Labarin Lissafi

-2700

Abacus

-387

Plato

-300

Euclid

appendices

bayanin kula

nassoshi


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3000 BCE - 2023

Labarin Lissafi



Tarihin lissafi yana magana ne game da asalin binciken da aka samu a cikin lissafi da hanyoyin lissafi da bayanin abubuwan da suka gabata.Kafin zamani na zamani da kuma yaduwar ilimi a duniya, rubutattun misalan sabbin ci gaban ilmin lissafi sun fito fili ne kawai a wasu yankuna.Daga 3000 KZ, jihohin Mesofotamiya na Sumer, Akkad da Assuriya, waɗandaMasar ta dā suka biyo baya da kuma jihar Ebla ta Levantine suka fara amfani da lissafi, algebra da geometry don dalilai na haraji, kasuwanci, kasuwanci da kuma a cikin alamu a yanayi, filin ilmin taurari da yin rikodin lokaci da tsara kalanda.Rubutun lissafin farko da ake samu sun fito daga Mesopotamiya da Masar – Plimpton 322 (Babila c. 2000 – 1900 KZ), [1] Rhind Mathematical Papyrus (Misira c. 1800 KZ) [2] da Moscow Mathematical Papyrus (Masar 90). BC).Duk waɗannan nassosi sun ambaci abin da ake kira Pythagorean triples, don haka, ta hanyar ƙididdigewa, ka'idar Pythagorean alama ita ce mafi daɗaɗɗen ci gaban ilmin lissafi da yadu bayan ilimin lissafi da lissafi.Nazarin ilimin lissafi a matsayin " horo na nuni " ya fara a karni na 6 KZ tare da Pythagoreans, waɗanda suka kirkiro kalmar "lissafi" daga tsohuwar Girkanci μάθημα (mathema), ma'ana "batun koyarwa".[3] Lissafin Girkanci ya inganta hanyoyin sosai (musamman ta hanyar gabatar da ra'ayi mai ban sha'awa da tsangwama na lissafi a cikin hujjoji) kuma ya fadada batun ilimin lissafi.[4] Ko da yake kusan ba su ba da gudummawa ga ilimin lissafi ba, Romawa na da sun yi amfani da ilimin lissafi wajen bincike, injiniyanci, injiniyanci, lissafin kuɗi, ƙirƙirar kalanda na wata da hasken rana, har ma da fasaha da fasaha.LissafinSinanci ya ba da gudummawar farko, gami da tsarin ƙimar wuri da fara amfani da lambobi mara kyau.[5] Tsarin lambobi na Hindu-Larabci da ka'idojin amfani da ayyukansa, da ake amfani da su a duk duniya a yau sun samo asali ne a cikin karni na farko na CE aIndiya kuma an watsa su zuwa yammacin duniya ta hanyar ilimin lissafi ta Musulunci ta hanyar aikin Muḥammad bin Musa al-Khwarizmi.[6] Har ila yau, ilimin lissafi na Musulunci ya inganta tare da fadada lissafin da wadannan wayewa suka sani.[7] Daidai da amma masu zaman kansu daga waɗannan hadisai sune lissafin da wayewar Maya na Mexico da Amurka ta tsakiya suka haɓaka, inda aka ba da ra'ayin sifili daidaitaccen alama a cikin lambobi na Maya.Yawancin rubutun Helenanci da na Larabci akan lissafi an fassara su zuwa Latin tun daga karni na 12 zuwa gaba, wanda ya haifar da ci gaban ilimin lissafi a Turai ta Tsakiya.Tun daga zamanin d ¯ a har zuwa tsakiyar zamanai, lokutan binciken ilmin lissafi sau da yawa yakan biyo baya bayan shekaru aru-aru.[8] Tun daga RenaissanceItaliya a cikin karni na 15, sababbin ci gaban ilmin lissafi, hulɗa tare da sababbin binciken kimiyya, an yi su a cikin ci gaba da ci gaba har zuwa yau.Wannan ya haɗa da babban aikin Ishaku Newton da Gottfried Wilhelm Leibniz a cikin haɓaka ƙididdiga marasa iyaka a cikin ƙarni na 17.
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Ziyarci Shago

Mathematics na Masar na da
Ƙungiyar ma'aunin Masar ta kamu. ©HistoryMaps
3000 BCE Jan 1 - 300 BCE

Mathematics na Masar na da

Egypt
An haɓaka ilimin lissafinƙasar Masar na dā kuma an yi amfani da su a cikin tsohuwar Masar c.3000 da c.300 KZ, daga Tsohon Mulkin Masar har zuwa kusan farkon Hellenistic Masar.Masarawa na d ¯ a sun yi amfani da tsarin lambobi don ƙidayawa da magance rubutattun matsalolin lissafi, galibi suna haɗa da ninkawa da juzu'i.Shaidar lissafin Masarawa ta iyakance ga ƙarancin adadin maɓuɓɓuka masu rai da aka rubuta akan papyrus.Daga cikin waɗannan matani an san cewa Masarawa na dā sun fahimci ra'ayoyin ilimin lissafi, kamar tantance sararin sama da ƙarar sifofi masu girma uku masu amfani ga aikin injiniyan gine-gine, da algebra, kamar hanyar matsayi na ƙarya da ma'auni.Shaidar da aka rubuta na yin amfani da lissafi ta samo asali tun aƙalla 3200 KZ tare da alamun hauren giwa da aka samu a Tomb Uj a Abydos.Waɗannan alamun suna da alama an yi amfani da su azaman alamar kayan kabari kuma wasu an rubuta su da lambobi.[18] Ana iya samun ƙarin shaidar yin amfani da tsarin lambar tushe na 10 akan Narmer Macehead wanda ke nuna hadaya na shanu 400,000, awaki 1,422,000 da fursunoni 120,000.[19] Shaidun archaeological sun nuna cewa tsarin kidayar Masar na d ¯ a ya samo asali ne a yankin kudu da hamadar Sahara.[20] Har ila yau, zane-zanen lissafi na fractal wanda ya yadu a tsakanin al'adun Afirka na kudu da hamadar Sahara suma ana samun su a cikin gine-ginen Masarawa da alamomin sararin samaniya.[20]Takaddun lissafi na farko na gaskiya kwanan wata zuwa Daular 12th (c. 1990-1800 KZ).Kundin Lissafi na Moscow, Rubutun Fata na Lissafi na Masar, Lahun Mathematical Papyri waɗanda wani yanki ne na tarin Kahun Papyri da Papyrus na Berlin 6619 duk sun kasance a wannan lokacin.Littafin Rhind Mathematical Papyrus wanda ya zo zuwa Tsakanin Tsakanin Tsaki na Biyu (a. 1650 KZ) an ce ya dogara ne akan wani tsohon rubutun lissafi daga daular 12th.[22]
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Sumerian Mathematics
Tsohon Sumer ©Anonymous
3000 BCE Jan 1 - 2000 BCE

Sumerian Mathematics

Iraq
Tsohuwar Sumeriyawa na Mesofotamiya sun ɓullo da tsari mai sarƙaƙƙiya na ilimin awo tun daga 3000 KZ.Daga shekara ta 2600 KZ zuwa gaba, Sumerians sun rubuta allunan ninkawa akan allunan yumbu kuma sun yi maganin motsa jiki na geometric da matsalolin rarraba.Farkon alamun lambobi na Babila suma sun samo asali ne tun daga wannan lokacin.[9]
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Abacus
Julius Kaisar a matsayin Yaro, Koyan Kidaya Amfani da Abacus. ©Peter Jackson
2700 BCE Jan 1 - 2300 BCE

Abacus

Mesopotamia, Iraq
Abacus (jam'i abaci ko abacuses), wanda kuma ake kira firam ɗin kirgawa, kayan aiki ne na ƙididdiga waɗanda aka yi amfani da su tun zamanin da.An yi amfani da shi a tsohuwar Gabas ta Kusa, Turai,China , da Rasha, shekaru millenni kafin ɗaukar tsarin lambobi na Hindu-Larabci.[127 <] > ainihin asalin abacus bai fito ba tukuna.Ya ƙunshi layuka na beads masu motsi, ko makamantansu, waɗanda aka ɗaure akan waya.Suna wakiltar lambobi.An saita ɗaya daga cikin lambobi biyu, kuma ana amfani da beads don yin aiki kamar ƙari, ko ma tushen murabba'i ko kubik.Abacus Sumerian ya bayyana tsakanin 2700 zuwa 2300 KZ.Ya riƙe tebur na ginshiƙai masu jere waɗanda ke iyakance jerin umarni na girman tsarin lamba na jima'i (tushe 60).[128]
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Tsohon Lissafin Babila
Tsohon Mesopotamiya ©Anonymous
2000 BCE Jan 1 - 1600 BCE

Tsohon Lissafin Babila

Babylon, Iraq
An rubuta lissafin Babila ta amfani da tsarin lamba na sexagesimal (tushe-60).[12] Daga wannan ana samun amfani da zamani na daƙiƙa 60 a cikin minti ɗaya, mintuna 60 a cikin awa ɗaya, da digiri 360 (60 × 6) a cikin da'irar, haka kuma ana amfani da daƙiƙa da mintuna na baka don nuna juzu'i. na digiri.Yana yiwuwa da sexagesimal tsarin da aka zaba domin 60 za a iya ko'ina raba 2, 3, 4, 5, 6, 10, 12, 15, 20 da kuma 30. [12] Har ila yau, sabaninMasarawa , Helenawa , da Romawa, da Mutanen Babila suna da tsarin darajar wuri, inda lambobi da aka rubuta a ginshiƙi na hagu suna wakiltar manyan ƙima, kamar a tsarin ƙima.[13] Ƙarfin tsarin ƙididdiga na Babila ya kasance a cikin cewa za a iya amfani da shi don wakiltar ɓangarorin a sauƙi kamar dukan lambobi;don haka ninka lambobi biyu masu ɗauke da juzu'i bai bambanta da ninka lambobi ba, kama da na zamani.[13] Tsarin al'ada na Babila shine mafi kyawun kowane wayewa har zuwa Renaissance, [14] da ikonsa ya ba shi damar cimma daidaiton lissafi na ban mamaki;misali, kwamfutar hannu ta Babila YBC 7289 tana ba da kimanin √2 daidai zuwa wurare biyar.[14] Babila ba su da, duk da haka, daidai da ma'aunin ƙima, don haka ƙimar wurin sau da yawa dole ne a faɗi daga mahallin.[13] A lokacin Seleucid , Babila sun ƙirƙiri alamar sifili a matsayin mai riƙe da matsayi na wofi;duk da haka an yi amfani dashi kawai don matsakaicin matsayi.[13] Wannan alamar sifili ba ta bayyana a matsayi na ƙarshe ba, don haka Babiloniyawa sun zo kusa amma ba su haɓaka tsarin ƙimar wuri na gaskiya ba.[13]Sauran batutuwan da lissafin Babila ya rufe sun haɗa da juzu'i, algebra, ma'auni da ma'auni na kubik, da lissafin lambobi na yau da kullun, da madaidaitan nau'ikan su.[15] Hakanan allunan sun haɗa da allunan ninkawa da hanyoyin magance madaidaiciyar ma'auni, ma'auni huɗu da ma'auni, babban nasara ga lokacin.[16] Allunan daga tsohuwar zamanin Babila suma sun ƙunshi sanannen sanarwa na farko na ka'idar Pythagorean.[17] Duk da haka, kamar yadda yake tare da lissafin Masar, lissafin Babila ba ya nuna rashin fahimtar bambanci tsakanin daidaitattun mafita da madaidaicin mafita, ko warware matsalar, kuma mafi mahimmanci, babu wata sanarwa mai mahimmanci na buƙatar hujjoji ko ka'idoji masu ma'ana.[13]Sun kuma yi amfani da wani nau'i na bincike na Fourier don ƙididdige wani ephemeris (tebur na matsayi na astronomical), wanda Otto Neugebauer ya gano a cikin 1950s.[11] Don yin lissafin motsi na sararin samaniya, Babila sun yi amfani da asali na lissafi da tsarin daidaitawa bisa ga husuma, sashen sammai da rana da taurari ke tafiya a ciki.
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Thales&#39;s Theorem
©Gabriel Nagypal
600 BCE Jan 1

