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searching for Convex body 100 found (141 total)

Minkowski's theorem (2,350 words) [view diff] no match in snippet view article find links to article

In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to the

Peineta (comb) (451 words) [view diff] exact match in snippet view article

the Hispanic world. The hair ornament, worn by women, consists of a convex body and a set of teeth that affix it to hair worn in a bun. The peineta was

Ulam's packing conjecture (514 words) [view diff] exact match in snippet view article find links to article

Unsolved problem in mathematics Is there any three-dimensional convex body with lower packing density than the sphere? More unsolved problems in mathematics

Miklós Simonovits (616 words) [view diff] exact match in snippet view article find links to article

algorithm using O(n7 log2 n) separation calls to approximate the volume of a convex body within a fixed relative error. Simonovits was also one of the most frequent

Exponential type (1,238 words) [view diff] no match in snippet view article find links to article

In complex analysis, a branch of mathematics, a holomorphic function is said to be of exponential type C if its growth is bounded by the exponential function

Packing density (555 words) [view diff] exact match in snippet view article find links to article

dilations of some other convex body. A particular supply collection of interest is all Euclidean motions of a fixed convex body K. In this case, we call

Armadillidae (816 words) [view diff] exact match in snippet view article find links to article

armadillidae taxa are not monophyletic. Armadillids generally have a strongly convex body shape, with some rather shallowly convex. Like members of the woodlice

Macbeath region (1,106 words) [view diff] exact match in snippet view article find links to article

the center of gravity of K in the bounding hyper-plane of H. Given a convex body K ⊂ R d {\displaystyle K\subset R^{d}} in canonical form, then any cap

Central limit theorem (9,171 words) [view diff] exact match in snippet view article find links to article

function constant inside a given convex body and vanishing outside; it corresponds to the uniform distribution on the convex body, which explains the term "central

Brunn–Minkowski theorem (2,993 words) [view diff] exact match in snippet view article find links to article

bodies. In this section we sketch a few of those insights. Consider a convex body K ⊆ R n {\textstyle K\subseteq \mathbb {R} ^{n}} . Let K ( x ) = K ∩

Lazar Lyusternik (272 words) [view diff] exact match in snippet view article find links to article

theorem of the three geodesics, a conjecture by Henri Poincaré that every convex body in 3-dimensions has at least three simple closed geodesics. The ellipsoid

Blapsium (253 words) [view diff] exact match in snippet view article find links to article

incompletely preserved, lacking a head, pronotum and legs. It has a broad, convex body. It has a very short metathorax, which suggests that it was possibly

Convex cap (1,603 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (n-1)} -dimensional Hausdorff measure. The wet part of a convex body can be defined as K ( t ) = K ( v ≤ t ) = { x ∈ K : v ( x ) ≤ t } {\displaystyle

Banach–Mazur compactum (772 words) [view diff] exact match in snippet view article find links to article

d(X,X)=1.} F. John's theorem on the maximal ellipsoid contained in a convex body gives the estimate: d ( X , ℓ n 2 ) ≤ n , {\displaystyle d(X,\ell _{n}^{2})\leq

Hugo Hadwiger (1,163 words) [view diff] exact match in snippet view article find links to article

combinatorial geometry concerns the minimum number of smaller copies of a convex body needed to cover the body, or equivalently the minimum number of light

Yellow-backed duiker (1,456 words) [view diff] exact match in snippet view article find links to article

1869 C. s. silvicultor (Afzelius, 1815) Yellow-backed duikers have a convex body shape, standing taller at the rump than the shoulders. They have very

Convex polygon (881 words) [view diff] exact match in snippet view article find links to article

a parallelogram. Inscribed/inscribing rectangles property: For every convex body C {\displaystyle C} in the plane, we can inscribe a rectangle r {\displaystyle

Włodzimierz Kuperberg (515 words) [view diff] exact match in snippet view article find links to article

showed that the ratio of packing density to covering density of any convex body in the plane is at least 3/4. His 1990 paper on double lattices with

Mantilla (1,014 words) [view diff] exact match in snippet view article find links to article

tortoiseshell color, originated in the 19th century. It consists of a convex body and a set of prongs and is often used in conjunction with the mantilla

Randomized algorithm (4,218 words) [view diff] exact match in snippet view article find links to article

\Theta (n)} bits if defending against a strong opponent. The volume of a convex body can be estimated by a randomized algorithm to arbitrary precision in

