Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Geometric |
GeometricAdjective1. (fine arts) characterized by simple geometric forms in design and decoration; "a buffalo hide painted with red and black geometric designs". 2. Of or relating to or determined by geometry. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "geometric" was first used in popular English literature: sometime before 1321. (references) |
(From Wikipedia, the free Encyclopedia)
The geometric distribution is a discrete probability distribution that describes the probability that a Bernoulli process will have its first success on the nth trial if the probability of success is p:
It has mean and variance
It is a special case of the negative binomial distribution where r = 1. Like its continuous analogue (the exponential distribution), the geometric distribution is "memoryless"; in fact, it is the only memoryless discrete distribution.
Until somebody adds more information, please refer to negative binomial distribution.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Geometric distribution."
(From Wikipedia, the free Encyclopedia)
The geometric mean of a set of positive data is defined as the product of all the members of the set, raised to a power equal to the reciprocal of the number of members. The geometric mean is useful to determine "average factors". For example, if a stock rose 10% in the first year, 20% in the second year and fell 15% in the third year, then we compute the geometric mean of the factors 1.10, 1.20 and 0.85 as (1.10 × 1.20 × 0.85)1/3 = 1.0391... and we conclude that the stock rose on average 3.91 percent per year.
The geometric mean of a data set is always smaller than or equal to the set's arithmetic mean (the two means are equal if and only if all members of the data set are equal). This allows the definition of the arithmetic-geometric mean, a mixture of the two which always lies in between.
See also: average, arithmetic mean, arithmetic-geometric mean, harmonic meanSource: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Geometric mean."
(From Wikipedia, the free Encyclopedia)
In mathematics, a geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant. For instance, the sequence 3, 6, 12, 24, 48, ... is a geometric progression with common quotient 2.If the initial term of a geometric progression is a and the common quotient of successive members is r, then the n-th term of the sequence is given by a·rn, n = 0, 1, 2, ...
The sum of the numbers in a geometric progression is called a geometric series. A convenient formula for geometric series is available.
See also arithmetic progression. Note that the two kinds of progression are related: taking the logarithm of each term in a geometric progression yields an arithmetic one.
One ordinarily distinguishes between two kinds of progressions, arithmetical and geometrical, corresponding to the proportions called arithmetical and geometrical. But the word 'proportion' seems rather inappropriate as applied to arithmetical proportion.
The idea of proportion is already well established by usage and it corresponds solely to what is called geometrical proportion; when we say generally that one thing is proportional to another, we understand by proportion equality of ratios only, as in geometrical proportion, and never equality of differences as in arithmetical proportion.
One cannot see why the proportion called arithmetical is any more arithmetical than that which is called geometrical, nor why the latter is more geometrical than the former. On the contrary, the primitive idea of geometrical proportion is based on arithmetic, for the notion of ratios springs essentially from the consideration of numbers
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Geometric progression."
(From Wikipedia, the free Encyclopedia)
Geometry is the branch of mathematics dealing with spatial relationships. From experience, or possibly intuitively, people characterize space by certain fundamental qualities, which are termed axioms in geometry. Such axioms are insusceptible of proof, but can be used in conjunction with mathematical definitions for points, straight lines, curves, surfaces, and solids to draw logical conclusions.
Because of its immediate practical applications, geometry was one of the first branches of mathematics to be developed. Likewise, it was the first field to be put on an axiomatic basis, by Euclid. The Greeks were interested in many questions about ruler-and-compass constructions. The next most significant development had to wait until a millennium later, and that was analytic geometry, in which coordinate systems are introduced and points are represented as ordered pairs or triples of numbers. This sort of representation has since then allowed us to construct new geometries other than the standard Euclidean version.
The central notion in geometry is that of congruence. In Euclidean geometry, two figures are said to be congruent if they are related by a series of reflections, rotations, and translationss.
Other geometries can be constructed by choosing a new underlying space to work with (Euclidean geometry uses Euclidean space, Rn) or by choosing a new group of transformations to work with (Euclidean geometry uses the inhomogeneous orthogonal transformations, E(n)). The latter point of view is called the Erlanger program. In general, the more congruences we have, the fewer invariants there are. As an example, in affine geometry any linear transformation is allowed, and so the first three figures are all congruent; distances and angles are no longer invariants, but linearity is.
A discrete form of geometry is treated under Pick's theorem.
See List of geometry topics.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Geometry."