Thales's Theorem

Babylon, Iraq
An fara lissafin lissafin Girka da Thales na Miletus (c. 624-548 KZ).Ba a san shi sosai game da rayuwarsa ba, ko da yake an yarda cewa yana ɗaya daga cikin masu hikima Bakwai na Girka.A cewar Proclus, ya yi tafiya zuwa Babila daga inda ya koyi ilmin lissafi da sauran darussa, ya zo da hujjar abin da ake kira Thales' Theorem a yanzu.[23]Thales ya yi amfani da lissafi don magance matsaloli kamar ƙididdige tsayin dala da nisan jiragen ruwa daga bakin teku.An ba shi lada tare da farkon amfani da tunani mai raɗaɗi da aka yi amfani da shi akan ilimin lissafi, ta hanyar samun lambobi huɗu zuwa Thales' Theorem.A sakamakon haka, an yaba shi a matsayin masanin lissafi na gaskiya na farko kuma sanannen mutum na farko wanda aka danganta binciken ilimin lissafi.[30]
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Pythagoras
Cikakken bayani na Pythagoras tare da kwamfutar hannu na rabo, daga Makarantar Athens ta Raphael.Fadar Vatican, Rome, 1509. ©Raphael Santi
580 BCE Jan 1

Pythagoras

Samos, Greece
Wani adadi mai ban mamaki shine Pythagoras na Samos (kimanin 580-500 KZ), wanda da alama ya ziyarciMasar da Babila , [24] kuma a ƙarshe ya zauna a Croton, Magna Graecia, inda ya fara 'yan'uwantaka.Pythagoreans sun yi imanin cewa "duk lamba ne" kuma suna sha'awar neman alakar lissafi tsakanin lambobi da abubuwa.[25] Pythagoras da kansa an ba shi bashi don bincike da yawa daga baya, ciki har da gina daskararru biyar na yau da kullun.Kusan rabin abubuwan da ke cikin Euclid's Elements ana danganta su ga Pythagoreans, gami da gano rashin hankali, wanda aka danganta ga Hippasus (c. 530-450 KZ) da Theodorus (fl. 450 KZ).[26] Pythagoreans ne suka kirkiro kalmar “lissafi”, kuma da su ne aka fara nazarin ilimin lissafi don kansa.Babban masanin lissafin da ke da alaƙa da ƙungiyar, duk da haka, yana iya kasancewa Archytas (kimanin 435-360 KZ), wanda ya warware matsalar ninka cube, ya gano ma'anar jituwa, kuma mai yiwuwa ya ba da gudummawa ga kayan gani da injiniyoyi.[26] Sauran masu ilimin lissafi masu aiki a wannan lokacin, ba su da cikakkiyar alaƙa da kowace makaranta, sun haɗa da Hippocrates na Chios (c. 470-410 KZ), Theaetetus (c. 417-369 KZ), da Eudoxus (c. 408-355 KZ). .
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Gano Lambobin Rashin Hankali
Waƙar Pythagoreans Zuwa Rana Mai Tashi. ©Fyodor Bronnikov
400 BCE Jan 1

Gano Lambobin Rashin Hankali

Metapontum, Province of Matera
Tabbacin farko na wanzuwar lambobi marasa ma'ana yawanci ana danganta su ga Pythagorean (wataƙila Hippasus na Metapontum), [39] wanda mai yiwuwa ya gano su yayin gano sassan pentagram.[40] Hanyar Pythagorean na yanzu da ta yi iƙirarin cewa dole ne a sami wasu isassun ƙanana, waɗanda ba za a iya raba su ba waɗanda za su iya dacewa daidai da ɗayan waɗannan tsayin da kuma ɗayan.Hippasus, a cikin karni na 5 KZ, duk da haka, ya iya gano cewa a gaskiya babu wani ma'aunin ma'auni na gama gari, kuma tabbatar da wanzuwar irin wannan a haƙiƙa ya saba wa juna.Masana lissafi na Girka sun kira wannan rabo na girman da ba a iya misaltuwa alogos, ko maras misaltuwa.Hippasus, duk da haka, ba a yaba masa don ƙoƙarinsa ba: bisa ga wani labari, ya yi bincikensa yayin da yake cikin teku, kuma 'yan uwansa Pythagoreans suka jefa shi a cikin ruwa saboda ya samar da wani abu a cikin sararin samaniya wanda ya karyata koyarwar ... cewa duk abubuwan da ke faruwa a sararin samaniya za a iya rage su zuwa duka lambobi da adadinsu.'[41] Ko mene ne sakamakon Hippasus da kansa, bincikensa ya haifar da babbar matsala ga ilimin lissafi na Pythagorean, tun da ya wargaza tunanin cewa lamba da lissafi ba za su iya rabuwa ba - tushen ka'idarsu.
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Plato
Plato's Academy mosaic - daga Villa na T. Siminius Stephanus a Pompeii. ©Anonymous
387 BCE Jan 1

Plato

Athens, Greece
Plato yana da mahimmanci a tarihin lissafi don ƙarfafawa da jagorantar wasu.[31] Kwalejinsa ta Platonic, a Athens, ta zama cibiyar lissafin duniya a karni na 4 KZ, kuma daga wannan makarantar ne manyan malaman lissafi na zamanin, irin su Eudoxus na Cnidus, suka zo.[32] Plato kuma ya tattauna tushen ilimin lissafi, [33] ya fayyace wasu ma'anoni (misali na layi a matsayin "tsawon mara nauyi"), kuma ya sake tsara zato.[34] Hanyar nazari ana danganta ga Plato, yayin da tsarin samun Pythagorean triples yana ɗauke da sunansa.[32]
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Geometry na kasar Sin
©HistoryMaps
330 BCE Jan 1

Geometry na kasar Sin

China
Aikin da ya fi dadewa kan ilmin lissafi akasar Sin ya fito ne daga littafin Mohist canon c.330 KZ, mabiyan Mozi (470-390 KZ).Mo Jing ya bayyana bangarori daban-daban na fagage da dama da ke da alaka da kimiyyar zahiri, sannan kuma ta samar da wasu kananan ka'idojin lissafi.[77] Ya kuma bayyana ra'ayoyin kewaye, diamita, radius, da girma.[78]
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Tsarin Decimal na kasar Sin
©Anonymous
305 BCE Jan 1

Tsarin Decimal na kasar Sin

Hunan, China
Tsinghua Bamboo Slips, wanda ke dauke da tebur na farko da aka sani da yawa (ko da yake Babila na da suna da tushe na 60), an buga shi a kusa da 305 KZ kuma watakila shine mafi tsufa na rubutun lissafi nakasar Sin .[68] Abin lura na musamman shine amfani da mathematics na Sinanci na tsarin ƙididdiga na ƙima, abin da ake kira "lambobin sanda" a cikin abin da aka yi amfani da sifofi daban-daban don lambobi tsakanin 1 zuwa 10, da ƙarin sifofi don iko na goma.[69] Don haka, za a rubuta lambar 123 ta amfani da alamar "1", sannan tambarin "100", sannan alamar "2" ta bi ta alamar "10", sannan alamar "" 3".Wannan shi ne tsarin lambobi mafi ci gaba a duniya a lokacin, da alama ana amfani da shi ƙarni da yawa kafin zamanin gama gari da kuma tun kafin haɓaka tsarin lambobinIndiya .[76] Ƙididdiga na sanda sun ba da izinin wakilcin lambobi kamar yadda ake so kuma sun ba da izinin yin lissafi akan kwanon suan, ko Abacus na kasar Sin.Ana kyautata zaton cewa jami'ai sun yi amfani da tebur mai ninkaya wajen kididdige fadin kasa, yawan amfanin gona da kuma adadin harajin da ake bin su.[68]
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Lissafin Hellenistic na Girka
©Aleksandr Svedomskiy
300 BCE Jan 1

Lissafin Hellenistic na Girka

Greece
Zamanin Hellenistic ya fara ne a ƙarshen karni na 4 KZ, bayan da Alexander the Great ya mamaye Gabashin Bahar Rum,Masar , Mesopotamiya , Tudun Iran , Asiya ta Tsakiya, da wasu sassanIndiya , wanda ya haifar da yaduwar harshe da al'adun Girka a cikin waɗannan yankuna. .Hellenanci ya zama harshen guraben karatu a ko'ina cikin duniyar Hellenistic, kuma lissafi na zamanin gargajiya ya haɗu da lissafin Masarawa da na Babila don haifar da ilimin Hellenistic.[27]Lissafi na Girkanci da falaki sun kai matsayinsa a lokacin Hellenistic da farkon zamanin Roman, kuma yawancin ayyukan da marubuta irin su Euclid (fl. 300 KZ), Archimedes (c. 287-212 KZ), Apollonius (c. 240-190) ke wakilta. KZ), Hipparchus (kimanin 190-120 KZ), da Ptolemy (kimanin 100-170 AZ) sun kasance matakin ci gaba sosai kuma da wuya ya ƙware a wajen ƙaramin da'ira.Cibiyoyin ilmantarwa da dama sun bayyana a zamanin Hellenistic, wanda mafi mahimmanci a cikinsu shine Mouseion a Alexandria, Masar, wanda ya jawo hankalin masana daga ko'ina cikin duniya Hellenistic (mafi yawan Girkanci, amma kuma Masarawa, Bayahude, Farisa, da sauransu).[28] Ko da yake 'yan kaɗan ne, masu lissafin Hellenistic sun yi magana da juna sosai;bugu ya ƙunshi wucewa da kwafi aikin wani a tsakanin abokan aiki.[29]
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Euclid
Cikakken ra'ayin Raphael na Euclid, yana koyar da ɗalibai a Makarantar Athens (1509-1511) ©Raffaello Santi
300 BCE Jan 1

Euclid

Alexandria, Egypt
A cikin karni na 3 KZ, cibiyar farko ta ilimin lissafi da bincike ita ce Musaeum na Alexandria.[36] A can ne Euclid (a shekara ta 300 KZ) ya koyar, kuma ya rubuta abubuwan da ake kira Elements, wanda aka yi la'akari da shi mafi nasara kuma mafi tasiri a kowane lokaci.[35]An yi la'akari da "mahaifin ilmin lissafi", Euclid ya fi shahara da littafin Elements, wanda ya kafa tushen ilimin lissafi wanda ya mamaye filin har zuwa farkon karni na 19.Tsarinsa, wanda a yanzu ake kira Euclidean geometry, ya ƙunshi sababbin sababbin abubuwa a hade tare da haɗin ra'ayoyin daga masana lissafin Girka na farko, ciki har da Eudoxus na Cnidus, Hippocrates na Chios, Thales da Theaetetus.Tare da Archimedes da Apollonius na Perga, Euclid gabaɗaya ana ɗaukarsa a cikin manyan masanan lissafi na zamanin da, kuma ɗaya daga cikin mafi tasiri a tarihin lissafi.Abubuwan da aka gabatar sun gabatar da matsananciyar lissafi ta hanyar axiomatic kuma shine farkon misali na sigar da har yanzu ake amfani da ita a lissafin lissafi a yau, na ma'anar, axiom, theorem, da hujja.Kodayake yawancin abubuwan da ke cikin abubuwan an riga an san su, Euclid ya tsara su zuwa tsari guda ɗaya, madaidaicin ma'ana.[37] Baya ga sanannun ka'idojin Euclidean Geometry, Abubuwan da ake nufi da su azaman littafin gabatarwa ga duk abubuwan da suka shafi ilmin lissafi na lokacin, kamar ka'idar lamba, algebra da ƙwaƙƙwaran geometry, [37] gami da tabbacin cewa tushen murabba'in biyu. rashin hankali ne kuma akwai manyan lambobi marasa iyaka.Euclid ya kuma yi rubuce-rubuce da yawa akan wasu batutuwa, kamar su sassan zane-zane, na'urorin gani, spherical geometry, da makanikai, amma rabin rubuce-rubucensa ne kawai suka tsira.[38]Algorithm na Euclidean yana ɗaya daga cikin tsoffin algorithms a cikin amfani gama gari.[93] Ya bayyana a cikin Euclid's Elements (c. 300 KZ), musamman a cikin Littafi na 7 (Shawarwari 1-2) da Littafi na 10 (Shari'a 2-3).A cikin littafi na 7, an tsara algorithm don lamba, yayin da a cikin Littafi na 10, an tsara shi don tsayin sassan layi.Shekaru da yawa bayan haka, Euclid's algorithm an gano kansa da kansa a Indiya da China, [94] da farko don warware ma'auni na Diophantine waɗanda suka taso a ilimin taurari da yin sahihan kalanda.
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Archimedes
©Anonymous
287 BCE Jan 1