Geometric tomography (166 words) [view diff] exact match in snippet view article find links to article

cross-sections by planes." A key theorem in this area states that any convex body in E n {\displaystyle E^{n}} can be determined by parallel, coplanar

Vertex (curve) (674 words) [view diff] exact match in snippet view article

that every simple closed space curve which lies on the boundary of a convex body, or even bounds a locally convex disk, must have four vertices. Every

Rectangle (2,193 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \displaystyle (AP)^{2}+(CP)^{2}=(BP)^{2}+(DP)^{2}.} For every convex body C in the plane, we can inscribe a rectangle r in C such that a homothetic

Ellipsoid method (3,704 words) [view diff] exact match in snippet view article find links to article

center of the current ellipsoid. The input is a rational number ε>0, a convex body K given by a weak separation oracle, and a number R such that S(0,R)

Mean width (631 words) [view diff] exact match in snippet view article find links to article

}}dS=b(K)} where δ K {\displaystyle \delta K} is the boundary of the convex body K {\displaystyle K} and d S {\displaystyle dS} a surface integral element

Euchelus atratus (332 words) [view diff] exact match in snippet view article find links to article

body whorl they number 12, exclusive of the interstitial riblets. The convex body whorl is rounded, quite abruptly and decidedly descending at the aperture

Catenoid (1,218 words) [view diff] exact match in snippet view article find links to article

doi:10.1007/BF00281743. H.C. Wente, "Tubular capillary surfaces in a convex body," p288, in P. Concus, K. Lancaster and R. Finn, Advances in Geometric

Gibbula zonata (249 words) [view diff] exact match in snippet view article find links to article

about 5 whorls are convex, those of the upper surface bicarinate. The convex body whorl is carinate or subcarinate. The oblique aperture is rounded-quadrangular

Tetrahedron packing (1,005 words) [view diff] exact match in snippet view article find links to article

density for packing congruent spheres is smaller than that for any other convex body. However, the more recent results have shown that this is not the case

Vitali Milman (533 words) [view diff] exact match in snippet view article find links to article

Milman gave a new proof of Dvoretzky's theorem, stating that every convex body in dimension N has a section of dimension d(N), with d(N) tending to

Auerbach's lemma (346 words) [view diff] exact match in snippet view article find links to article

{(ei|·)}). An equivalent statement is the following: any centrally symmetric convex body in R n {\displaystyle \mathbf {R} ^{n}} has a linear image which contains

Heilbronn triangle problem (2,575 words) [view diff] exact match in snippet view article find links to article

Zeng, Zhenbing (1995), "Heilbronn problem for six points in a planar convex body", in Du, Ding-Zhu; Pardalos, Panos M. (eds.), Minimax and Applications

Edward J. McShane (1,152 words) [view diff] case mismatch in snippet view article find links to article

MR 0075280. McShane, E. J. (1962). "The Radius of Gyration of a Convex Body". Proceedings of the American Mathematical Society. 13 (6): 922–926.

Hedgehog (geometry) (1,545 words) [view diff] exact match in snippet view article

but nowhere differentiable and have infinite length. Every strictly convex body in the plane defines a projective hedgehog, its middle hedgehog, the

Estermann measure (334 words) [view diff] exact match in snippet view article find links to article

symmetry of the smallest centrally-symmetric set containing a given convex body K {\displaystyle K} , then the centrally-symmetric set itself is the

Outer billiards (1,664 words) [view diff] exact match in snippet view article find links to article

space. In this case, there is a natural choice of line tangent to a convex body at each point. One obtains these tangents by starting with the normals

Surface of constant width (581 words) [view diff] exact match in snippet view article find links to article

between pairs of parallel tangent lines. More generally, any compact convex body D has one pair of parallel supporting planes in a given direction. A

Fritz John (851 words) [view diff] exact match in snippet view article find links to article

contributions to convex geometry, including his famous result that within every convex body there is one unique ellipsoid of maximal volume, now called the John

Platydemus (269 words) [view diff] exact match in snippet view article find links to article

Species of the genus Platydemus are characterized by a massive, slightly convex body with a broad creeping sole and very large eyes. The copulatory apparatus

Black-winged hatchetfish (293 words) [view diff] exact match in snippet view article find links to article

this fish after his first wife Martha. Black-winged hatchetfish has a convex body. It has a very deep ventral profile with its anal fin set back. This

Kovner–Besicovitch measure (467 words) [view diff] exact match in snippet view article find links to article

center of symmetry of the largest centrally-symmetric set within a given convex body K {\displaystyle K} , then the centrally-symmetric set itself is the

