ConseggioLigure/seed-instruct-lij-eng huggingface dataset:
Traduxi sto testo in ingleise:
Comme demostra i talli attrovæ in scê òsse, ciù in là de reconosce comme se conta i oggetti fixichi, i pòpoli da preistöia porrieivan avei reconosciuto anche comme contâ de quantitæ astræte, comme o tempo (giorni, stagioin e anni).
A traduçion in ingleise do testo a l’é:
As evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time—days, seasons, or years.
Traduxi sto testo da-o zeneise à l’ingleise:
À partî da-o secolo VI a.C., co-i discepoli de Pitagora, co-a matematica grega i Greghi antighi an comensou à studiâ scistematicamente a matematica comme matëia separâ.
A traduçion in ingleise do testo a l’é:
Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right.
Quæ a l’é a traduçion ingleise de sto testo?
O ciù grande matematico de l’antighitæ pe-o sòlito o l’é individuou inte Archimede de Sciragusa (c. 287-212 a.C.).
A traduçion in ingleise do testo a l’é:
The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse.
Traduxi da-o ligure à l’ingleise:
A conquista ciù importante da matematica islamica o l’é stæto o desviluppo de l’algebra.
A traduçion in ingleise do testo a l’é:
The most notable achievement of Islamic mathematics was the development of algebra.
Quæ a l’é a traduçion ingleise de sto testo?
Inta primma etæ moderna, a matematica a l’à comensou à sviluppâse ciù a-a spedia inte l’Euröpa de ponente.
A traduçion in ingleise do testo a l’é:
During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
Ti peu tradue sto testo in ingleise?
Fòscia o matematico ciù importante do secolo XIX o l’é stæto o todesco Carl Friedrich Gauss, ch’o l’à dæto ben ben de contribuçioin inte di campi comme l’algebra, a geometria differençiale, a teorie de matrixe, a teoria di numeri e a statistica.
A traduçion in ingleise do testo a l’é:
Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, analysis, differential geometry, matrix theory, number theory, and statistics.
Traduxi sto testo da-o ligure à l’ingleise:
De scoverte matematiche vëgnan fæte ancon a-a giornâ d’ancheu.
A traduçion in ingleise do testo a l’é:
Mathematical discoveries continue to be made today.
Ti peu tradue sto testo in ingleise?
Ciù into detaggio, mathēmatikḗ tékhnē voeiva dî «l’arte matematica».
A traduçion in ingleise do testo a l’é:
In particular, mathēmatikḗ tékhnē meant "the mathematical art."
Traduxi da-o ligure à l’ingleise:
In ingleise, o sostantivo «mathematics» o veu o verbo a-o scingolare.
A traduçion in ingleise do testo a l’é:
In English, the noun mathematics takes a singular verb.
Ti peu tradue sto testo in ingleise?
À tutti i mòddi, Aristòtele o l’à nottou che anche unn’attençion solo che a-a quantitæ a no peu distingue a matematica da de sciense comme a fixica; segondo lê, a matematica a l’é distinta da-e istanse da realtæ pe meo de l’astraçion e do studio da quantitæ comme «separabile da-o pensceo».
A traduçion in ingleise do testo a l’é:
However, Aristotle also noted a focus on quantity alone may not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart.
Traduxi in lengua ingleise:
A particolaritæ de l’intuiçionismo a l’é o refuo de çerte idee matematiche conscideræ valide segondo atre definiçioin.
A traduçion in ingleise do testo a l’é:
A peculiarity of intuitionism is that it rejects some mathematical ideas considered valid according to other definitions.
Traduxi da-o zeneise à l’ingleise:
Haskell Curry o l’à definio a matematica solo comme «a sciensa di scistemi formali».
A traduçion in ingleise do testo a l’é:
Haskell Curry defined mathematics simply as "the science of formal systems".
Traduxi sto testo da-o zeneise à l’ingleise:
Popper o l’à nottou ascì che «ammettiò che un scistema o segge empirico o scientifico solo s’o peu ëse misso a-a preuva da l’esperiensa».
A traduçion in ingleise do testo a l’é:
Popper also noted that "I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience."
Traduxi sto testo da-o zeneise à l’ingleise:
L’intuiçion e a sperimentaçion an zugou un ròllo primmäio ascì pe-e ipòtexi tanto che e inta matematica comme inte (atre) sciense.