Archimedes

Syracuse, Free municipal conso
Archimedes na Syracuse ana ɗaukarsa a matsayin ɗaya daga cikin manyan masana kimiyya a zamanin da.An yi la'akari da babban masanin lissafi na tsohon tarihin, kuma ɗaya daga cikin mafi girma a kowane lokaci, [42] Archimedes ya yi tsammanin lissafin zamani da bincike ta hanyar amfani da ra'ayi na ƙananan ƙananan da kuma hanyar gajiya don samowa da kuma tabbatar da tsattsauran ra'ayi na ka'idojin geometrical.[43] Waɗannan sun haɗa da yanki na da'ira, saman fili da ƙarar wani yanki, yankin ellipse, wurin da ke ƙarƙashin parabola, juzu'i na ɓangaren juyi na juyi, ƙarar sashi na wani yanki. hyperboloid na juyin juya hali, da kuma yankin karkace.[44]Sauran nasarorin ilimin lissafi na Archimedes sun haɗa da samun kimar pi, ma'ana da binciken karkatar da Archimedean, da ƙirƙira tsarin yin amfani da juzu'i don bayyana adadi masu yawa.Har ila yau, ya kasance ɗaya daga cikin na farko da ya fara amfani da lissafi ga abubuwan mamaki na jiki, yana aiki akan statics da hydrostatics.Nasarorin da Archimedes ya samu a wannan yanki sun haɗa da tabbacin dokar lever, [45] da yaɗuwar amfani da manufar cibiyar nauyi, [46] da kuma ƙaddamar da dokar buoyancy ko ƙa'idar Archimedes.Archimedes ya mutu a lokacin daaka kewaye Syracuse , lokacin da wani sojan Roma ya kashe shi duk da umarnin cewa kada a cutar da shi.
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Misalin Apollonius
©Domenico Fetti
262 BCE Jan 1

Misalin Apollonius

Aksu/Antalya, Türkiye
Afollonius na Perga (c. 262-190 BCE ya yi sanadiyar cigaba da nazarin sassan defic ta hanyar bambancin jirgin ruwan na biyu da ke sare mazugi biyu.[47] Ya kuma kirkiro kalmomin da ake amfani da su a yau don sassan conic, wato parabola ("wuri kusa" ko "kwatanta"), "ellipse" ("rashi"), da "hyperbola" ("jifa bayan").[48] ​​Ayyukansa na Conics yana ɗaya daga cikin sanannun kuma adana ayyukan lissafi tun zamanin da, kuma a cikinsa ya samo jigogi da yawa game da sassan conic waɗanda za su tabbatar da kima ga masana lissafi na baya da taurari masu nazarin motsi na duniya, kamar Isaac Newton.[49] Duk da yake Apollonius ko wani masanin lissafi na Girkanci ba su yi tsalle don daidaita ilimin lissafi ba, maganin Apollonius na masu lankwasa yana ta wasu hanyoyi kama da jiyya na zamani, kuma wasu daga cikin ayyukansa suna tsammanin haɓakar ilimin lissafi ta Descartes wasu 1800. bayan shekaru.[50]
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Babi tara akan fasahar Lissafi
©Luo Genxing
200 BCE Jan 1

Babi tara akan fasahar Lissafi

China
A shekara ta 212 KZ, Sarkin Qin Shi Huang ya ba da umarnin a ƙone duk littattafan da ke daular Qin banda waɗanda aka ba da izini a hukumance.Ba a yi biyayya ga wannan doka a duk duniya ba, amma sakamakon wannan tsari ba a san komai ba game da tsohuwar lissafinkasar Sin kafin wannan zamani.Bayan littafin kona 212 KZ, daular Han (202 KZ-220 CE) ta samar da ayyukan ilimin lissafi wanda mai yiwuwa ya fadada akan ayyukan da suka ɓace.Bayan littafin kona 212 KZ, daular Han (202 KZ-220 CE) ta samar da ayyukan ilimin lissafi wanda mai yiwuwa ya fadada akan ayyukan da suka ɓace.Mafi mahimmancin waɗannan su ne Babi Tara akan fasahar lissafi, cikakken lakabin wanda ya bayyana a shekara ta 179 CE, amma ya kasance a wani ɓangare a ƙarƙashin wasu lakabi a baya.Ya ƙunshi matsalolin kalmomi 246 da suka shafi aikin noma, kasuwanci, aikin lissafin lissafi zuwa tsayin tsayin adadi da ma'auni na hasumiya na pagoda na kasar Sin, injiniyanci, bincike, kuma ya haɗa da kayan da ke kan kusurwar dama.[79] Ya haifar da hujjar lissafi don ka'idar Pythagorean, [81] da tsarin lissafi don kawar da Gaussian.[80] Har ila yau, rubutun ya ba da kimar π, [79] wanda masana lissafin kasar Sin tun asali sun kai kimanin 3 har sai Liu Xin (d. 23 CE) ya ba da adadi na 3.1457 kuma daga baya Zhang Heng (78-139) ya kiyasta pi kamar 3.1724, [ 82] da 3.162 ta hanyar ɗaukar tushen murabba'in 10. [83.]Lambobi mara kyau sun bayyana a karon farko a cikin tarihi a cikin Babi Tara akan Fasahar Lissafi amma suna iya ƙunsar tsofaffin abubuwa da yawa.[84] Masanin lissafi Liu Hui (c. karni na 3) ya kafa dokoki don ƙari da ragi na lambobi mara kyau.
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Hipparchus &amp; Trigonometry
&quot;Hipparchus a cikin dakin kallo na Alexandria.&quot;Ridpath tarihin duniya.1894. ©John Clark Ridpath
190 BCE Jan 1

Hipparchus & Trigonometry

İznik, Bursa, Türkiye
Ƙarni na 3 KZ ana ɗaukarsa gabaɗaya a matsayin "Golden Age" na lissafin Girkanci, tare da ci gaba a cikin tsantsar ilimin lissafi daga yanzu cikin raguwar dangi.[51] Duk da haka, a cikin ƙarni da suka biyo baya an sami ci gaba mai mahimmanci a cikin ilimin lissafi, musamman trigonometry, musamman don magance bukatun masanan taurari.[51] Hipparchus na Nicaea (c. 190-120 KZ) ana la'akari da shi wanda ya kafa trigonometry don harhada tebirin trigonometric na farko da aka sani, kuma a gare shi ya kasance saboda tsarin amfani da da'irar digiri 360.[52]
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Almagest na Ptolemy
©Anonymous
100 Jan 1

Almagest na Ptolemy

Alexandria, Egypt
A cikin karni na 2 AD, masanin falaki na Greco-Masari Ptolemy (daga Iskandariyya, Masar) ya gina dalla-dalla dalla-dalla allunan trigonometric (tebur na mawaƙa na Ptolemy) a cikin Littafi 1, babi na 11 na Almagest.Ptolemy ya yi amfani da tsayin igiya don ayyana ayyukan trigonometric nasa, ƙaramin bambanci daga al'adar sine da muke amfani da ita a yau.Ƙarnuka sun shuɗe kafin a samar da ƙarin cikakkun bayanai, kuma littafin Ptolemy ya kasance ana amfani da shi don yin lissafin trigonometric a ilmin taurari a cikin shekaru 1200 masu zuwa a cikin Byzantine na da, Musulunci, da kuma, daga baya, Yammacin Turai.Hakanan ana ba da Ptolemy tare da ka'idar Ptolemy don samun adadin trigonometric, kuma mafi ingancin ƙimar π a wajen China har zuwa lokacin tsakiyar zamanai, 3.1416.[63]
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Ka&#39;idar Rago ta Sinanci
©张文新
200 Jan 1

Ka'idar Rago ta Sinanci

China
A cikin ilmin lissafi, ka'idar da ta rage ta kasar Sin ta bayyana cewa, idan mutum ya san ragowar adadin adadin Euclidean na lamba n da adadi da yawa, to za a iya tantance ragowar rabon n ta nau'in wadannan lambobi, bisa sharadin cewa. Masu rarrabuwar kawuna biyu ne (babu masu rarraba guda biyu da ke raba ma'auni guda ɗaya banda 1).Sanannen bayanin da aka fi sani da ka'idar ita ce ta masanin lissafi na kasar Sin Sun-tzu a cikin Sun-tzu Suan-ching a karni na 3 AZ.
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Diophantine Analysis
©Tom Lovell
200 Jan 1

Diophantine Analysis

Alexandria, Egypt
Bayan wani lokaci na tsayawa bayan Ptolemy, lokacin tsakanin 250 zuwa 350 CE wani lokaci ana kiransa "Zaman Azurfa" na lissafin Girkanci.[53] A wannan lokacin, Diophantus ya sami ci gaba mai mahimmanci a cikin algebra, musamman bincike mara iyaka, wanda kuma aka sani da "Diophantine analysis".[54] Nazarin ma'auni na Diophantine da ƙididdigar Diophantine wani yanki ne mai mahimmanci na bincike har yau.Babban aikinsa shi ne Arithmetica, tarin matsalolin algebra 150 da ke magance ainihin mafita don ƙaddara da ƙima.[55] Arithmetica ya yi tasiri sosai a kan masana lissafi daga baya, irin su Pierre de Fermat, wanda ya isa sanannen Theorem ɗinsa na ƙarshe bayan ya yi ƙoƙari ya faɗi wata matsala da ya karanta a cikin Arithmetica (wato raba murabba'i zuwa murabba'i biyu).[56] Diophantus kuma ya sami ci gaba mai mahimmanci a cikin ƙididdiga, Arithmetica shine farkon misalin algebra da alamar aiki tare.[55]
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Labarin Zero
©HistoryMaps
224 Jan 1

Labarin Zero

India
LambobinMasarawa na dā sun kasance na tushe 10. Sun yi amfani da hiroglyphs don lambobi kuma ba su da matsayi.A tsakiyar karni na 2 KZ, lissafin Babila yana da tsarin ƙididdige ƙididdiga na tushe guda 60.Rashin ƙimar matsayi (ko sifili) an nuna shi ta sarari tsakanin lambobi na jima'i.Kalandar Dogon Ƙididdiga ta Mesoamerican da aka haɓaka a kudu-ta-tsakiyar Mexico da Amurka ta tsakiya ta buƙaci amfani da sifili azaman mai riƙewa a cikin tsarin ƙididdigar matsayi na vigesimal (tushe-20).Tunanin sifili azaman rubutaccen lambobi a cikin ƙimar wurin ƙima an haɓaka shi a Indiya.[65] Ana amfani da alamar sifili, babban digo mai yuwuwa ita ce mafarin alamar tambarin da har yanzu take yanzu, ana amfani da ita a ko'ina cikin rubutun Bakhshali, jagorar aiki mai amfani kan lissafi na 'yan kasuwa.[66] A cikin 2017, samfurori guda uku daga rubutun an nuna su ta hanyar radiocarbon da suka fito daga ƙarni uku daban-daban: daga CE 224-383, CE 680-779, da CE 885-993, yana mai da ita Kudancin Asiya mafi tsufa rikodin amfani da sifili. alama.Ba a san yadda aka tattara guntuwar bawon birch daga ƙarni daban-daban waɗanda suka kafa rubutun tare.[67] Dokokin da ke kula da amfani da sifili sun bayyana a cikin Brahmasputha Siddhanta na Brahmagupta (ƙarni na 7), wanda ya bayyana jimlar sifili da kanta a matsayin sifili, kuma ba daidai ba ta rarraba ta sifili kamar:Lamba mai kyau ko mara kyau idan aka raba shi da sifili ƙaramin juzu'i ne tare da sifili azaman ƙima.Sifili da aka raba da mummunan lamba ko tabbataccen lamba ko dai sifili ne ko an bayyana shi azaman juzu'i tare da sifili azaman mai ƙididdigewa da iyakataccen adadi azaman ƙima.Sifili da aka raba da sifili ba shi da sifili.
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Hypatia
©Julius Kronberg
350 Jan 1