Partula mooreana (310 words) [view diff] no match in snippet view article find links to article

translucent, pale yellowish horn-color, apex darker; whorls 5, flatly convex, body whorl, with or without from one to three narrow, pale, brown revolving

Bocksbeutel (783 words) [view diff] exact match in snippet view article find links to article

cross-section is approximately 2:1, and the ratio of the height of the convex body to the cylindrical neck of the bottle is approximately 2.5:1. The Bocksbeutel

Liotella rotula (347 words) [view diff] exact match in snippet view article find links to article

Interstices are distantly microscopically spirally striate. The large, convex body whorl contains 17 radial riblets. It is rounded at the periphery, but

Alexandrov's uniqueness theorem (1,743 words) [view diff] exact match in snippet view article find links to article

and totals 4π can be represented uniquely as the surface of a smooth convex body in three dimensions. The uniqueness of this representation is a result

Acidocerinae (1,139 words) [view diff] exact match in snippet view article find links to article

Acidocerines can be generally recognized by their oval and moderately convex body shapes with slender maxillary palps and uniformly slender tibiae (usually

Synaptocochlea stellata (401 words) [view diff] exact match in snippet view article find links to article

5¼ mm. The shell is ear-shaped, with a minute spire and a very large, convex body whorl. Its surface is somewhat shining, black with scattered whitish

Afidentula bisquadripunctata (199 words) [view diff] no match in snippet view article find links to article

and Nepal. Body length is about 4.00 to 4.10 mm. Body round-oval, and convex. Body surfaces distinctly setose with yellowish hairs. Head, mouthparts, pronotum

List of real analysis topics (1,603 words) [view diff] exact match in snippet view article find links to article

integrable, symmetric, unimodal, non-negative function over an n-dimensional convex body (K) does not decrease if K is translated inwards towards the origin see

Aquatica hydrophila (410 words) [view diff] exact match in snippet view article find links to article

long, and the female is 11–15 mm (0.43–0.59 in) long. The elongate, convex body is 4–5 mm (0.16–0.20 in) long. It is covered with golden hairs. The prothorax

Zorochros titanus (137 words) [view diff] no match in snippet view article find links to article

titanus is a species of click beetle found in Sri Lanka. Body distinctly convex. Body length is approximately about 4 mm. Lateral carina of pronotum incomplete

Choriaster (639 words) [view diff] exact match in snippet view article find links to article

harmless to humans. Choriaster granulatus is a large sea star with a convex body and five short arms. The arms have rounded tips, making it appear "phallic"

Parupeneus pleurostigma (309 words) [view diff] no match in snippet view article find links to article

slightly convex and the margin of caudal-fin lobes is straight to slightly convex. Body color range from pinkish to yellowish gray, with a broad black spot on

Cionus hortulanus (265 words) [view diff] exact match in snippet view article find links to article

millimetres (0.12–0.18 in). These tiny beetles have a short, oblong and convex body, a conical thorax and a long thin rostrum. Thorax and elytra are covered

Nisotra (550 words) [view diff] exact match in snippet view article find links to article

agricultural pests. Nisotra can be recognised by: a thickset and distinctly convex body; the pronotum as wide of the elytra basally; the pronotum anterior margin

Buccinum baerii (321 words) [view diff] exact match in snippet view article find links to article

54 mm. The thin shell has an elongate to ovate shape with a large broad, convex body whorl. The conical spire is pointed. There are numerous, rounded spiral

Catharsius capucinus (166 words) [view diff] exact match in snippet view article find links to article

Nepal. Average length if about 18 to 26 mm has a shortly oval, and very convex body. Dorsum black and shiny. Pronotum opaque, whereas red color antennae

Conomedusites (551 words) [view diff] exact match in snippet view article find links to article

that its body has four lobes. Conomedusites are described as a small convex body made up of four nearly equal lobes that are divided by sharpy defined

Ligia natalensis (215 words) [view diff] exact match in snippet view article find links to article

natalensis is silver-grey with darker grey markings. Its moderately convex body is twice as long as it is wide, 16–17 millimetres (0.63–0.67 in), with

Microdytes maculatus (236 words) [view diff] exact match in snippet view article find links to article

smaller species has an oblong-oval, slightly rhomboid, and moderately convex body. Total length is about 1.6 to 1.9 mm. Head rufo-testaceous. Clypeus not

