromosome count is 2n = 44. F. magellanica...

Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange...

the earth is not entirely spherical but instead generally exhibits an ellipsoid shape- which is a result of the centrifugal forces the planet generates...

The asci (spore sacs) measure about 90–120 × 18–28 μm and contain 4–8 ellipsoid, muriform ascospores. The spores measure about 20–25 × 10–15 μm and have...

position representation Latitude / Longitude Map projection Reference ellipsoid Satellite geodesy Spatial reference system Spatial relations Vertical...

interior of the moon. Amalthea is irregularly shaped, with the best ellipsoidal approximation being 250 × 146 × 128 km. From this, Amalthea's surface...

collaborators and built around 1570: a unique element in Milan is the ellipsoidal dome that traces the course of the hallway and the stairs, which are...

(zonate); an extremely peppery taste; a sweetish odor; spores that are ellipsoid, and not amyloid (that is, not absorbing iodine when stained with Melzer's...

annulus. The spores are hexagonal to subrhomboid in frontal view and ellipsoid in side view, (5.6)6.7–8(9) x (4) 4.8–6.4 (7.2) x 4–4.8 (5.5) μm. The...