Notes
Minkombo
Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1]
Euclid , N'wa tinhlayo wa muGriki, Lembe-xidzana ra vu3 BC, Hikuya hi Raphael .[1]
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8]
Dyondzo-Tinhlayo (Mathematics) (Kusuka exiGrikini μάθημα máthēma, “Vutivi, kuhlahluva, kudyondza”) idyondzo ya tinhloko-mhaka to fana ni Ntsengo (tinomboro),[2] vuhleri,[3] vundhawu,[2] na macincele.[4][5][6] kuni kuhambanahabana ka mavonele exikarhi kavan'wa-Tinhlayo na van'wa-Filisofi mayelana na nhlamuselo ya Dyondzo-Tinhlayo.[7][8]
Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind.
Dyondzo-Tinhlayo iyankoka ngopfu eswiyengeni swamitirho, kuhlanganisa na ntivo-ntumbuluko, enjhiniyeringi, mirhi yavuongori, swatima kuhlanganisa na ntivo-vutomi.
There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.[17]
Kuhava ndzilakano lowuvonakalaka exikarhi ka ntivo-tinhlayo lowu tengeke na ntivo-tinhlayo lowu tirhisiwaka.[17]
The history of mathematics can be seen as an ever-increasing series of abstractions.
Matimu ya dyondzo-tinhlayo yingahavoniwa tani hi tinhlamuselo tamavonele.
The first abstraction, which is shared by many animals,[18] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.
Mavonele yosungula mafana namavonelo yaswiharhi,[18] kungava kuri tinomboro: kutwisisa leswaku maapula mambirhi maringana hintsengo namaswira mambirhi.
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, years.[19]
Ehenhleni kokota ku hlaya swilo leswivonakaka, vanhu vakhale avaswikota kuhlaya naleswi vangaswivoniki, kufana na nkarhi, masiku, tinguva namalembe.[19]
Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[20] The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time.
Kuhava vumboni bya dyondzo-tinhlayo kufikela eka lembe ra 3000 BC, loko va aki vaBabilona na va aki va Gibhita vasungula to tirhisa aritimatiki (Nhlayo-Vunyingi), aljebra (Nhlayo-vuringanisi) na Jiyometiri (Nhlayo-Vuaki) leswaku vahlengeleta xibhalo, kuhlaya mali, naku aka, kuhlanganisa na ntivo-tinyeleti.[20] The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time.
Mathematics
Dyondzo-Tinhlayo
The invention of the wheel revolutionized trade and war.
Kutumbuluxiwa ka vilwa ku tise ku cinca loku kulu eka mahanyelo na vutomi bya vanhu.
It did not take long to discover that wheeled wagons could be used to carry heavy loads. Fast (rotary) potters' wheels enabled early mass production of pottery.
Aswitekanga nkarhi kutsumbula leswaku vilwa ringa pfuna ku endla golonyi leyinga tithisiwaka kurhwala swilo leswitikaka na kulwa tinyimpi.
But it was the use of the wheel as a transformer of energy (through water wheels, windmills, and even treadmills) that revolutionized the application of nonhuman power sources.
Thlandla kambirhi vilwa risungule kutirhisiwa kuphehla matimba kusuka eka matimba ya mati kuya eka matimba ya moya.
Man's technological ascent began in earnest in what is known as the Neolithic period ("New stone age").
Thekinoloji yavanhu yisungule kuhluvuka no antswa swoghasi eka malembe yohetelela yakhale kuta haleno ka nguva leyitolovelekeke (Ano Domini).
The invention of polished stone axes was a major advance that allowed forest clearance on a large scale to create farms.
Kutirhisiwa ka mathulusi yamaribye lamachukuchuweke, swipfune vanhu leswaku vaendla mathulusi lama lotiweke kahle leswaku makota kutsema kahle.
Agriculture fed larger populations, and the transition to sedentism allowed simultaneously raising more children, as infants no longer needed to be carried, as nomadic ones must.
Swihloka swamaribye leswi chukuchiweke swi endle leswaku vanhu vakota to tsema misinya leyikulu no endla swirhapa swo rima. Vurimi byi cince mahanyele no antswisa vutomi bya vanhu swonghasi.