Hypatia

Alexandria, Egypt
Mace ta farko mai ilimin lissafi da tarihi ya rubuta ita ce Hypatia ta Alexandria (CE 350-415).Ta rubuta ayyuka da yawa akan ilimin lissafi.Saboda rikicin siyasa, al’ummar Kirista a Iskandariya sun tube ta a bainar jama’a kuma aka kashe ta.Ana ɗaukar mutuwarta wani lokaci a matsayin ƙarshen zamanin lissafin Girkanci na Alexandria, kodayake aikin ya ci gaba a Athens har wani ƙarni tare da adadi kamar Proclus, Simplicius da Eutocius.[57] Ko da yake Proclus da Simplicius sun fi masana falsafa fiye da mathematics, sharhin su akan ayyukan da suka gabata tushe ne masu mahimmanci akan lissafin Girkanci.Rufe Cibiyar Nazarin Neo-Platonic na Athens da sarki Justinian ya yi a shekara ta 529 AZ ana gudanar da shi ne a al'adance a matsayin alamar ƙarshen zamanin lissafin Girka, kodayake al'adar Girka ta ci gaba da lalacewa a cikin daular Byzantine tare da masana lissafi irin su Anthemius na Tralles da Isidore. na Miletus, gine-ginen Hagia Sophia.[58] <> Duk da haka, lissafin Byzantine ya ƙunshi galibin tafsirai, ba tare da ɗimbin hanyar ƙididdigewa ba, kuma a wannan lokacin ana samun cibiyoyin ƙirƙira lissafi a wani wuri.[59]
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505 Jan 1

Trigonometry na Indiya

Patna, Bihar, India
An fara ba da shaidar babban taron sine na zamani a cikin Surya Siddhanta (yana nuna tasirin Hellenistic mai ƙarfi) [64] , kuma an ƙara rubuta kaddarorinsa ta karni na 5 (CE) masanin lissafin Indiya da masanin falaki Aryabhata.[60] Surya Siddhanta ya yi bayanin ka’idoji don kididdige motsin taurari daban-daban da kuma wata dangane da taurari daban-daban, diamita na taurari daban-daban, da kuma kididdige kewayawar taurarin taurari daban-daban.An san rubutun don wasu sanannun tattaunawa na ɓangarorin jima'i da ayyukan trigonometric.[61]
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510 Jan 1

Tsarin Decimal na Indiya

India
A wajen shekara ta 500 AZ, Aryabhatta ya rubuta Aryabhatiya, ƙaramin ƙarami, wanda aka rubuta a cikin ayar, wanda aka yi niyya don ƙara ƙa'idodin lissafin da aka yi amfani da su a cikin ilimin taurari da kuma tantancewar lissafi.[62] Ko da yake kusan rabin abubuwan da aka shigar ba daidai ba ne, a cikin Aryabhatiya ne tsarin darajar wuri na goma ya fara bayyana.
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780 Jan 1

Muhammad ibn Musa al-Khwarizmi

Uzbekistan
A karni na 9, masanin lissafi Muḥammad ibn Mūsā al-Khwārizmī ya rubuta wani muhimmin littafi a kan lambobi na Hindu-Larabci kuma daya kan hanyoyin warware daidaito.Littafinsa On the Calculation with Hindu Numerals, wanda aka rubuta kimanin 825, tare da aikin Al-Kindi, sun taimaka wajen yada lissafin Indiya da lambobin Indiya zuwa Yamma.Kalmar Algorithm ta samo asali ne daga Latinization na sunansa, Algoritmi, da kalmar algebra daga taken ɗayan ayyukansa, Al-Kitāb al-mukhtashar fī hīsāb al-ğabr wa'l-muqābala (Littafi Mai Girma akan Lissafi ta Kammalawa da Daidaitawa).Ya ba da cikakken bayani game da maganin algebra na ma'auni huɗun tare da ingantattun tushen tushe, [87] kuma shi ne farkon wanda ya koyar da algebra a matakin farko kuma don kansa.[88] Ya kuma tattauna ainihin hanyar “raguwa” da “daidaitawa”, yana mai nuni ga jujjuya sharuddan da aka rage zuwa wancan gefen ma’auni, wato soke irin sharuddan da ke gaba dayan ma’auni.Wannan ita ce aikin da al-Khwārizmi ya siffanta shi da al-jabr.[89] Har ila yau, algebra nasa bai damu ba "da jerin matsalolin da za a warware, amma bayanin da ya fara da kalmomin farko wanda haɗin gwiwar dole ne ya ba da dukkanin samfurori masu yiwuwa don daidaitawa, wanda daga yanzu ya zama ainihin abin nazari. "Har ila yau, ya yi nazarin lissafin ƙididdiga don kansa da kuma "a cikin nau'i na nau'i, in dai ba kawai ya fito a cikin hanyar magance matsala ba, amma an kira shi musamman don ayyana matsala marar iyaka."[90]
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Abu Kamil
©Davood Diba
850 Jan 1

Abu Kamil

Egypt
Abu Kamil Shuja' bn Aslam ibn Muhammad Ibn Shuja' fitaccen masanin lissafinkasar Masar ne a lokacin Golden Age na Musulunci.Ana la'akari da shi masanin lissafi na farko don yin amfani da tsari da kuma karɓar lambobi marasa ma'ana a matsayin mafita da ƙididdiga ga ƙididdiga.[91] Fibonacci ya yi amfani da dabarun lissafinsa daga baya, don haka ya ba Abu Kamil damar wani muhimmin bangare na gabatar da algebra zuwa Turai.[92]
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Mayan Lissafi
©Louis S. Glanzman
900 Jan 1

Mayan Lissafi

Mexico
A cikin Amurkawa na Pre-Columbian, wayewar Maya da suka bunƙasa a Mexico da Amurka ta tsakiya a cikin ƙarni na farko AZ sun haɓaka al'ada ta musamman ta ilimin lissafi wanda, saboda keɓewar yanki, gabaɗaya ta kasance mai zaman kanta daga ƙwararrun ilimin Turai,Masari , da Asiya.[92] Mayan lambobi sun yi amfani da tushe na ashirin, tsarin vigesimal, maimakon tushe na goma wanda ya zama tushen tsarin decimal da yawancin al'adun zamani ke amfani da su.[92] Mayan sun yi amfani da lissafin lissafi don ƙirƙirar kalandar Maya da kuma hasashen abubuwan da suka faru a sararin samaniya a cikin mahaifarsu ta taurarin Maya.[92] Yayin da za a iya fahimtar manufar sifili a cikin ilimin lissafi na al'adu da yawa na zamani, Maya sun ƙirƙira ma'auni na alama.[92]
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Al-Karaji
©Osman Hamdi Bey
953 Jan 1

Al-Karaji

Karaj, Alborz Province, Iran
Abu Bakr Muḥammad ibn al Hasan al-Karajī masanin lissafin Farisa ne a ƙarni na 10 kuma injiniya wanda ya bunƙasa a Bagadaza.An haife shi a Karaj, wani gari kusa da Tehran.Manyan ayyukansa guda uku da suka tsira sune: Al-Badi' fi'l-hisab (Mai Al'ajabi akan lissafi), Al-Fakhri fi'l-jabr wa'l-muqabala (Mai ɗaukaka akan algebra), da Al-Kafi fi'l- hisab (Ya isa akan lissafi).Al-Karaji ya yi rubutu akan ilmin lissafi da injiniyanci.Wasu suna la'akari da shi kawai yana sake fasalin ra'ayoyin wasu (Diophantus ya rinjaye shi) amma yawancin suna ɗaukarsa a matsayin mafi asali, musamman don farkon 'yantar da algebra daga lissafin lissafi.Daga cikin malaman tarihi, aikin da ya fi yin nazari a kai shi ne littafinsa na algebra al-fakhri fi al-jabr wa al-muqabala, wanda ya rayu tun zamanin daular a cikin akalla kwafi hudu.Ayyukansa a kan algebra da polynomials sun ba da ka'idoji don ayyukan ƙididdiga don ƙarawa, ragi da ninka yawan abubuwa;ko da yake an tauye shi don raba polynomial ta hanyar monomials.
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Algebra na Sinanci
©Anonymous Chinese artist of the Song Dynasty
960 Jan 1 - 1279

Algebra na Sinanci

China
Alamar babban ruwa na lissafinkasar Sin ya faru ne a karni na 13 a cikin rabin karshen daular Song (960-1279), tare da bunkasa algebra na kasar Sin.Mafi mahimmancin rubutu daga wancan lokacin shine Madubin Maɗaukaki na Abubuwa huɗu na Zhu Shijie (1249-1314), yana ma'amala da warware ma'auni mafi girma na algebra a lokaci guda ta amfani da hanya mai kama da hanyar Horner.[] [70] The Precious Mirror Har ila yau, yana ƙunshe da zane na triangle na Pascal tare da ƙididdiga na haɓakawa na binomial ta hanyar wutar lantarki ta takwas, ko da yake duka biyu suna fitowa a cikin ayyukan Sinanci tun farkon 1100. filin sihiri da da'irar sihiri, wanda Yang Hui ya bayyana a zamanin da kuma ya kammala shi (CE 1238-1298).[71]LissafinJafananci , lissafinKoriya , da kuma lissafin Vietnamese ana kallon al'ada a matsayin wanda ya samo asali daga lissafin Sinanci kuma mallakar yankin al'adun gabashin Asiya na tushen Confucian.[72] Lissafin Koriya da Jafananci sun sami tasiri sosai daga ayyukan algebraic da aka samar a lokacin daular Song ta Sin, yayin da lissafin Vietnamese yana da bashi mai yawa ga shahararrun ayyukan daular Ming ta Sin (1368-1644).[73] Alal misali, ko da yake an rubuta litattafan lissafin Vietnamanci a cikin harshen Sinanci ko na asali na Chữ Nôm na Vietnam, dukkansu sun bi tsarin Sinanci na gabatar da tarin matsaloli tare da algorithms don warware su, sannan kuma amsoshin lambobi.[74] Ilimin lissafi a Vietnam da Koriya galibi suna da alaƙa da ƙwararrun ofishin kotuna na masana lissafi da na taurari, yayin da a Japan ya fi yawa a fagen makarantu masu zaman kansu.[75]
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Lambobin Hindu-Larabci
Malamai ©Ludwig Deutsch
974 Jan 1

Lambobin Hindu-Larabci

Toledo, Spain
Turawa sun koyi lambobin larabci kimanin karni na 10, ko da yake yaduwarsu ta kasance a hankali.Karni biyu bayan haka, a birnin Béjaïa na Aljeriya, wani masani dan kasar Italiya Fibonacci ya fara cin karo da lambobin;aikinsa yana da mahimmanci wajen sanar da su a duk faɗin Turai.Kasuwancin Turawa, littattafai, da mulkin mallaka sun taimaka wajen yaɗa yawan larabci a duniya.Lambobin sun sami amfani da su a duk duniya fiye da yadda ake yaɗuwar haruffan Latin na zamani, kuma sun zama ruwan dare a cikin tsarin rubuce-rubuce inda wasu tsarin lambobi suka kasance a baya, kamar lambobin Sinanci da Jafananci.An fara ambaton lambobi daga 1 zuwa 9 a Yamma a cikin Codex Vigilanus na 976, tarin haske na takardu na tarihi daban-daban da suka rufe wani lokaci daga zamanin da zuwa karni na 10 a Hispania.[68]
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Leonardo Fibonacci
Hoton mutumin Italiya na Medieval ©Vittore Carpaccio
1202 Jan 1