A traduçion in ingleise do testo a l’é:
Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences.
Comm’à l’é a traduçion ingleise de sto testo?
Pe fâ un exempio, o fixico Richard Feynman o l’à inventou a formulaçion integrale do percorso da mecanica quantistica deuviando unna combinaçion de raxonamento matematico e intuiçion fixica, e a teoria de strinche in veuga a-a giornâ d’ancheu (saieiva à dî unna teoria scientifica ancon in fase de sviluppo ch’a çerca d’azzonze e quattro fòrse fondamentale da natua) a l’inspira ancon da neuva matematica.
A traduçion in ingleise do testo a l’é:
For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.
Traduxi sto testo da-o zeneise à l’ingleise:
De spesso se distingue fra a matematica pua e quella applicâ.
A traduçion in ingleise do testo a l’é:
A distinction is often made between pure mathematics and applied mathematics.
Traduxi in ingleise:
Comme inta ciù parte di campi de studio, l’esploxon da conoscensa inte l’epoca scientifica a l’à portou a-a speçializzaçion: oua gh’é çentenæa d’aree speçializzæ inta matematica e l’urtima Mathematics Subject Classification a l’arriva a-e 46 pagine.
A traduçion in ingleise do testo a l’é:
As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.
Traduxi da-o zeneise à l’ingleise:
Tanti studioxi de matematica mensoñan l’elegansa da matematica, a seu estetica intrinseca e a seu bellessa interiô.
A traduçion in ingleise do testo a l’é:
Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty.
Traduxi da-o ligure à l’ingleise:
G. H. Hardy iten A Mathematician’s Apology o l’à manifestou a convinçion che ste conscideraçioin estetiche seggian abasta, da pe liatre, pe giustificâ o studio da matematica pua.
A traduçion in ingleise do testo a l’é:
G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics.
Traduxi da-o zeneise à l’ingleise:
Un teorema espresso comme caratterizzaçion de l’oggetto da ste caratteristiche o l’é o premio.
A traduçion in ingleise do testo a l’é:
A theorem expressed as a characterization of the object by these features is the prize.
Traduxi da-o ligure à l’ingleise:
Eulero (1707-1783) o l’é responsabile de ben ben de nottaçioin deuviæ ancon a-a giornâ d’ancheu.
A traduçion in ingleise do testo a l’é:
Euler (1707–1783) was responsible for many of the notations in use today.
Traduxi sto testo da-o zeneise à l’ingleise:
O linguaggio matematico o comprende ascì tanti termini speçializzæ comme «omeomorfismo» ò «integrabile», che n’an nisciun scignificato a-o de feua da matematica.
A traduçion in ingleise do testo a l’é:
Mathematical language also includes many technical terms such as homeomorphism and integrable that have no meaning outside of mathematics.
Comm’à l’é a traduçion ingleise de sto testo?
I studioxi de matematica fan referensa à sta lògica e à sta preçixon de linguaggio comme «rigô».
A traduçion in ingleise do testo a l’é:
Mathematicians refer to this precision of language and logic as "rigor".
Traduxi da-o ligure à l’ingleise:
Questo o l’é pe evitâ di «teoremi» sbaliæ, basæ in sce de intuiçioin fallibile; di caxi pægi, inta stöia da matëia, se n’é verificou ben ben.
A traduçion in ingleise do testo a l’é:
This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.
Traduxi sto testo in ingleise:
A fäsa interpretaçion do rigô a l’é a raxon pe-e çerte tra e fäse conceçioin da matematica che s’attreuvan ciù de frequente.
A traduçion in ingleise do testo a l’é:
Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics.
Traduxi in lengua ingleise:
Da l’atra parte, i ascistenti de preuve permettan de verificâ tutti i detaggi che no peuan ëse fornii inte unna preuva scrita à man e dan a çertessa da correttessa de preuve longhe comme quella do teorema de Feit-Thompson.
A traduçion in ingleise do testo a l’é:
On the other hand, proof assistants allow verifying all details that cannot be given in a hand-written proof, and provide certainty of the correctness of long proofs such as that of the Feit–Thompson theorem.