Synonym: GeometricSynonym: geometrical (adj). (additional references) |
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Theater & Movies | |||
Consumer Goods | |||
Source: compiled by the editor from various references; see credits. | |||
| Thumbnail | Description & Credit | Thumbnail | Description & Credit |
 | ALBATROSS IV rigging and antennas superimpose geometric patterns on sunset. Credit: Paths Less Taken - NOAA at the Ends of the Earth. |  | Interior, rotunda, general view from east. Photograph by Jack E. Boucher, November 1976. (Reproduction Number: HABS IOWA,97-SIOCI,3-17) Completed in 1918 to designs by Purcell & Elmslie, the Woodbury County Courthouse is a rare example of a Prairie style design for a large public building. The Prairie style is known for its bold and simple geometric forms and distinctive ornamentation inspired by nature, and was made famous by Louis Sullivan and his student Frank Lloyd Wright, key figures in the Prairie school who developed systems of abstracting architectural decoration from sources in nature. The term Prairie style refers to the style’s origins in the American Midwest, and its evocation of that region’s fertile prairies and flat terrain. The interior rotunda shown here is the focal point of the courthouse. It incorporates simple rectangles and squares with a stained glass dome and uses terra cotta ornament reminiscent of the prairie. Credit: Library of Congress. |
 | Geometric art on canvas with huge ornate signature. Credit: Library of Congress. |  | Geometric figure of earth, sun, and moon calculated by Aristarchus to approximate real scale of the solar system. Credit: Library of Congress. |
Source: pictures compiled by the editor from various references; see picture credits. | |||
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| "Textures 4" by K.C. Hohensee Commentary: "Textures... some fun, others geometric, and others just plain... green." | "Ceiling" by Paige Foster Commentary: "The ceiling under a breezeway at the strip mall next door. I thought the geometric design was cool." |
Source: photographs selected by the editor, with permission from the photographers. | |
| Title | Author | Quote |
Les Miserables | Hugo, Victor | However, if the geometric line is in place anywhere, it surely is in the stercorary trenches of a great city |
Source: compiled by the editor from various references. | ||
| Subject | Topic | Quote |
Health | It is a microscopic sphere encasing a 20-sided geometric figure called an icosahedron. (references) | |
In the search for them, scientists are studying a phenomenon known as visual memory--the ability to remember and reproduce geometric patterns, for instance. (references) | ||
People with agnosia may have difficulty recognizing the geometric features of an object or face or may be able to perceive the geometric features but not know what the object is used for or whether a face is familiar or not. Agnosia can be limited to one sensory modality such as vision or hearing. (references) | ||
Business | Handcrafted embroidery with geometric and floral patterns is also very popular. (references) | |
Bipolar grounded plugs for 250 volts and 10-20 amps, and plugs of Class I insulated equipment must meet the dimensional and geometric requirements of IRAM Standard 2073, except if they are specifically designed for restricted access areas in hospitals. (references) | ||
Pearl and frosted finishes; white over color as a highlight; origami folds pressed into garments; color blocking; painted fabric resembling the orient; huge Hawaiian floral and graphic prints; geometric prints such as polka dots and block prints; sheen and gloss; tie died wraps and skirts; tone on tone print to create dimension; modular dressing; fluid floral and watery leaf prints. (references) | ||
Source: compiled by the editor from ICON Group International, Inc.; see credits. | ||
| "Geometric" is generally used as an adjective (general or positive) -- approximately 98.98% of the time. "Geometric" is used about 589 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Adjective (general or positive) | 98.98% | 583 | 10,863 |
| Noun (proper) | 1.02% | 6 | 143,867 |
| Total | 100.00% | 589 | N/A |
Source: compiled by the editor from several corpora; see credits.
Expressions using "geometric": computer aided geometric design ♦ geometric geometrical ♦ geometric isomer ♦ Geometric lathe ♦ geometric mean ♦ geometric pace ♦ Geometric pen ♦ geometric progression ♦ geometric reasoning ♦ geometric series ♦ geometric shape ♦ Geometric spider ♦ Geometric square ♦ mean geometric chord. Additional references. | |
| Hyphenated Usage | |
Beginning with "geometric": geometric-types. | |
Ending with "geometric": italo-geometric, near-geometric. | |
| Source: compiled by the editor from various references; see credits. | |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Language | Translations for "geometric"; alternative meanings/domain in parentheses. | |
Albanian | gjeometrik (geometrical). (various references) | |
Arabic | هندسي (geometrical). (various references) | |
Bulgarian | геометричен. (various references) | |
Chinese | 几何学. (various references) | |
Czech | geometrický. (various references) | |