Leonardo Fibonacci

Pisa, Italy
A cikin karni na 12, malaman Turai sun yi tafiya zuwa Spain da Sicily suna neman rubutun Larabci na kimiyya, ciki har da Al-Khwārizmī's The Compendious Book on Calculation by Completion and Bancing, wanda Robert na Chester ya fassara zuwa Latin, da cikakken rubutun Euclid's Elements, wanda aka fassara a cikin daban-daban. iri na Adelard na Bath, Herman na Carinthia, da Gerard na Cremona.[95] Waɗannan da sauran sababbin hanyoyin sun haifar da sabuntawar lissafi.Leonardo na Pisa, wanda a yanzu ake kira Fibonacci, ya koyi game da lambobi na Hindu-Larabci a kan tafiya zuwa yanzu Béjaïa, Algeria tare da mahaifinsa ɗan kasuwa.(Turai har yanzu suna amfani da lambobi na Roman.) A can, ya lura da tsarin lissafi (musamman algorism) wanda saboda matsayi na lambobi na Hindu-Larabci ya fi dacewa kuma ya sauƙaƙe kasuwanci.Ba da daɗewa ba ya gane fa'idodi da yawa na tsarin Hindu-Larabci, wanda, ba kamar lambobin Roman da aka yi amfani da su a lokacin ba, ya ba da izinin ƙididdige sauƙi ta amfani da tsarin ƙimar wuri.Leonardo ya rubuta Liber Abaci a cikin 1202 (an sabunta shi a cikin 1254) yana gabatar da fasaha zuwa Turai kuma ya fara dogon lokaci na yada ta.Har ila yau, littafin ya kawo Turai abin da ake kira jerin Fibonacci (wanda aka sani ga masu ilimin lissafin Indiya na daruruwan shekaru kafin haka) [96] wanda Fibonacci ya yi amfani da shi a matsayin misali mai ban mamaki.
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Series mara iyaka
©Veloso Salgado
1350 Jan 1

Series mara iyaka

Kerala, India
Masanin ilimin lissafi na Girka Archimedes ya samar da sanannen taƙaitaccen bayani na farko na jerin marasa iyaka tare da hanyar da har yanzu ake amfani da ita a fannin lissafi a yau.Ya yi amfani da hanyar gajiyawa don ƙididdige wurin da ke ƙarƙashin baka na parabola tare da taƙaita jerin abubuwan da ba su da iyaka, kuma ya ba da cikakkiyar ƙima na π.[86] Makarantar Kerala ta ba da gudummawa da yawa ga fagagen jerin ƙididdiga marasa iyaka da ƙididdiga.
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Ka&#39;idar yiwuwa
Gerolamo Cardano ©R. Cooper
1564 Jan 1

Ka'idar yiwuwa

Europe
Ka'idar ilimin lissafi na zamani na yuwuwar ya samo asali ne a cikin ƙoƙarin yin nazarin wasanni na damar da Gerolamo Cardano yayi a karni na sha shida, da Pierre de Fermat da Blaise Pascal a karni na sha bakwai (misali "matsalar maki").[105] Christiaan Huygens ya buga littafi kan batun a cikin 1657. [106] A cikin karni na 19, abin da ake la'akari da ma'anar yuwuwar al'ada ya cika ta Pierre Laplace.[107]Da farko, ka'idar yiwuwar an fi la'akari da abubuwan da suka faru, kuma hanyoyinta sun kasance masu haɗaka.A ƙarshe, la'akari na nazari ya tilasta shigar da ci gaba da masu canji a cikin ka'idar.Wannan ya ƙare a ka'idar yuwuwar zamani, akan harsashin da Andrey Nikolaevich Kolmogorov ya kafa.Kolmogorov ya haɗu da ra'ayi na samfurin sararin samaniya, wanda Richard von Mises ya gabatar, da kuma auna ka'idar kuma ya gabatar da tsarinsa na axiom don ka'idar yiwuwar a 1933. Wannan ya zama tushen axiomatic mafi yawa wanda ba a yi jayayya ba don ka'idar yiwuwar zamani;amma, akwai wasu zaɓuɓɓuka, kamar ɗaukar iyaka maimakon ƙari mai ƙididdigewa ta Bruno de Finetti.[108]
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Logarithms
Johannes Kepler ne adam wata ©August Köhler
1614 Jan 1

Logarithms

Europe
Karni na 17 ya ga karuwar ra'ayoyin lissafi da kimiyya da ba a taba ganin irinsa ba a fadin Turai.Galileo ya lura da watannin Jupiter a kewayen wannan duniyar, ta yin amfani da na'urar hangen nesa ta Hans Lipperhey's.Tycho Brahe ya tattara bayanai masu yawa na lissafin da ke kwatanta matsayin taurari a sararin sama.Ta wurin matsayinsa na mataimakin Brahe, Johannes Kepler ya fara fallasa kuma ya yi mu'amala sosai da batun motsin duniya.Lissafin Kepler ya kasance mai sauƙi ta hanyar ƙirƙirar logarithms na zamani da John Napier da Jost Bürgi suka yi.Kepler ya yi nasara wajen samar da ka'idojin lissafi na motsin duniya.Tsarin lissafi na nazari wanda René Descartes (1596-1650) ya kirkira ya ba da damar yin ƙirƙira waɗancan ra'ayoyin a kan jadawali, a cikin daidaitawar Cartesian.
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Tsarin Gudanarwa na Cartesian
Rene Descartes ©Frans Hals
1637 Jan 1

Tsarin Gudanarwa na Cartesian

Netherlands
Kartesian yana nufin masanin lissafin Faransa kuma masanin falsafa René Descartes, wanda ya buga wannan ra'ayi a cikin 1637 yayin da yake zaune a Netherlands.Pierre de Fermat ne ya gano shi da kansa, wanda kuma ya yi aiki a matakai uku, kodayake Fermat bai buga binciken ba.[109] Limamin Faransa Nicole Oresme yayi amfani da gine-gine irin na Cartesian tun kafin lokacin Descartes da Fermat.[110]Dukansu Descartes da Fermat sun yi amfani da axis guda ɗaya a cikin jiyya kuma suna da tsayin tsayin daka wanda aka auna dangane da wannan axis.An gabatar da manufar yin amfani da gatari biyu daga baya, bayan da aka fassara Descartes' La Géométrie zuwa Latin a 1649 ta Frans van Schooten da ɗalibansa.Waɗannan masu sharhi sun gabatar da ra'ayoyi da yawa yayin ƙoƙarin fayyace ra'ayoyin da ke cikin aikin Descartes.[111]Haɓaka tsarin haɗin gwiwar Cartesian zai taka muhimmiyar rawa wajen haɓaka ƙididdiga ta Isaac Newton da Gottfried Wilhelm Leibniz.[112 <] > Bayanin haɗin kai guda biyu na jirgin daga baya ya zama gama gari a cikin ra'ayi na sararin samaniya.[113]Yawancin sauran tsarin daidaitawa an haɓaka su tun daga Descartes, kamar daidaitawar polar don jirgin sama, da daidaitawar sikeli da cylindrical don sarari mai girma uku.
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1670 Jan 1

Lissafi

Europe
Calculus shine nazarin lissafin lissafi na ci gaba da canji, kamar yadda geometry ke nazarin siffa, algebra kuma shine nazarin gabaɗayan ayyukan lissafi.Yana da manyan rassa guda biyu, lissafin lissafi daban-daban da lissafin dunƙulewa;na farko ya shafi canjin canjin nan take, da gangaren lankwasa, yayin da na karshen ya shafi tarin yawa, da wuraren da ke ƙarƙashin ko tsakanin masu lanƙwasa.Waɗannan rassa guda biyu suna da alaƙa da juna ta ainihin ka'idar ƙididdiga, kuma suna amfani da mahimman ra'ayi na haɗuwa da jerin abubuwan da ba su da iyaka da ƙima zuwa ƙayyadaddun iyaka.[97]Ishaku Newton da Gottfried Wilhelm Leibniz sun ƙirƙira ƙididdiga mara iyaka da kansa a ƙarshen karni na 17.[98] Daga baya aiki, gami da ƙididdige ra'ayin iyakoki, sanya waɗannan abubuwan haɓakawa a kan ingantaccen tushe mai ma'ana.A yau, kalkulus yana da amfani da yawa a cikin kimiyya, injiniyanci, da kimiyyar zamantakewa.Isaac Newton ya haɓaka amfani da lissafi a cikin dokokinsa na motsi da gravitation na duniya.Gottfried Wilhelm Leibniz ne ya tsara waɗannan ra'ayoyin zuwa ƙididdige ƙididdiga na gaskiya, wanda Newton ya zarge shi da laifin sata.Yanzu ana ɗaukarsa a matsayin mai ƙirƙira mai zaman kansa kuma mai ba da gudummawa ga ƙididdiga.Gudunmawarsa ita ce ta samar da ƙayyadaddun ƙa'idodin ƙa'idodi don yin aiki tare da adadi mara iyaka, ba da izinin ƙididdige ƙididdiga na biyu da mafi girma, da kuma samar da ka'idar samfurin da tsarin sarkar, a cikin nau'ikan su daban-daban da haɗin kai.Ba kamar Newton ba, Leibniz ya ba da himma sosai a cikin zaɓin abubuwan da ya zaɓa.[99]Newton shine farkon wanda ya fara amfani da lissafi ga ilimin kimiyyar lissafi na gabaɗaya kuma Leibniz ya ƙirƙira da yawa daga cikin bayanin da aka yi amfani da shi a cikin lissafi a yau.[100] Mahimman bayanai waɗanda Newton da Leibniz suka bayar sune ka'idodin bambance-bambance da haɗin kai, suna jaddada cewa bambance-bambance da haɗin kai sune matakai masu banƙyama, na biyu da mafi girma, da kuma ra'ayi na kimanin nau'i na nau'i-nau'i.
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1736 Jan 1

Ka'idar Graph

Europe
A cikin ilmin lissafi, ka'idar jadawali ita ce nazarin jadawali, waɗanda sigar lissafi ce da ake amfani da su don ƙirar alakar da ke tsakanin abubuwa.jadawali a cikin wannan mahallin yana kunshe ne da madaidaitan (wanda kuma ake kira nodes ko maki) waɗanda aka haɗa ta gefuna (wanda ake kira mahada ko layi).Ana yin bambance-bambance tsakanin zane-zane marasa jagora, inda gefuna suka haɗu da nisa biyu daidai gwargwado, da kuma zane-zane, inda gefuna suka haɗu da nisa biyu a asymmetrically.Zane-zane ɗaya ne daga cikin manyan abubuwan da ake nazari a cikin mathematics.Takardar da Leonhard Euler ya rubuta akan gadoji bakwai na Königsberg kuma aka buga a 1736 ana ɗaukarsa a matsayin takarda ta farko a tarihin ka'idar zane.[114] .Ƙididdigar Euler da ke da alaƙa da adadin gefuna, madaidaitan, da fuskoki na polyhedron convex an yi nazari kuma sun haɗa shi da Cauchy [115] da L'Huilier, [116] kuma yana wakiltar farkon reshen lissafin da aka sani da topology.
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1738 Jan 1

Rarraba ta al'ada

France
A cikin ƙididdiga, rarraba na yau da kullun ko rarraba Gaussian nau'in rarraba yuwuwar ci gaba ne don madaidaicin ƙima na gaske.Rarraba na yau da kullun yana da mahimmanci a cikin ƙididdiga kuma galibi ana amfani da su a cikin ilimin halitta da na zamantakewa don wakiltar madaidaitan masu canji na gaske waɗanda ba a san rabonsu ba.[124 <] > Muhimmancinsu wani ɓangare ne saboda ka'idar iyaka ta tsakiya.Ya furta cewa, a ƙarƙashin wasu yanayi, matsakaicin yawancin samfurori (dubawa) na ma'auni na bazuwar tare da iyakataccen ma'ana da bambance-bambancen ita ce maɗaukakin bazuwar-wanda rarraba ya haɗa zuwa rarraba na al'ada yayin da adadin samfurori ya karu.Don haka, adadin jiki waɗanda ake tsammanin su zama jimillar matakai masu zaman kansu, kamar kurakuran aunawa, galibi suna da rarrabawa waɗanda suka kusan al'ada.[125] Wasu mawallafa [126] sun dangana daraja ga gano na al'ada rarraba zuwa de Moivre, wanda a cikin 1738 aka buga a cikin na biyu edition na "The Doctrine of Chances" da nazarin coefficients a cikin binomial fadada na (a). b) n.
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1740 Jan 1

Euler's Formula

Berlin, Germany
Dabarar Euler, mai suna bayan Leonhard Euler, dabara ce ta lissafi a cikin hadadden bincike wanda ke kafa tushen alakar da ke tsakanin ayyukan trigonometric da hadadden aikin juzu'i.Tsarin Euler yana da yawa a cikin lissafi, physics, chemistry, da injiniyanci.Masanin kimiyyar lissafi Richard Feynman ya kira lissafin "jewel ɗinmu" da "mafi kyawun dabarar lissafi".Lokacin x = π, ana iya sake rubuta tsarin Euler a matsayin eiπ + 1 = 0 ko eiπ = -1, wanda aka sani da asalin Euler.
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1763 Jan 1