Additionally, children could contribute labor to the raising of crops more readily than they could to the hunter-gatherer economy.[32][33]
Vurimi byi endle swikoteka to hlengeleta vanhu endzawini leyitsonga naswona vakota ku tihanyisa hiswakudya leswi vaswirimaka.[32][33]
Metal tools
Mathulisi yansimbhi
Continuing improvements led to the furnace and bellows and provided the ability to smelt and forge native metals (naturally occurring in relatively pure form).[36] Gold, copper, silver, and lead, were such early metals. The advantages of copper tools over stone, bone, and wooden tools were quickly apparent to early humans, and native copper was probably used from near the beginning of Neolithic times (about 8000 BC).[37] Native copper does not naturally occur in large amounts, but copper ores are quite common and some of them produce metal easily when burned in wood or charcoal fires. Eventually, the working of metals led to the discovery of alloys such as bronze and brass (about 4000 BC).
Kuantswisiwa kaxihiso, swi tswale vutshila byo tirha hitinsimbhi.[36] Nsuku, Koporo, nasiliva itinsimbhi leti vatihiseleke leswaku va endla mathulusi lamatiyeke no karhiha swinene.
Energy and transport
Matimba yotirha na Vutleketli
The wheel was invented circa 4000 BC.
Vilwa ritumbuluxiwe kwalomu ka lembe ra 4000 BC.
Innovations continued through the Middle Ages with innovations such as silk, the horse collar and horseshoes in the first few hundred years after the fall of the Roman Empire.
Thekinoloji yamanhuva lawa yihluvuke swonghasi loko hi ringanisa na tithekinoloji ta vanhu vakhale.
Medieval technology saw the use of simple machines (such as the lever, the screw, and the pulley) being combined to form more complicated tools, such as the wheelbarrow, windmills and clocks.
Kutumbuluxiwa ka swilo leswi fanaka na bandhi ra hanci, swifambo swa timbongolo naswin'wana swi antswise ndlela yotleketla vanhu na mpahla.
The Renaissance brought forth many of these innovations, including the printing press (which facilitated the greater communication of knowledge), and technology became increasingly associated with science, beginning a cycle of mutual advancement.
Kutumbuluxiwa ka swipirhi, swipanera, mabharha yo susumeta na tiwachi naswona swi antswise vutomi na mahanyele.
The advancements in technology in this era allowed a more steady supply of food, followed by the wider availability of consumer goods.
Nhluvuko wa thekinoloji wu endla leswaku swakudya na swa mabindzi swi olova ku tleketliwa no xavisiwa hi kuolova.
The automobile revolutionized personal transportation.
Golonyi yosungula yi antswisa ndlela yamaendzo.
Starting in the United Kingdom in the 18th century, the Industrial Revolution was a period of great technological discovery, particularly in the areas of agriculture, manufacturing, mining, metallurgy and transport, driven by the discovery of steam power.
Kusukela hi lembe-xidzana ra 18, kupfuriwa katinkomponi kupfune no hlohlotela kuantswisiwa ka tithekinoloji to tala, ngopfungopfu eka vurimi, vuaki, timayini, swiceriwa na vutleketli.
Technology took another step in a second industrial revolution with the harnessing of electricity to create such innovations as the electric motor, light bulb and countless others.
Thekinoloji yitlele yi antswisiwa hiku tsumburiwa ka kuphehla gezi leswaku kuvumbiwa motoro, malambhu yagezi naswina swohambana-hambana.
Scientific advancement and the discovery of new concepts later allowed for powered flight, and advancements in medicine, chemistry, physics and engineering. The rise in technology has led to skyscrapers and broad urban areas whose inhabitants rely on motors to transport them and their daily bread.
Kuhluvuka ka vutivi bya Sayensi kutise nhluvuko wa swihaha-mpfuka, vutshunguri, tikhemikhali kuhlanganisa na vunjiniyeri. nhluvuko wa thekinoloji wu tise miako yo leha leswi endleke leswaku vanhu vakuma tindzawu to tshama.
Communication was also greatly improved with the invention of the telegraph, telephone, radio and television.
Tindlela to vulaula namabulo swi antswisiwe ngopfu hi kufika ka thelegrafi, riqingo, xiyanimoya na thelevixini.
The late 19th and early 20th centuries saw a revolution in transportation with the invention of the airplane and automobile.
Lembe-xidzana ra vu 19 nakusungula ka ravu 20, kutsumburiwe tindlela to antswisa vutleketli hi kutirhisa swihaha-mphfuka na timovha.
See also
Thlela uvona swin'wana
References
Minkombo ya tluka
A steam turbine with the case opened.
Mphehlo wagezi hikutirhisa njhini ya ripomelo rohisa.