Traduxi in ingleise:
In azzonta à ste preoccupaçioin prinçipæ gh’é ascì de sottodivixoin dedicæ à l’esploraçioin di collegamento da-o cheu da matematica +a di atri campi: da-a lògica, a-a teoria di insemmi (fondaçioin), a-a matematica empirica de varie sciense (matematica applicâ) e ciù de reçente a-o studio rigoroso de l’inçertessa.
A traduçion in ingleise do testo a l’é:
In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
Quæ a l’é a traduçion ingleise de sto testo?
Quarche mancansa d’accòrdio in scî fondamenti da matematica a l’é ancon viva a-a giornâ d’ancheu.
A traduçion in ingleise do testo a l’é:
Some disagreement about the foundations of mathematics continues to the present day.
Quæ a l’é a traduçion ingleise de sto testo?
A lògica moderna a se dividde inta teoria da ricorscion, quella di modelli e quella da preuva, a e l’é ligâ streitamente à l’informatica teòrica e a-a teoria de categorie.
A traduçion in ingleise do testo a l’é:
Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science, as well as to category theory.
Traduxi sto testo da-o zeneise à l’ingleise:
A teoria da computabilitæ a sstudia i limiti de varri modelli teròrichi di computer, compreiso quello ciù conosciuo: a machina de Turing.
A traduçion in ingleise do testo a l’é:
Computability theory examines the limitations of various theoretical models of the computer, including the most well-known model—the Turing machine.
Traduxi da-o ligure à l’ingleise:
A conscideraçion di numeri naturali a pòrta anche a-i numeri transfinii, che formalizzan o conçetto de «infinio».
A traduçion in ingleise do testo a l’é:
Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of "infinity".
Traduxi sto testo da-o zeneise à l’ingleise:
Coscì se peu studiâ di gruppi, di anelli, di campi e di atri scistemi astræti; inte l’insemme, sti studdi (pe struttue definie da de operaçioin algebriche) forman o dominio de l’algebra astræta.
A traduçion in ingleise do testo a l’é:
Thus one can study groups, rings, fields and other abstract systems; together such studies (for structures defined by algebraic operations) constitute the domain of abstract algebra.
Traduxi da-o ligure à l’ingleise:
A trigonometria a l’é a ramma da matematica ligâ a-e relaçioin tra i loei e i angoli di triangoli e co-e fonçioin trigonometriche.
A traduçion in ingleise do testo a l’é:
Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions.
Traduxi da-o ligure à l’ingleise:
I gruppi de Lie vëgnan deuviæ pe studiâ o spaçio, a struttua e o cangio.
A traduçion in ingleise do testo a l’é:
Lie groups are used to study space, structure, and change.
Traduxi in ingleise:
Chì e fonçioin se presentan comme un conçetto primmäio ch’o descrive unna quantitæ ch’a cangia.
A traduçion in ingleise do testo a l’é:
Functions arise here as a central concept describing a changing quantity.
Quæ a l’é a traduçion ingleise de sto testo?
Uña de tante applicaçioin de l’analixi fonçionale a l’é a mecanica quantica.
A traduçion in ingleise do testo a l’é:
One of many applications of functional analysis is quantum mechanics.
Quæ a l’é a traduçion ingleise de sto testo?
I studioxi de statistica (travaggiando inte un progetto de reçerca) crean di «dæti ch’an de senso» pe mezo do campionamento casuale e con di esperimenti randomizzæ; o disegno de un campion statistico ò de un esperimento o speçifica l’analixi di dæti (primma che i dæti mæximi seggian à dispoxiçion).
A traduçion in ingleise do testo a l’é:
Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data becomes available).
Traduxi in ingleise:
L’analixi numerica a studia di metodi pe-i problemi d’analixi pe mezo de l’analixi fonçionale e a teoria de l’approscimaçion; l’analixi numerica a comprende o studio de l’approscimaçion e da discretizzaçion latu sensu, con unn’attençion particolare a-i erroî d’arrotondaçion.
A traduçion in ingleise do testo a l’é:
Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis includes the study of approximation and discretisation broadly with special concern for rounding errors.
Traduxi sto testo da-o zeneise à l’ingleise:
A medaggia Chern a l’é stæta introduta do 2010 pe premiâ i successi che meitan d’ëse regordæ pe delongo.