Bayes' Theorem

England, UK
A ka'idar yiwuwa da kididdiga, Bayes' theorem (a madadin dokar Bayes ko mulkin Bayes), mai suna bayan Thomas Bayes, ya bayyana yuwuwar aukuwa, dangane da sanin yanayin yanayin da ka iya alaƙa da taron.[122] Alal misali, idan an san haɗarin tasowa matsalolin kiwon lafiya yana karuwa da shekaru, ka'idar Bayes yana ba da damar haɗarin mutum na shekarun da aka sani don auna shi daidai ta hanyar daidaita shi dangane da shekarun su, maimakon kawai zato. cewa mutum ya kasance irin na yawan jama'a gaba daya.A ka'idar yiwuwa da kididdiga, Bayes' theorem (a madadin dokar Bayes ko mulkin Bayes), mai suna bayan Thomas Bayes, ya bayyana yuwuwar aukuwa, dangane da sanin yanayin yanayin da ka iya alaƙa da taron.[122] Alal misali, idan an san haɗarin tasowa matsalolin kiwon lafiya yana karuwa da shekaru, ka'idar Bayes yana ba da damar haɗarin mutum na shekarun da aka sani don auna shi daidai ta hanyar daidaita shi dangane da shekarun su, maimakon kawai zato. cewa mutum ya kasance irin na yawan jama'a gaba daya.
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Dokar Gauss
Karl Friedrich Gauss ©Christian Albrecht Jensen
1773 Jan 1

Dokar Gauss

France
A kimiyyar lissafi da electromagnetism, ka'idar Gauss, wacce aka fi sani da Gauss's flux theorem, (ko wani lokacin ana kiranta Gauss theorem) wata doka ce da ke da alaƙa da rarraba wutar lantarki zuwa filin lantarki da aka samu.A cikin nau'insa, ya bayyana cewa jujjuyawar filin lantarki daga cikin rufaffiyar sararin samaniya ba bisa ka'ida ba ya yi daidai da cajin wutar lantarki da ke kewaye da saman, ba tare da la'akari da yadda ake rarraba wannan cajin ba.Ko da yake doka ita kaɗai ba ta isa ta ƙayyade filin lantarki a saman saman da ke rufe duk wani cajin cajin ba, wannan na iya yiwuwa a yanayin da daidaito ya ba da izinin daidaiton filin.Inda babu irin wannan ma'auni, ana iya amfani da dokar Gauss a cikin nau'in nau'in nau'in nau'in nau'in nau'in nau'in nau'in nau'in nau'in nau'in nau'in nau'in nau'in nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i nau'i).Joseph-Louis Lagrange ne ya fara tsara dokar [101] a cikin 1773, [102] sannan Carl Friedrich Gauss ya biyo baya a 1835, [103] duka a cikin mahallin jan hankali na ellipsoids.Yana ɗaya daga cikin ma'auni na Maxwell, wanda ya samar da ginshiƙi na electrodynamics na gargajiya.Ana iya amfani da dokar Gauss don samo dokar Coulomb, [104] da akasin haka.
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1800 Jan 1

Ka'idar Rukuni

Europe
A cikin abstract algebra, ka'idar ƙungiya tana nazarin tsarin algebra da aka sani da ƙungiyoyi.Manufar ƙungiya ita ce tsakiyar algebra mai ƙima: sauran sanannun tsarin algebra, kamar zobba, filaye, da sararin samaniya, ana iya ganin su azaman ƙungiyoyi waɗanda aka ba su ƙarin ayyuka da axioms.Ƙungiyoyi suna maimaita a cikin ilimin lissafi, kuma hanyoyin ka'idar rukuni sun yi tasiri ga sassa da yawa na algebra.Ƙungiyoyin algebra masu layi da ƙungiyoyin ƙarya rassa biyu ne na ka'idar rukuni waɗanda suka sami ci gaba kuma sun zama yanki na jigo a cikin nasu dama.Tarihin farkon ka'idar rukuni ya samo asali ne daga karni na 19.Ɗaya daga cikin muhimman nasarorin ilimin lissafi na karni na 20 shine ƙoƙarin haɗin gwiwa, wanda ya ɗauki fiye da shafukan mujallu 10,000 kuma akasari an buga shi tsakanin 1960 da 2004, wanda ya ƙare a cikin cikakken rarraba ƙungiyoyi masu sauƙi.
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1807 Jan 1

Fourier Analysis

Auxerre, France
A cikin ilmin lissafi, bincike na Fourier shine nazarin yadda za a iya wakilta ko kimanta ayyuka na gaba ɗaya ta jimlar ayyuka masu sauƙi na trigonometric.Binciken Fourier ya girma daga nazarin jerin Fourier, kuma ana kiransa da sunan Joseph Fourier, wanda ya nuna cewa wakiltar aiki a matsayin jimlar ayyuka na trigonometric yana sauƙaƙa nazarin canjin zafi sosai.Batun bincike na Fourier ya ƙunshi ɗimbin nau'ikan lissafi.A cikin ilimin kimiyya da injiniyanci, ana kiran tsarin lalata aiki zuwa sassan oscillatory sau da yawa ana kiransa Fourier analysis, yayin da aikin sake gina aikin daga waɗannan guntu ana kiransa Fourier synthesis.Misali, ƙayyadaddun mitoci na ɓangarorin da ke cikin bayanan kiɗa zai haɗa da ƙididdige canjin Fourier na bayanin kula na kida.Mutum zai iya sake haɗa sauti iri ɗaya ta haɗa da abubuwan mitar kamar yadda aka bayyana a cikin bincike na Fourier.A cikin lissafi, kalmar Fourier analysis sau da yawa tana nufin nazarin ayyukan biyu.Tsarin bazuwar da kansa ana kiransa canjin Fourier.Fitowarsa, sauyin Fourier, galibi ana ba da takamaiman suna, wanda ya dogara da yanki da sauran kaddarorin aikin da ake canzawa.Haka kuma, an tsawaita ainihin manufar bincike na Fourier na tsawon lokaci don yin amfani da shi zuwa ga mafi yawan yanayi da yanayi na gaba ɗaya, kuma galibi ana kiran filin gabaɗaya da nazarin jituwa.Kowane juyi da aka yi amfani da shi don bincike (duba jerin sauye-sauye masu alaƙa da Fourier) yana da juzu'in juzu'i mai kama da za a iya amfani da su don haɗawa.
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1850 Jan 1 - 1870

Daidaiton Maxwell

Cambridge University, Trinity
Equations Maxwell, ko Maxwell–Heaviside equations, wani sashe ne na ma'auni na banbance banbancen ma'auni wanda, tare da ka'idar karfi ta Lorentz, sun samar da tushe na electromagnetism na gargajiya, na'urorin gani na gargajiya, da na'urorin lantarki.Ma'auni suna ba da samfurin lissafi don lantarki, na gani, da fasahar rediyo, kamar samar da wutar lantarki, injinan lantarki, sadarwa mara waya, ruwan tabarau, radar, da sauransu. filayen.Sunan ma'auni ne bayan masanin kimiyyar lissafi kuma masanin lissafi James Clerk Maxwell, wanda, a cikin 1861 da 1862, ya buga farkon nau'i na ma'auni wanda ya haɗa da dokar tilasta Lorentz.Maxwell ya fara amfani da ma'auni don ba da shawarar cewa haske wani lamari ne na lantarki.Sigar zamani na ma'auni a cikin tsarin su na gama gari an ƙididdige shi ga Oliver Heaviside.Matsakaicin suna da manyan bambance-bambancen guda biyu.Ƙididdigar ƙananan ƙananan suna da amfani na duniya amma ba su da amfani don ƙididdigewa gama gari.Suna danganta filayen lantarki da maganadisu zuwa jimillar caji da jimillar halin yanzu, gami da rikitattun caji da igiyoyin ruwa a cikin kayan a ma'aunin atomic.Ma'auni na macroscopic suna bayyana sabbin filayen taimako guda biyu waɗanda ke bayyana manyan halayen kwayoyin halitta ba tare da yin la'akari da cajin ma'auni na atomic ba da abubuwan ƙididdigewa kamar juyi.Koyaya, amfani da su yana buƙatar ƙayyadaddun ƙayyadaddun sigogi na gwaji don bayanin abubuwan mamaki na martanin lantarki na kayan.Ana kuma amfani da kalmar "equations na Maxwell" don daidaitattun hanyoyin da za'a iya amfani da su.An fi son nau'ikan ma'auni na Maxwell dangane da ƙarfin lantarki da ƙarfin maganadisu don warware ma'auni a sarari azaman matsalar ƙimar iyaka, injiniyoyi na nazari, ko don amfani da injin injin ƙira.Ƙirƙirar haɗin kai (a kan lokacin sarari maimakon sarari da lokaci daban) yana sa daidaituwar ma'aunin Maxwell tare da bayyanar alaƙa ta musamman.Ƙididdigar Maxwell a cikin lokaci mai lanƙwasa, wanda aka saba amfani da shi a cikin ƙarfin kuzari da ilimin kimiyyar gravitational, sun dace da haɗin kai na gaba ɗaya.A haƙiƙa, Albert Einstein ya ɓullo da alaƙa na musamman kuma na gabaɗaya don ɗaukar saurin haske maras bambanci, sakamakon ma'aunin Maxwell, tare da ƙa'idar cewa motsin dangi kawai yana da sakamako na zahiri.Buga ma'auni ya nuna alamar haɗewar ka'idar don abubuwan da aka bayyana a baya daban-daban: maganadisu, wutar lantarki, haske, da radiyo masu alaƙa.Tun daga tsakiyar karni na 20, an fahimci cewa ma'auni na Maxwell ba su ba da cikakken bayanin abubuwan al'ajabi na lantarki ba, amma a maimakon haka sun kasance ƙayyadaddun ka'ida na ingantacciyar ka'idar jimla electrodynamics.
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1870 Jan 1

Saita Ka'idar

Germany
Set theory shine reshe na ilimin lissafi wanda bincike ya tsara, wanda za'a iya kwatanta shi a matsayin tarin abubuwa.Ko da yake ana iya tattara abubuwa kowane iri a cikin saiti, saitin ka'idar, a matsayin reshe na lissafi, galibi ya shafi waɗanda suka dace da ilimin lissafi gabaɗaya.Masanin lissafi na Jamus Richard Dedekind da Georg Cantor ne suka fara nazarin ka'idar saiti na zamani a cikin 1870s.Musamman, Georg Cantor ana ɗaukarsa a matsayin wanda ya kafa ka'idar saiti.Tsarukan da ba a tsara su ba da aka bincika a wannan matakin farko suna tafiya ƙarƙashin sunan ka'idar saiti na butulci.Bayan gano paradoxes a cikin ka'idar saiti (irin su Paradox na Russell, Cantor's paradox da Burali-Forti paradox), an gabatar da tsarin axiomatic iri-iri a farkon karni na ashirin, wanda Zermelo-Fraenkel ya kafa ka'idar (tare da ko ba tare da axiom na zabi) har yanzu shine mafi sanannun kuma mafi nazari.Saita ka'idar yawanci ana amfani da ita azaman tushen tushen tsarin gabaɗayan ilimin lissafi, musamman ta hanyar ka'idar saiti na Zermelo-Fraenkel tare da axiom na zaɓi.Bayan kafuwar aikinsa, saitin ka'idar kuma yana ba da tsarin haɓaka ka'idar lissafi na rashin iyaka, kuma tana da aikace-aikace iri-iri a cikin ilimin kimiyyar kwamfuta (kamar a ka'idar algebra), falsafa da ilimin tauhidi.Tushen rokonsa, tare da abubuwan da ke tattare da shi, abubuwan da ke tattare da ra'ayin rashin iyaka da aikace-aikacen sa da yawa, sun sanya ka'idar ta zama wani yanki mai mahimmanci ga masana dabaru da falsafar lissafi.Bincike na zamani a cikin ka'idar saiti ya ƙunshi ɗimbin batutuwa, kama daga tsarin layin lamba na ainihi zuwa nazarin daidaiton manyan Cardinal.
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Ka&#39;idar Wasan
John von Neumann ©Anonymous
1927 Jan 1