Cyclotoma cingalensis (156 words) [view diff] no match in snippet view article find links to article

small, convex beetle has a length of about 3.9 to 5.4 mm. Body highly convex. Body long, very smooth and shiny. Body covered with dense and coarse punctures

Ugandaltica (146 words) [view diff] exact match in snippet view article find links to article

a specialist Afrotropical entomologist. A very small beetle with a convex body. Short antennae. Smooth frons and vertex. Frontal tubercles absent. Three-segmented

Conus denizi (400 words) [view diff] no match in snippet view article find links to article

convex sutural ramps. Sides of the last whorl are straight or slightly convex. Body whorl is smooth except for 8-10 spiral grooves that occupy almost the

Cercyon lineolatus (302 words) [view diff] exact match in snippet view article find links to article

sized terrestrial hydrophilid beetle with an elongated oval, moderately convex body has an average length of about 3.7 mm. Dorsum weakly shiny, however,

Triarthrus (1,471 words) [view diff] exact match in snippet view article find links to article

trilobite (up to about 5 centimetres or 2.0 inches) and its moderately convex body is about twice as long as wide (excluding spines). Like in all Olenidae

Ateuchus guatemalensis (136 words) [view diff] exact match in snippet view article find links to article

dimorphism. The male is about 7.9mm in length, with an elongate-oval and convex body, glossy black beetle with reddish to greenish sheen. The female is similar

Crofton formula (1,560 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n=3} gives the classic example "the average shadow of a convex body is 1/4 of its surface area". General n {\displaystyle n} gives generalization

Norm (mathematics) (5,937 words) [view diff] exact match in snippet view article

formulas. For instance, the Minkowski functional of a centrally-symmetric convex body in R n {\displaystyle \mathbb {R} ^{n}} (centered at zero) defines a

Scymnus nubilus (683 words) [view diff] no match in snippet view article find links to article

Maximum body weight is about 1.5 mg. Body small, elongate, and moderately convex. Body dark brown ventrally, and densely covered with fine, short, transparent

Homothety (2,065 words) [view diff] exact match in snippet view article find links to article

conjecture on the number of strictly smaller homothetic copies of a convex body that may be needed to cover it Homothetic function (economics), a function

Alan M. Frieze (1,274 words) [view diff] exact match in snippet view article find links to article

finding an ϵ {\displaystyle \epsilon } approximation to the volume of a convex body K {\displaystyle K} in n {\displaystyle n} -dimensional Euclidean space

Integer programming (4,192 words) [view diff] case mismatch in snippet view article find links to article

ISBN 9781470423216. MR 3625571. Kannan, Ravi (1987-08-01). "Minkowski's Convex Body Theorem and Integer Programming". Mathematics of Operations Research

Aspidimerus nigrovittatus (171 words) [view diff] no match in snippet view article find links to article

is a species of lady beetle found in Sri Lanka. Body subovate, and convex. Body color pale yellow with bright, sparse pubescence. Elytra broad on each

Phyllognathus dionysius (304 words) [view diff] no match in snippet view article find links to article

is about 16.0 to 23.0 mm in length. Body short, compact, globose and convex. Body shiny red brown in color. Margins of head, clypeus, pronotum, scutellum

Dvoretzky's theorem (1,220 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \epsilon >0} , we call a ϵ {\displaystyle \epsilon } -sphere a convex body K {\displaystyle K} such that there exists a ball B {\displaystyle B}

Gömböc (1,904 words) [view diff] exact match in snippet view article find links to article

convex is essential as it is trivial to construct a mono-monostatic non-convex body: an example would be a ball with a cavity inside it. It was already well

Ronen Eldan (441 words) [view diff] case mismatch in snippet view article find links to article

Polynomial Number of Random Points Does Not Determine the Volume of a Convex Body". Discrete & Computational Geometry. 46 (1). Springer Science and Business

Lloyd Dines (707 words) [view diff] exact match in snippet view article find links to article

David; Dines, L. L. (1940). "On the supporting-plane property of a convex body". Bull. Amer. Math. Soc. 46 (6): 482–489. doi:10.1090/s0002-9904-1940-07242-8

Hydaticus pacificus (522 words) [view diff] exact match in snippet view article find links to article

mark on elytron. Subspecies discindens has an oblong-oval, moderately convex body which is broadest distinctly behind middle. Total length is 13.1 to 16

Reinhold Hoppe (762 words) [view diff] exact match in snippet view article find links to article

(2008), "The kissing number, blocking number and covering number of a convex body", in Goodman, Jacob E.; Pach, János; Pollack, Richard (eds.), Surveys