A traduçion in ingleise do testo a l’é:
The Chern Medal was introduced in 2010 to recognize lifetime achievement.
Traduxi sto testo da-o ligure à l’ingleise:
Sta lista a l’à razzonto unna gran çelebritæ tra i studioxi da matematica e a-o manco neuve di problemi an attrovou de soluçion.
A traduçion in ingleise do testo a l’é:
This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved.
Traduxi in lengua ingleise:
O valô do pi grego o l’é stæto carcolou pe-a primma vòtta da lê.
A traduçion in ingleise do testo a l’é:
The value of Pi was first calculated by him.
Traduxi in lengua ingleise:
O termine «matematica» o l’é stæto cuniou da-i discepoli de Pitagora, co-i quæ comensa o studio da matematica mæxima.
A traduçion in ingleise do testo a l’é:
It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins.
Traduxi sto testo da-o ligure à l’ingleise:
Apreuvo à unna conteisa politica, a communitæ crestiaña de Lusciandra a l’aiva castigâ, co-o pensâ ch’a fïse interessâ lê ascì; l’aivan despuggiâ e gh’aivan rascciou a scheña con de scheuggioe (gh’é chì dixe con di coppi).
A traduçion in ingleise do testo a l’é:
Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles).
Traduxi sto testo da-o ligure à l’ingleise:
I finançiamenti pe-a traduçion de testi de sciensa inte de atre lengue vegnivan stançiæ durante o regno de çerti califfi e resultava che çerti studioxi vegnivan di esperti inte euvie che traduxeivan; a seu vòtta reçeveivan ancon do sostëgno pe anâ avanti co-o sviluppo de çerte sciense.
A traduçion in ingleise do testo a l’é:
Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences.
Traduxi sto testo da-o zeneise à l’ingleise:
Unna caratteritica degna de nòtta de tanti studioxi che travaggian sotta a-o governo mossulman inte l’etæ de mezo a l’ea a seu polimatiçitæ.
A traduçion in ingleise do testo a l’é:
A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths.
Traduxi in lengua ingleise:
Inte sto periodo de tranxiçion da unna coltua prinçipalmente feudale e ecclexiastica à unn’atra prevalentemente secolare, tanti studioxi de matematica degni de nòtta aivan di atri travaggi: Luca Pacioli (fondatô da contabilitæ); Gerolamo Cardano (primmo fondatô da probabilitæ e de l’esprescion binomiale); Robert Recorde (mego) e François Viète (avvocou).
A traduçion in ingleise do testo a l’é:
During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer).
Comm’à l’é a traduçion ingleise de sto testo?
E universcitæ britanniche de quello periodo aivan adottou de metodologie za presente inte quelle italiañe e todesche, ma dæto che de fæto aivan za unna çerta libertæ e autonomia, da liatri i cangi ean za comensæ con l’Etæ di Lummi; e mæxime influense ch’an inspirou Humboldt.
A traduçion in ingleise do testo a l’é:
British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
Comm’à l’é a traduçion ingleise de sto testo?
I studenti poeivan fâ da reçerca inte di seminäi e labortatöi e comensavan à scrive de texi de dottorato con ciù tanto contegnuo scientifico.
A traduçion in ingleise do testo a l’é:
Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content.
Quæ a l’é a traduçion ingleise de sto testo?
I matematichi e i matematichi applicæ en conscideræ i doî representanti de carriere dite STEM (sciensa, tecnologia, inzegnaia e matematica).
A traduçion in ingleise do testo a l’é:
Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers.
Traduxi sto testo da-o zeneise à l’ingleise:
I attuäi an da fâ ascì con de costioin finançiäie, comme quelle ligæ a-o livello de contribuçioin penscionistiche neçessäie pe produe un çerto reddito de penscion e o mòddo comme unn’açienda a dovieiva investî de resorse pe mascimizzâ a rendia di investimenti a-a luxe do poscibile reisego.
A traduçion in ingleise do testo a l’é:
Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk.
Traduxi sto testo in ingleise:
O scistema de geroglifichi che i egiçi deuviavan pe-a representaçion di numeri, comme ascì i numeri romoen che saieivan arrivæ dòppo, ne vegnivan da-i scimboli deuviæ pe contâ.