Ka'idar Wasan

Budapest, Hungary
Ka'idar wasa ita ce nazarin ƙirar lissafi na hulɗar dabarun mu'amala tsakanin wakilai masu hankali.[117 <] > Yana da aikace-aikace a duk fagagen kimiyyar zamantakewa, haka nan kuma a fannin dabaru, kimiyyar tsarin da kimiyyar kwamfuta.Ana amfani da ra'ayoyin ka'idar wasan sosai a fannin tattalin arziki kuma.[118] Hanyoyin gargajiya na ka'idar wasan sun yi magana game da wasanni na mutum biyu na sifili, wanda kowane ɗan takara ya sami riba ko asarar da ya samu daidai da asarar da sauran mahalarta.A cikin karni na 21st, ci gaban ka'idodin wasan ya shafi nau'ikan alaƙar ɗabi'a;yanzu laima ce ga kimiyyar yanke shawara mai ma'ana a cikin mutane, dabbobi, da kuma kwamfutoci.Ka'idar wasan ba ta wanzu a matsayin filin wasa na musamman har sai John von Neumann ya buga takarda akan Ka'idar Wasannin Dabarun a cikin 1928. [119] Von Neumann ta asali hujja ta yi amfani da ƙayyadaddun ƙayyadaddun ka'ida ta Brouwer akan ci gaba da taswira zuwa cikin ƙaramin tsari, wanda ya zama daidaitaccen hanya a ka'idar wasa da tattalin arzikin lissafi.Takardarsa ta biyo bayan littafinsa na 1944 Theory of Games and Economic Havior tare da Oskar Morgenstern.[120] Bugu na biyu na wannan littafi ya ba da ka'idar axiomatic na amfani, wanda ya sake haifar da tsohuwar ka'idar amfani (na kudi) ta Daniel Bernoulli a matsayin horo mai zaman kanta.Ayyukan Von Neumann a cikin ka'idar wasan sun ƙare a cikin wannan littafi na 1944.Wannan tushen aikin yana ƙunshe da hanya don nemo madaidaicin mafita ga wasannin sifili na mutum biyu.Ayyukan na gaba sun fi mayar da hankali kan ka'idar wasan haɗin gwiwa, wanda ke nazarin ingantattun dabaru ga ƙungiyoyin daidaikun mutane, tare da ɗaukan cewa za su iya aiwatar da yarjejeniya tsakanin su game da dabarun da suka dace.[121]
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Appendices



APPENDIX 1

The History of Mathematics and Its Applications


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APPENDIX 2

The Map of Mathematics


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Footnotes



  1. Friberg, J. "Methods and traditions of Babylonian mathematics. Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations", Historia Mathematica, 8, 1981, pp. 277-318.
  2. Neugebauer, Otto (1969) [1957]. The Exact Sciences in Antiquity. Acta Historica Scientiarum Naturalium et Medicinalium. Vol. 9 (2 ed.). Dover Publications. pp. 1-191. ISBN 978-0-486-22332-2. PMID 14884919. Chap. IV "Egyptian Mathematics and Astronomy", pp. 71-96.
  3. Turnbull (1931). "A Manual of Greek Mathematics". Nature. 128 (3235): 5. Bibcode:1931Natur.128..739T. doi:10.1038/128739a0. S2CID 3994109.
  4. Heath, Thomas L. (1963). A Manual of Greek Mathematics, Dover, p. 1: "In the case of mathematics, it is the Greek contribution which it is most essential to know, for it was the Greeks who first made mathematics a science."
  5. Joseph, George Gheverghese (1991). The Crest of the Peacock: Non-European Roots of Mathematics. Penguin Books, London, pp. 140-48.
  6. Kaplan, Robert (1999). The Nothing That Is: A Natural History of Zero. Allen Lane/The Penguin Press, London.
  7. Juschkewitsch, A. P. (1964). Geschichte der Mathematik im Mittelalter. Teubner, Leipzig.
  8. Eves, Howard (1990). History of Mathematics, 6th Edition, "After Pappus, Greek mathematics ceased to be a living study, ..." p. 185; "The Athenian school struggled on against growing opposition from Christians until the latter finally, in A.D. 529, obtained a decree from Emperor Justinian that closed the doors of the school forever." p. 186; "The period starting with the fall of the Roman Empire, in the middle of the fifth century, and extending into the eleventh century is known in Europe as the Dark Ages ... . Schooling became almost nonexistent." p. 258.
  9. Duncan J. Melville (2003). Third Millennium Chronology, Third Millennium Mathematics. St. Lawrence University.
  10. Maor, Eli (1998). Trigonometric Delights. Princeton University Press. p. 20. ISBN 0-691-09541-8.
  11. Prestini, Elena (2004). The evolution of applied harmonic analysis: models of the real world. Birkhauser. ISBN 978-0-8176-4125-2., p. 62
  12. Boyer, C.B. (1991) [1989], A History of Mathematics (2nd ed.), New York: Wiley , ISBN 978-0-471-54397-8, p. 25.
  13. Boyer 1991, "Mesopotamia" p. 26.
  14. Boyer 1991, "Mesopotamia" p. 27.
  15. Aaboe, Asger (1998). Episodes from the Early History of Mathematics. New York: Random House. pp. 30-31.
  16. Boyer 1991, "Mesopotamia" p. 33.
  17. Boyer 1991, "Mesopotamia" p. 39.
  18. Imhausen, Annette (2006). "Ancient Egyptian Mathematics: New Perspectives on Old Sources". The Mathematical Intelligencer. 28 (1): 19-27. doi:10.1007/bf02986998. S2CID 122060653.
  19. Burton, David (2005). The History of Mathematics: An Introduction. McGraw-Hill. ISBN 978-0-07-305189-5.
  20. Eglash, Ron (1999). African fractals : modern computing and indigenous design. New Brunswick, N.J.: Rutgers University Press. pp. 89, 141. ISBN 0813526140.
  21. Eglash, R. (1995). "Fractal Geometry in African Material Culture". Symmetry: Culture and Science. 6-1: 174-177.
  22. Katz V, Imhasen A, Robson E, Dauben JW, Plofker K, Berggren JL (2007). The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. ISBN 978-0-691-11485-9.
  23. Panchenko, D. V. (Dmitrii Vadimovich) (1993). "Thales and the Origin of Theoretical Reasoning". Configurations. 1 (3): 387-414. doi:10.1353/con.1993.0024. ISSN 1080-6520.
  24. Boyer, Carl B.; Merzbach, Uta C. (2011), A History of Mathematics (3rd ed.), John Wiley & Sons, Inc., ISBN 978-0-471-54397-8, pp. 40-89.
  25. Boyer, Carl (1968). A History of Science. p. 45. ISBN 0471543977.
  26. Netz, Reviel (2014), Huffman, Carl A. (ed.), "The problem of Pythagorean mathematics", A History of Pythagoreanism, Cambridge: Cambridge University Press, pp. 167-184, ISBN 978-1-107-01439-8, retrieved 2021-05-26
  27. Green, P. (1990). Alexander to Actium: The Historical Evolution of the Hellenistic Age (1 ed.). University of California Press. ISBN 978-0-520-08349-3. JSTOR 10.1525/j.ctt130jt89.
  28. Luce, J. V. (1988). "Greek Science in its Hellenistic Phase". Hermathena (145): 23-38. ISSN 0018-0750. JSTOR 23040930.
  29. Acerbi, F. (2018). Keyser, Paul T; Scarborough, John (eds.). "Hellenistic Mathematics". Oxford Handbook of Science and Medicine in the Classical World. pp. 268-292. doi:10.1093/oxfordhb/9780199734146.013.69. ISBN 978-0-19-973414-6. Retrieved 2021-05-26.
  30. Boyer 1991, "Mesopotamia" p. 43.
  31. Boyer 1991, "Mesopotamia" p. 86.
  32. Boyer 1991, "Mesopotamia" p. 88.
  33. Calian, George F. (2014). "One, Two, Three... A Discussion on the Generation of Numbers". New Europe College.
  34. Boyer 1991, "Mesopotamia" p. 87.
  35. Boyer 1991, "Euclid of Alexandria" p. 119.
  36. Boyer 1991, "Euclid of Alexandria" p. 100.
  37. Boyer 1991, "Euclid of Alexandria" p. 104.
  38. Boyer 1991, "Euclid of Alexandria" p. 102.
  39. Kurt Von Fritz (1945). "The Discovery of Incommensurability by Hippasus of Metapontum". The Annals of Mathematics.
  40. James R. Choike (1980). "The Pentagram and the Discovery of an Irrational Number". The Two-Year College Mathematics Journal
  41. Kline, M. (1990). Mathematical Thought from Ancient to Modern Times, Vol. 1. New York: Oxford University Press (original work published 1972), p. 32.
  42. John M. Henshaw (10 September 2014). An Equation for Every Occasion: Fifty-Two Formulas and Why They Matter. JHU Press. p. 68.
  43. Powers, J (2020). "Did Archimedes do calculus?" (PDF).
  44. O'Connor, J.J.; Robertson, E.F. (February 1996). "A history of calculus". University of St Andrews.
  45. Goe, G. (1972). "Archimedes' theory of the lever and Mach's critique". Studies in History and Philosophy of Science Part A. 2 (4): 329-345.
  46. Berggren, J. L. (1976). "Spurious Theorems in Archimedes' Equilibrium of Planes: Book I".
  47. Boyer 1991, "Euclid of Alexandria" p. 145.
  48. Boyer 1991, "Euclid of Alexandria" p. 146.
  49. Boyer 1991, "Euclid of Alexandria" p. 152.
  50. Boyer 1991, "Euclid of Alexandria" p. 156.
  51. Boyer 1991, "Euclid of Alexandria" p. 175.
  52. Boyer 1991, "Euclid of Alexandria" p. 162.
  53. Boyer 1991, "Euclid of Alexandria" p. 178.
  54. Boyer 1991, "Euclid of Alexandria" p. 180.
  55. Boyer 1991, "Euclid of Alexandria" p. 181.
  56. Boyer 1991, "Euclid of Alexandria" p. 183.
  57. Boyer 1991, "Revival and Decline of Greek Mathematics" p.190-94.
  58. Boyer 1991, "Revival and Decline of Greek Mathematics" p. 193.
  59. Boyer 1991, "Revival and Decline of Greek Mathematics" p. 194.
  60. Boyer 1991, p. 215.
  61. John Bowman (2000). Columbia Chronologies of Asian History and Culture. Columbia University Press. p. 596. ISBN 978-0-231-50004-3.
  62. Boyer 1991, "China and India" p. 210.
  63. Boyer 1991, "Greek Trigonometry and Mensuration" p. 168.
  64. Boyer 1991, "China and India" p. 208.
  65. Bourbaki, Nicolas Elements of the History of Mathematics (1998), p. 46.
  66. Weiss, Ittay (20 September 2017). "Nothing matters: How India's invention of zero helped create modern mathematics". The Conversation.
  67. Devlin, Hannah (13 September 2017). "Much ado about nothing: ancient Indian text contains earliest zero symbol". The Guardian. ISSN 0261-3077.
  68. Qiu, Jane (7 January 2014). "Ancient times table hidden in Chinese bamboo strips". Nature. doi:10.1038/nature.2014.14482. S2CID 130132289. Retrieved 15 September 2014.
  69. Katz, Victor J. (2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press, ISBN 978-0-691-11485-9, pp. 194-99.
  70. Boyer 1991, "China and India" p. 202.
  71. Boyer 1991, "China and India" p. 205.
  72. Volkov, Alexei (2009), "Mathematics and Mathematics Education in Traditional Vietnam", in Robson, Eleanor; Stedall, Jacqueline (eds.), The Oxford Handbook of the History of Mathematics, Oxford: Oxford University Press, pp. 153-76, ISBN 978-0-19-921312-2, p.153-56
  73. Volkov 2009, pp. 154-55
  74. Volkov 2009, pp. 156-57
  75. Volkov 2009, p. 155
  76. Boyer 1991, "China and India" p. 198.
  77. Needham, Joseph; Wang, Ling (1995) [1959], Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth, vol. 3, Cambridge: Cambridge University Press, ISBN 978-0-521-05801-8, pp. 91-92
  78. Needham & Wang 1995, p. 94
  79. Boyer 1991, "China and India" p. 198.
  80. Straffin, Philip D. (1998), "Liu Hui and the First Golden Age of Chinese Mathematics", Mathematics Magazine, 71 (3): 163-81, doi:10.1080/0025570X.1998.11996627, p. 164.
  81. Needham & Wang 1995, p. 22
  82. Needham & Wang 1995, p. 99-100
  83. Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B. (2004), Pi: A Source Book, New York: Springer, ISBN 978-0-387-20571-7, p. 27
  84. Boyer 1991, "China and India" p. 202
  85. Zill, Dennis G.; Wright, Scott; Wright, Warren S. (2009). Calculus: Early Transcendentals (3 ed.). Jones & Bartlett Learning. p. xxvii. ISBN 978-0-7637-5995-7. Extract of p. 27
  86. O'Connor, J.J. & Robertson, E.F. (February 1996). "A history of calculus". University of St Andrews. Retrieved 2007-08-07.
  87. Boyer 1991, "The Arabic Hegemony" p. 230
  88. Gandz and Saloman (1936), The sources of Khwarizmi's algebra, Osiris i, pp. 263-77
  89. Boyer 1991, "The Arabic Hegemony" p. 229
  90. Rashed, R.; Armstrong, Angela (1994). The Development of Arabic Mathematics. Springer. pp. 11-12. ISBN 978-0-7923-2565-9. OCLC 29181926.
  91. Sesiano, Jacques (2000). "Islamic mathematics". In Selin, Helaine; D'Ambrosio, Ubiratàn (eds.). Mathematics Across Cultures: The History of Non-Western Mathematics. Springer. p. 148. ISBN 1-4020-0260-2.
  92. O'Connor, John J.; Robertson, Edmund F., "Abu Kamil", MacTutor History of Mathematics archive, University of St Andrews
  93. Knuth, D. E. (1997). The Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd ed.). Addison-Wesley. ISBN 0-201-89684-2, p. 318.
  94. Stillwell, J. (1997). Numbers and Geometry. New York: Springer-Verlag. ISBN 0-387-98289-2, p. 31.
  95. Marie-Therese d'Alverny, "Translations and Translators", pp. 421-62 in Robert L. Benson and Giles Constable, Renaissance and Renewal in the Twelfth Century, (Cambridge: Harvard University Press, 1982).
  96. Singh, Parmanand (1985), "The So-called Fibonacci numbers in ancient and medieval India", Historia Mathematica, 12 (3): 229-44, doi:10.1016/0315-0860(85)90021-7
  97. DeBaggis, Henry F.; Miller, Kenneth S. (1966). Foundations of the Calculus. Philadelphia: Saunders. OCLC 527896.
  98. Boyer, Carl B. (1959). The History of the Calculus and its Conceptual Development. New York: Dover. OCLC 643872
  99. Mazur, Joseph (2014). Enlightening Symbols / A Short History of Mathematical Notation and Its Hidden Powers. Princeton University Press. p. 166. ISBN 978-0-691-17337-5.
  100. Frautschi, Steven C.; Olenick, Richard P.; Apostol, Tom M.; Goodstein, David L. (2007). The Mechanical Universe: Mechanics and Heat (Advanced ed.). Cambridge [Cambridgeshire]: Cambridge University Press. ISBN 978-0-521-71590-4. OCLC 227002144.
  101. Duhem, Pierre (1891). Lecons sur l'electricite et le magnetisme (in French). Paris Gauthier-Villars. vol. 1, ch. 4, p. 22-23. shows that Lagrange has priority over Gauss. Others after Gauss discovered "Gauss' Law", too.
  102. Lagrange, Joseph-Louis (1773). "Sur l'attraction des spheroides elliptiques". Memoires de l'Academie de Berlin (in French): 125.
  103. Gauss, Carl Friedrich (1877). Theoria attractionis corporum sphaeroidicorum ellipticorum homogeneorum methodo nova tractata (in Latin). (Gauss, Werke, vol. V, p. 1). Gauss mentions Newton's Principia proposition XCI regarding finding the force exerted by a sphere on a point anywhere along an axis passing through the sphere.
  104. Halliday, David; Resnick, Robert (1970). Fundamentals of Physics. John Wiley & Sons. pp. 452-453.
  105. LIGHTNER, JAMES E. (1991). "A Brief Look at the History of Probability and Statistics". The Mathematics Teacher. 84 (8): 623-630. doi:10.5951/MT.84.8.0623. ISSN 0025-5769. JSTOR 27967334.
  106. Grinstead, Charles Miller; James Laurie Snell. "Introduction". Introduction to Probability. pp. vii.
  107. Daston, Lorraine J. (1980). "Probabilistic Expectation and Rationality in Classical Probability Theory". Historia Mathematica. 7 (3): 234-260. doi:10.1016/0315-0860(80)90025-7.
  108. ""The origins and legacy of Kolmogorov's Grundbegriffe", by Glenn Shafer and Vladimir Vovk" (PDF). Retrieved 2012-02-12.
  109. Bix, Robert A.; D'Souza, Harry J. "Analytic geometry". Encyclopedia Britannica. Retrieved 6 August 2017.
  110. Kent, Alexander J.; Vujakovic, Peter (4 October 2017). The Routledge Handbook of Mapping and Cartography. Routledge. ISBN 9781317568216.
  111. Burton, David M. (2011), The History of Mathematics/An Introduction (7th ed.), New York: McGraw-Hill, ISBN 978-0-07-338315-6, p. 374.
  112. Berlinski, David. A Tour of the Calculus.
  113. Axler, Sheldon (2015). Linear Algebra Done Right - Springer. Undergraduate Texts in Mathematics. p. 1. doi:10.1007/978-3-319-11080-6. ISBN 978-3-319-11079-0.
  114. Biggs, N.; Lloyd, E.; Wilson, R. (1986), Graph Theory, 1736-1936, Oxford University Press
  115. Cauchy, A. L. (1813), "Recherche sur les polyedres - premier memoire", Journal de l'ecole Polytechnique, 9 (Cahier 16): 66-86.
  116. L'Huillier, S.-A.-J. (1812-1813), "Memoire sur la polyedrometrie", Annales de Mathematiques, 3: 169-189.
  117. Myerson, Roger B. (1991). Game Theory: Analysis of Conflict. Harvard University Press.ISBN 9780674341166.
  118. Shapley, Lloyd S.; Shubik, Martin (1 January 1971). "Game Theory in Economics: Chapter1, Introduction, The Use of Models". Archived from the original on 23 April 2023.Retrieved 23 April 2023.
  119. von Neumann, John (1928). "Zur Theorie der Gesellschaftsspiele" [On the Theory of Gamesof Strategy]. Mathematische Annalen [Mathematical Annals] (in German). 100 (1): 295-320.doi:10.1007/BF01448847. S2CID 122961988.
  120. Mirowski, Philip (1992). "What Were von Neumann and Morgenstern Trying to Accomplish?".In Weintraub, E. Roy (ed.). Toward a History of Game Theory. Durham: Duke UniversityPress. pp. 113-147. ISBN 978-0-8223-1253-6.
  121. Leonard, Robert (2010), Von Neumann, Morgenstern, and the Creation of Game Theory, New York: Cambridge University Press, doi:10.1017/CBO9780511778278, ISBN 978-0-521-56266-9
  122. Joyce, James (2003), "Bayes' Theorem", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2019 ed.), Metaphysics Research Lab, Stanford University, retrieved 2020-01-17.
  123. Normal Distribution, Gale Encyclopedia of Psychology
  124. Lyon, A. (2014). Why are Normal Distributions Normal?, The British
  125. Journal for the Philosophy of Science.
  126. Johnson, Norman L.; Kotz, Samuel; Balakrishnan, Narayanaswamy (1994). Continuous Univariate Distributions, Volume 1. Wiley. ISBN 978-0-471-58495-7.(1994, p. 85)
  127. Boyer, Carl B.; Merzbach, Uta C. (1991). A History of Mathematics (2nd ed.). JohnWiley & Sons, Inc. ISBN 978-0-471-54397-8, pp. 252-253.
  128. Ifrah, Georges (2001). The Universal History of Computing: From the Abacus to theQuantum Computer. New York, NY: John Wiley & Sons, Inc. ISBN 978-0-471-39671-0., p. 11