Most electricity is produced by thermal power stations with turbines like this one. Electricity consumption and living standards are highly correlated.[1] Electrification was voted the most important engineering achievement of the 20th century.[2]
Nkavelo wagezi wufambisana ngopfu na kuhluvuka ka mahanyele ya vanhu.[1] Mphehlo wagezi wu hlawuriwe tanihi xihluvukisi lexihlawulekeke eka lembexidzana ravukhume-mbirhi.[2]
Technology ("science of craft", from Greek τέχνη, techne, "art, skill, cunning of hand"; and -λογία, -logia[3]) is the collection of techniques, skills, methods and processes used in the production of goods or services or in the accomplishment of objectives, such as scientific investigation. Technology can be the knowledge of techniques, processes, etc. or it can be embedded in machines, computers, devices and factories, which can be operated by individuals without detailed knowledge of the workings of such things.
Thekinoloji ("Ntivovuthlarhi hita kuvumba", risuka eka viti ra Xigriki τέχνη, techne, "Vupfapfarhuti kumbe Vutshila"; kuhlanganisa na -λογία, -logia[3]) i nhlengelo wa vutshila, vuswikoti na maendlele yo tumbuluxa switirhisiwa kumbe vukorhokeri kumbe kuhetisisa vukambisisi bya Sayensi. Thekinoloji yinga thlela yi hlamuseriwa tanihi vutivi bya maendlelo ya mintirho.
The human species' use of technology began with the conversion of natural resources into simple tools.
Kutirhisiwa ka thekinoloji kusungule hi kutumbuluxa switirhisiwa swo tirha hiswona kusukela eka mbango.
The prehistoric discovery of how to control fire and the later Neolithic Revolution increased the available sources of food and the invention of the wheel helped humans to travel in and control their environment.
Kusukela eku dyondzeni tindlela to tirhisa ndzilo, kurima na tindlela to vevukisa maendzo hikutirhisa vilwa.
Developments in historic times, including the printing press, the telephone, and the Internet, have lessened physical barriers to communication and allowed humans to interact freely on a global scale.
Kuhluvuka ka manguva lawa kuhlanganisa kuganglisa ka tibuku, tinqingo na inthaneti, swi vevukise tindlela to vulavurisana namabulu.
The steady progress of military technology has brought weapons of ever-increasing destructive power, from clubs to nuclear weapons.
Kuhluvuka ka malwelo yatinyipi, namathlarhi switise kuonha lokukulu lokuvangeriwaka hi mathlarhi yanyutliya.
Technology has many effects. It has helped develop more advanced economies (including today's global economy) and has allowed the rise of a leisure class.
Thekinoloji yithlele yupfuna kuhluvukisa tamabindzu yamisava naku kurisa rifuwo.
Many technological processes produce unwanted by-products, known as pollution, and deplete natural resources, to the detriment of Earth's environment. Various implementations of technology influence the values of a society and new technology often raises new ethical questions. Examples include the rise of the notion of efficiency in terms of human productivity, a term originally applied only to machines, and the challenge of traditional norms.
Hambiswiritano swin'wana switandzhaku swo biha naswona leswi onhaka mbangu.
Medieval and modern history (300 AD – present)
Mangula lawa: 300 AD – Kufika namunthla
Paleolithic (2.5 million YA – 10,000 BC)
Ekusunguleni: 2.5 miliyoni – 10,000 BC
The use of tools by early humans was partly a process of discovery and of evolution. Early humans evolved from a species of foraging hominids which were already bipedal,[21] with a brain mass approximately one third of modern humans.[22] Tool use remained relatively unchanged for most of early human history.
Vanhu vakhale vatidyondzise Vutivi byovumba mathulusi yo tirha hiwona, katsongo katsongo hikuya hi swilaveko swavutomi.
Approximately 50,000 years ago, the use of tools and complex set of behaviors emerged, believed by many archaeologists to be connected to the emergence of fully modern language.[23]
Kutshembiwa leswaku kuvumba ririmi na mbalavuriswano hi yona thekinoloji yosungula.[23]
Stone tools
Mathulusi ya maribye
Hand axes from the Acheulian period
Xihloka xosungula
Hominids started using primitive stone tools millions of years ago. The earliest stone tools were little more than a fractured rock, but approximately 40,000 years ago, pressure flaking provided a way to make much finer work.
Vanhu vakhale vasungule kulota maribye leswaku vakota kuvumba mathulusi yofana na bewula, swikomu na mathlarhi yohlota. Kwalomu ka malembe ya 40,000 lamahundzeke, vanhu vasungule malotele yo vevuka leswaku vavumba mathulusi yo antswa.
Fire
Ndzilo