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binomial theorem farbin-e donâmin Fr.: théorème du binôme A rule for writing an equivalent expansion of an expression such as (a + b)^{n} without having to perform all multiplications involved. → binomial expansion. The general expression is (a + b)^{n} = &Sigma (n,k)a^{k}b^{n - k}, where the summation is from k = 0 to n, and (n,k) = n!/[r!(n - k)!]. For n = 2, (a + b)^{2} = a^{2} + 2ab + b^{2}. Historically, the binomial theorem as applied to (a + b)^{2} was known to Euclid (320 B.C.) and other early Greek mathematicians. In the tenth century the Iranian mathematician Karaji (953-1029) knew the binomial theorem and its accompanying table of → binomial coefficients, now known as → Pascal's triangle. Subsequently Omar Khayyam (1048-1131) asserted that he could find the 4th, 5th, 6th, and higher roots of numbers by a special law which did not depend on geometric figures. Khayyam's treatise concerned with his findings is lost. In China there appeared in 1303 a work containing the binomial coefficients arranged in triangular form. The complete generalization of the binomial theorem for all values of n, including negative integers, was established by Isaac Newton (1642-1727). |
bio- zist- (#) Fr.: bio- Bio-, Gk., from bios "life," from PIE base *gweie- "to live;" cf. O.Pers./Av. gay- "to live," Av. gaya- "life," gaeθâ- "being, world, mankind," jivya-, jva- "aliving, alive," Skt. jivah "alive, living;" Mid.Pers. zivastan "to live," zivik, zivandag "alive, living," L. vivus "living, alive," vita "life," O.E. cwic "alive," E. quick, Lith. gyvas "living, alive." Zist "life, existence," from zistan "to live," Mid.Pers. zivastan "to live," zivižn "life," O.Pers./Av. gay-, as explained above. |
bioastronomy zistaxtaršenâsi (#) Fr.: bioastronomie A common branch of astronomy and biology dealing with the study of life throughout the Universe; synonymous with → astrobiology and → exobiology. Bioastronomy, from → bio- + → astronomy. Zistaxtaršenâsi, from zist-, → bio-, + axtaršenâsi, → astronomy. |
biodiversity zistgunâguni Fr.: biodiversité The → variety of → plant and → animal → species in a particular → environment. |
bioinformatics zist-azdâyik Fr.: bioinformatique The retrieval and analysis of biochemical and biological data using mathematics and computer science, as in the study of genomes (Dictionary.com). → bio-; → informatics. |
biologist zistšenâs (#) Fr.: biologiste An expert or specialist in biology. |
biology zistženâsi (#) Fr.: biologie The study of living organisms and their interactions with the non living world. |
bioluminescence zist-foruzesti Fr.: bioluminescence The production and emission of light by a living organism as the result of a chemical reaction (→ chemiluminescence). In other words, bioluminescence is chemiluminescence from living organisms. It is widespread in the marine environment, but rare in terrestrial and especially freshwater environments. → chemi-; → luminescence. |
biophysicist zistfizikdân (#) Fr.: biophysicien A specialist in → biophysics. |
biophysics zistfizik (#) Fr.: biophysique The science that deals with biological structures and processes involving the application of physical principles and methods. |
biosphere zistsepehr (#) Fr.: biosphère The part of a planet or moon within which life can occur. It may include the crust, oceans, and atmosphere. |
Biot-Savart law qânun-e Biot-Savart (#) Fr.: loi de Biot-Savart The → magnetic field due to → electric current flowing in a long straight conductor is directly proportional to the current and inversely proportional to the distance of the point of observation from the conductor. The law is derivable from → Ampere's law, but was obtained experimentally by the authors. Named after the French physicists Jean-Baptiste Biot (1774-1862) and Félix Savart (1791-1841); → law. |
biotic environment pargir-e zistik Fr.: environnement biotique Ecology: The environment consisting of living organisms, which interact with each other and with their non-living surroundings. Biotic adj. of → biotics; of → environment. |
biotics zistik Fr.: biotique The science concerned with the functions of life, or vital activity and force. From biotic, from Gk. biotikos "of or pertaining to life," from → bio- + -tic a suffix equivalent in meaning to → -ic. |
bipolar doqotbi (#) Fr.: bipolaire Having two poles; having two opposite main structures or components. Bipolar, from → bi- + → polar, from → pole. Doqotbi, from do-, → bi-, + qotbi, → polar, from qotb, → pole. |
bipolar flow tacân-e doqotbi Fr.: flot bipolaire Same as → bipolar outflow. |
bipolar jet šân-e doqotbi Fr.: jet bipolaire One of two beams of high-temperature, ionized gas ejected in two opposite directions associated with a → protostar. The collimated jets, a consequence of the → accretion process, can extend over distances of several → light-years. |
bipolar nebula miq-e doqotbi Fr.: nébuleuse bipolaire An interstellar cloud of ionized gas with two main lobes which lie symmetrically on either side of a central star. The bipolar shape is generally due to the ejection of material by the central star in opposing directions. |
bipolar outflow ostacân-e doqotbi Fr.: flot bipolaire A flow of gaseous material in two opposite directions emanating from protostellar regions or from → evolved stars during the early post-→ AGB evolution. In protostellar regions → molecular outflows are pushed by → bipolar jets. |
birefringence došekast (#) Fr.: biréfringence A property of some crystalline materials (e.g. calcite, quartz) which have different indices of refraction associated with different crystallographic directions. Therefore, the crystal splits incident transmitted light into two beams, each polarized perpendicularly to the other. Also called double refraction. Birefringence, from → bi- + refringence, from L. refringere "to break up," from → re- "back" + combination form of frangere "to break." Došekast, from do- "two," → bi- + šekast "breaking," from šekastan "to break up," Mid.Pers. škastan, Av. skand- "to break." |
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