References



References

  • Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B. (2004), Pi: A Source Book, New York: Springer, ISBN 978-0-387-20571-7
  • Boyer, C.B. (1991) [1989], A History of Mathematics (2nd ed.), New York: Wiley, ISBN 978-0-471-54397-8
  • Cuomo, Serafina (2001), Ancient Mathematics, London: Routledge, ISBN 978-0-415-16495-5
  • Goodman, Michael, K.J. (2016), An introduction of the Early Development of Mathematics, Hoboken: Wiley, ISBN 978-1-119-10497-1
  • Gullberg, Jan (1997), Mathematics: From the Birth of Numbers, New York: W.W. Norton and Company, ISBN 978-0-393-04002-9
  • Joyce, Hetty (July 1979), "Form, Function and Technique in the Pavements of Delos and Pompeii", American Journal of Archaeology, 83 (3): 253–63, doi:10.2307/505056, JSTOR 505056, S2CID 191394716.
  • Katz, Victor J. (1998), A History of Mathematics: An Introduction (2nd ed.), Addison-Wesley, ISBN 978-0-321-01618-8
  • Katz, Victor J. (2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press, ISBN 978-0-691-11485-9
  • Needham, Joseph; Wang, Ling (1995) [1959], Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth, vol. 3, Cambridge: Cambridge University Press, ISBN 978-0-521-05801-8
  • Needham, Joseph; Wang, Ling (2000) [1965], Science and Civilization in China: Physics and Physical Technology: Mechanical Engineering, vol. 4 (reprint ed.), Cambridge: Cambridge University Press, ISBN 978-0-521-05803-2
  • Sleeswyk, Andre (October 1981), "Vitruvius' odometer", Scientific American, 252 (4): 188–200, Bibcode:1981SciAm.245d.188S, doi:10.1038/scientificamerican1081-188.
  • Straffin, Philip D. (1998), "Liu Hui and the First Golden Age of Chinese Mathematics", Mathematics Magazine, 71 (3): 163–81, doi:10.1080/0025570X.1998.11996627
  • Tang, Birgit (2005), Delos, Carthage, Ampurias: the Housing of Three Mediterranean Trading Centres, Rome: L'Erma di Bretschneider (Accademia di Danimarca), ISBN 978-88-8265-305-7.
  • Volkov, Alexei (2009), "Mathematics and Mathematics Education in Traditional Vietnam", in Robson, Eleanor; Stedall, Jacqueline (eds.), The Oxford Handbook of the History of Mathematics, Oxford: Oxford University Press, pp. 153–76, ISBN 978-0-19-921312-2


Further Reading

  • Aaboe, Asger (1964). Episodes from the Early History of Mathematics. New York: Random House.
  • Bell, E.T. (1937). Men of Mathematics. Simon and Schuster.
  • Burton, David M. The History of Mathematics: An Introduction. McGraw Hill: 1997.
  • Corry, Leo (2015), A Brief History of Numbers, Oxford University Press, ISBN 978-0198702597
  • Gillings, Richard J. (1972). Mathematics in the Time of the Pharaohs. Cambridge, MA: MIT Press.
  • Grattan-Guinness, Ivor (2003). Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. The Johns Hopkins University Press. ISBN 978-0-8018-7397-3.
  • Heath, Sir Thomas (1981). A History of Greek Mathematics. Dover. ISBN 978-0-486-24073-2.
  • Hoffman, Paul (1998). The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. Hyperion. ISBN 0-7868-6362-5.
  • Kline, Morris. Mathematical Thought from Ancient to Modern Times.
  • Menninger, Karl W. (1969). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. ISBN 978-0-262-13040-0.
  • Stigler, Stephen M. (1990). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press. ISBN 978-0-674-40341-3.
  • Struik, D.J. (1987). A Concise History of Mathematics, fourth revised edition. Dover Publications, New York.
  • van der Waerden, B.L., Geometry and Algebra in Ancient Civilizations, Springer, 1983, ISBN 0-387-12159-5.