A traduçion in ingleise do testo a l’é:
The hieroglyphic system for Egyptian numerals, like the later Roman numerals, descended from tally marks used for counting.
Quæ a l’é a traduçion ingleise de sto testo?
I primmi scistemi de numeraçion che comprendeivan a numeraçion poxiçionale no ean à base dexe, compreiso quello à base sciuscianta pe i numeri babiloneixi e quelli à base vinti di numeri maya.
A traduçion in ingleise do testo a l’é:
Early number systems that included positional notation were not decimal, including the sexagesimal (base 60) system for Babylonian numerals, and the vigesimal (base 20) system that defined Maya numerals.
Traduxi in ingleise:
Primma de euvie de Euclide (ca. 300 a.c.) i studdi di Greghi in sciâ matematica arrivavan à toccâ e creddense filosòfiche e mistiche.
A traduçion in ingleise do testo a l’é:
Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs.
Traduxi da-o zeneise à l’ingleise:
I antighi Greghi n’aivan un scimbolo pe-o zero fin a-o periodo ellenistico, e deuviavan un scistema de trei scimboli pe representâ i numeri: un pe-e unitæ, un pe-e dëxeñe e l’urtimo pe-e çentanæa.
A traduçion in ingleise do testo a l’é:
The ancient Greeks lacked a symbol for zero until the Hellenistic period, and they used three separate sets of symbols as digits: one set for the units place, one for the tens place, and one for the hundreds.
Ti peu tradue sto testo in ingleise?
O seu ritmo de divixon longa o l’ea o mæximo e l’algoritmo de reixe quaddrâ giffra pe giffra, deuviou popolarmente fin a-o secolo XX, o l’ea conosciuo a-o mæximo Archimede (ch’o porriæ fiña aveilo inventou).
A traduçion in ingleise do testo a l’é:
Their long division algorithm was the same, and the digit-by-digit square root algorithm, popularly used as recently as the 20th century, was known to Archimedes (who may have invented it).
Ti peu tradue sto testo in ingleise?
I cineixi antighi aivan di studdi avansæ in sce l’artimetica che remontan a-a dinastia Shang e che van avanti fin à quella Tang, da di numeri di fase fin à l’algebra avansâ.
A traduçion in ingleise do testo a l’é:
The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra.
Comm’à l’é a traduçion ingleise de sto testo?
Pe-e çentanæa an deuviou i scimboli de unitæ, e coscì avanti.
A traduçion in ingleise do testo a l’é:
For the hundreds place, they then reused the symbols for the units place, and so on.
Traduxi in ingleise:
I antighi cineixi an descoverto, compreiso e applicou pe-i primmi i numeri negativi de unna forma scignificativi.
A traduçion in ingleise do testo a l’é:
The ancient Chinese were the first to meaningfully discover, understand, and apply negative numbers.
Ti peu tradue sto testo in ingleise?
O seu contemporaneo, o vesco sciriaco Severus Sebokht (650 d.C.), o l’aiva dito: «I indien an un metodo de carcolo che nisciuña poula a saiæ abasta pe lödâlo».
A traduçion in ingleise do testo a l’é:
His contemporary, the Syriac bishop Severus Sebokht (650 AD) said, "Indians possess a method of calculation that no word can praise enough.
Traduxi sto testo da-o zeneise à l’ingleise:
I arabi ascì aivan impreiso sto neuve metodo, e gh’an dæto o nomme de «hesab».
A traduçion in ingleise do testo a l’é:
The Arabs also learned this new method and called it hesab.
Traduxi sto testo da-o zeneise à l’ingleise:
O sviluppo de l’algebra into mondo islamico de l’etæ de mezo, e inte l’Euröpa da Renascion ascì, o l’é stæto unna conseguensa de l’enorme semplificaçion do carcolo pe mezo da nottaçion à base dexe.
A traduçion in ingleise do testo a l’é:
The flourishing of algebra in the medieval Islamic world, and also in Renaissance Europe, was an outgrowth of the enormous simplification of computation through decimal notation.
Quæ a l’é a traduçion ingleise de sto testo?
E eprescioin aritmetiche dev’ësan valuæ segondo a sequensa d’operaçion che se veu effettuâ.
A traduçion in ingleise do testo a l’é:
Arithmetic expressions must be evaluated according to the intended sequence of operations.