Vanitrochus semiustus (266 words) [view diff] exact match in snippet view article find links to article

striae. There are four spiral cinguli on the penultimate whorl. The convex body whorl is elongated, with a zone of white and chestnut spots at the periphery

Scymnus coccivora (331 words) [view diff] exact match in snippet view article find links to article

1.90 mm. It is a small ladybird with an elongate oval and moderately convex body. Dorsal surface clothed with dense pubescence. Body color ranges from

William Rowan Hamilton (4,968 words) [view diff] exact match in snippet view article find links to article

the phenomenon, namely that the wave surface is not the boundary of a convex body. A fuller understanding awaited the microlocal analysis of the middle

Hydrophilus palpalis (310 words) [view diff] exact match in snippet view article find links to article

(Dibolocelus) palpalis). This large species has an oval and moderately convex body. The basic color of the body is dark brown or black. Antennae are 9-segmented

Systolic geometry (3,953 words) [view diff] exact match in snippet view article find links to article

} An alternative formulation is as follows. Any centrally symmetric convex body of surface area A can be squeezed through a noose of length π A {\displaystyle

Powellisetia paroeca (407 words) [view diff] no match in snippet view article find links to article

marked off by a groove from whorls proper, of which there are 3, lightly convex, body-whorl very slightly subangled for a short distance in front of suture

Grigori Perelman (6,324 words) [view diff] exact match in snippet view article find links to article

P87. Perelʹman, G. Ya. (1987). "k-radii of a convex body". Siberian Mathematical Journal. 28 (4): 665–666. Bibcode:1987SibMJ..28..665P. doi:10.1007/BF00973857

Eluma praticola (192 words) [view diff] exact match in snippet view article find links to article

egg-bearing females reach 7 millimetres (0.28 in) in length. The species has a convex body and has the ability to conglobate. It is brown in color, the epimera

Károly Bezdek (1,731 words) [view diff] exact match in snippet view article find links to article

published in K. Bezdek, The problem of illumination of the boundary of a convex body by affine subspaces, Mathematika 38 (1991), 362–375. A proof of László

Curve of constant width (3,608 words) [view diff] exact match in snippet view article find links to article

of opposite points, but these points are not necessarily vertices. A convex body has constant width if and only if the Minkowski sum of the body and its

Coandă effect (5,453 words) [view diff] exact match in snippet view article find links to article

which a slender stream of air makes on the surface of water. Bring a convex body into contact with the side of the stream and the place of the dimple

Anthrenus cechovskyi (263 words) [view diff] exact match in snippet view article find links to article

Dermestidae. It is known from Nepal. This insect has a slightly rounded, convex body, measuring between 2.1 and 2.9 mm in length. It has large oval eyes,

Schizidium (362 words) [view diff] exact match in snippet view article find links to article

Schizidium is a genus of woodlice, found from Greece to Iran. It has a convex body, and is capable of volvation (rolling into a ball) without leaving fissures

Anthrenus margarethae (296 words) [view diff] exact match in snippet view article find links to article

of carpet beetle native to South Africa. This insect has a strongly convex body covered in scales, measuring between 2.2 and 2.6 mm in length and 1.5

Finite sphere packing (2,655 words) [view diff] exact match in snippet view article find links to article

{\displaystyle K_{i}} (instead of the sphere, we can also take an arbitrary convex body for K {\displaystyle K} ). For a linear arrangement (sausage), the convex

Introduction to systolic geometry (2,294 words) [view diff] exact match in snippet view article find links to article

More precisely it can be described as follows. Any centrally symmetric convex body of surface area A {\displaystyle A} can be squeezed through a noose of

Peinetón (4,938 words) [view diff] exact match in snippet view article find links to article

to the tastes of each woman. The one-piece accessory had a slightly convex body, it came in a variety of different shapes and featured profuse ornamentation

Opaque set (4,100 words) [view diff] exact match in snippet view article find links to article

J. (1986), "The shortest curve that meets all the lines that meet a convex body", The American Mathematical Monthly, 93 (10): 796–801, doi:10.2307/2322935

Choi–Jamiołkowski isomorphism (3,205 words) [view diff] exact match in snippet view article find links to article

find in general given a Choi state. The set of qudit channels forms a convex body. This means that a convex sum of channels still leads to a channel, and

Truncated triangular pyramid number (1,196 words) [view diff] exact match in snippet view article find links to article

It is hypothesised that a regular tetrahedron might possibly be the convex body having the smallest possible packing density. In contrast to this, the