Danish | geometrisk ræsonneren (geometric reasoning), geometrisk middeltal (geometric mean, geometrical average), geometrisk landskildpadde (geometric tortoise), geometrisk gennemsnit (geometric mean, geometrical average), stereoisomer (geometric isomer, stereo isomer, stereoisomer), fordeling af gennemsnit (and the geometric mean, central tendency, the generalized concept of the average value of a distribution.Typical measures of central tendency are the mean, the median, the mode). (various references) | |
Dutch | geometrische landschildpad (geometric tortoise), geometrisch redeneren (geometric reasoning), geometrisch gemiddelde (geometric mean, geometrical average), stereo-isomeer (geometric isomer, stereoisomer), meetkundige rij (geometric progression, geometric sequence), meetkundige reeks (geometric series), meetkundig gemiddelde (geometric mean, geometrical average), centrale tendens (and the geometric mean, central tendency, the generalized concept of the average value of a distribution.Typical measures of central tendency are the mean, the median, the mode). (various references) | |
Finnish | geometrinen. (various references) | |
French | géométrique (geometrical). (various references) | |
German | geometrisch (geometrical). (various references) | |
Greek | γεωμετρικόσ, γεωμετρικός, Γεωμετρικός. (various references) | |
Hebrew | הנדסי, גאומטרי. (various references) | |
Hungarian | mértani (geometrical), geometriai (geometrical). (various references) | |
Indonesian | geometris (geometrical). (various references) | |
Italian | geometrico. (various references) | |
Japanese Kanji | ジェット燃料 (diethylene glycol, diopter, gem, gemstone, gender, gender gap, general, general strike, generalist, generate, generation, generation gap, generator, generic, generic brand, genetic, genetic algorithms, genetic system, genocide, gentleman, geography, geology, geometry, Geotopia, gerontocracy, gerontology, Japanese External Trade Organization, jealousy, jelly, Jenkins, Jerry, jet fuel, JETRO, The End). (various references) | |
Japanese Katakana | ジオメトリック . (various references) | |
Korean | 기하학 (Geometrical, Geometry). (various references) | |
Manx | towse-oaylleeagh (geometrical). (various references) | |
Pig Latin | eometricgay.(various references) | |
Portuguese | geométrico (geometrical). (various references) | |
Romanian | geometric (formal, geometrical, geometrically). (various references) | |
Russian | геометрический. (various references) | |
Serbo-Croatian | geometrijski (geometrical). (various references) | |
Spanish | geométrico (geometrical). (various references) | |
Swedish | geometrisk. (various references) | |
Turkish | geometrik (geometrical). (various references) | |
Ukrainian | геометричний (geometrical). (various references) | |
| Source: compiled by the editor from various translation references. | ||
Derivations | |
Words beginning with "geometric": geometrical, geometrically, geometrician, geometricians, geometrics. (additional references) | |
Words containing "geometric": nongeometrical. (additional references) | |
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"Geometric" is suggested in spellcheckers for the following: ecometric, egometric, Eormenric, Gelmetti, Gemerek, geomatic, geometra, geometria, geometrics, Giamberti, Girometti, Seametrix. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "geometric" (pronounced jē'ume"trik) |
| 7 | -u m e" t r i k | barometric, dissymmetric, econometric, gravimetric, parametric. |
| 6 | -m e" t r i k | metric, optometric. |
| 5 | -e" t r i k | obstetric. |
| 4 | -t r i k | anthropocentric, citric, concentric, eccentric, egocentric, electric, ethnocentric, gastric, geocentric, geriatric, hydroelectric, nitric, pediatric, photoelectric, psychiatric, tantric, vitric. |
| 3 | -r i k | alphanumeric, atmospheric, Baldric, barbaric, boric, caloric, choric, cleric, Derrick, esoteric, euphoric, fabric, generic, hemispheric, historic, hyperbaric, hysteric, ionospheric, lyric, mercuric, mesenteric, meteoric, numeric, pinprick, prehistoric, pyrrhic, rubric, satiric, sophomoric, stearic, stratospheric, sulfuric, vampiric. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "c-e-e-g-i-m-o-r-t" | |
-1 letter: meteoric. | |
-2 letters: cortege, coterie, ergotic, mortice. | |
-3 letters: cerite, cermet, emetic, emigre, emoter, erotic, gemote, goiter, goitre, meteor, metier, metric, recite, reemit, regime, remote, retime, tierce. | |
-4 letters: citer, comer, comet, comte, corgi, creme, crime, egret, emote, erect, ergot, gemot, greet, grime, griot, merge, merit, meter, metre, metro, micro, miter, mitre, moire, orgic, recti, recto, remet. | |
| Words containing the letters "c-e-e-g-i-m-o-r-t" | |
+1 letter: ergometric, geometrics. | |
+2 letters: egocentrism, geometrical, microgamete. | |
+3 letters: aeromagnetic, counterimage, egocentrisms, geochemistry, geometrician, meteorologic, microgametes. | |
+4 letters: counterimages, embryogenetic, ferromagnetic, gastrectomies, geometrically, geometricians, heterogametic, magnetometric, morphogenetic, spermatogenic, tragicomedies. | |
+5 letters: conglomerative, discouragement, electroforming, geochemistries, laryngectomies, magnetospheric, meteorological, nongeometrical, overmedicating, thermomagnetic. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Commercial | 5. Images: Slideshow 6. Images: Photo Album 7. Images: Digital Art 8. Quotations: Fiction | 9. Quotations: Non-fiction 10. Usage Frequency 11. Expressions 12. Expressions: Internet | 13. Translations: Modern 14. Derivations 15. Rhymes 16. Anagrams | 17. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
