Mun haɗu da lissafi kowane dakika ba tare da mun lura da shi ba. Girman abubuwa da nisa, sifofi da kuma hanyoyin tafiya duk jigogi ne. Ma'anar lambar π sanannun ma daga waɗanda suka kasance masu kima a makaranta daga lissafi, kuma waɗanda, da sanin wannan lambar, ba za su iya lissafin yankin da'ira ba. Ilimi da yawa daga fannin ilimin lissafi na iya zama na farko - kowa ya san cewa hanya mafi gajarta ta ɓangaren rectangular tana kan zane. Amma don tsara wannan ilimin a cikin tsarin koyarwar Pythagorean, ya ɗauki ɗan adam shekaru dubbai. Geometry, kamar sauran ilimin kimiyya, ya bunkasa ba daidai ba. Replacedarawar ƙaruwa a Girka ta dā an maye gurbin ta da dattin Rome na d, a, wanda aka maye gurbinsa da Zamanin Duhu. Wani sabon tashin hankali a tsakiyar zamanai ya maye gurbinsa da ainihin fashewar ƙarni na 19 da na 20. Geometry ya juya daga ilimin kimiya zuwa fannin babban ilmi, kuma ci gaban sa ya ci gaba. Kuma duk ya fara ne da lissafin haraji da dala ...
1. Mai yiwuwa, ilimin farko na ilimin lissafi ya samo asali ne daga tsoffin Masarawa. Sun zauna a cikin ƙasa mai ni'ima da Kogin Nilu ya yi ambaliya. An biya haraji daga ƙasar da ke akwai, kuma don wannan kuna buƙatar lissafin yankinta. Yankin murabba'i da murabba'i mai layi ya koyi yin lissafi kwatankwaci, dangane da ƙananan ƙananan lambobi. Kuma an dauki da'irar a matsayin murabba'i, wanda bangarorinsa suke da 8/9 na diamita. Adadin π a wannan yanayin yakai kimanin 3.16 - kwatankwacin daidaito.
2. Masarawa waɗanda ke aikin geometry na gini an kira su harpedonapts (daga kalmar "igiya"). Ba za su iya yin aiki da kansu ba - suna buƙatar taimako-bayi, tun don yin alama a saman ya zama dole a shimfiɗa igiyoyi na tsayi daban-daban.
Masu ginin dala ba su san tsayinsu ba
3. Babiloniyawa sune farkon waɗanda suka yi amfani da kayan aikin lissafi don magance matsalolin yanayin ƙasa. Sun riga sun san ka'idar, wanda daga baya za'a kira shi Theorem na Pythagorean. Mutanen Babila sun rubuta duk ayyukan a cikin kalmomi, wanda ya sa suka zama masu wahala (bayan haka, har ma alamar “+” ta bayyana ne kawai a ƙarshen ƙarni na 15). Duk da haka lissafin Babilawa yayi aiki.
4. Thales na Miletsky sun tsara tsarin ilimin ilimin lissafi na lokacin. Masarawa sun gina dala, amma ba su san tsayinsu ba, kuma Thales ya iya auna shi. Tun kafin Euclid, ya tabbatar da ka'idojin ilimin lissafi na farko. Amma, wataƙila, babban gudummawar da Thales ya bayar a fannin sadarwa shi ne sadarwa tare da matasa Pythagoras. Wannan mutumin, tuni ya tsufa, ya maimaita waƙar game da ganawarsa da Thales da mahimmancinta ga Pythagoras. Kuma wani ɗalibin Thales mai suna Anaximander ya zana taswirar duniya ta farko.
Thales na Miletus
5. Lokacin da Pythagoras ya tabbatar da ka'idarsa, yana gina alwatika mai kusurwa uku dama tare da murabba'ai a gefenta, kaduwarsa da kaduwarsa ga ɗaliban ya yi yawa har ɗalibai suka yanke shawarar cewa an riga an san duniya, ta kasance kawai don bayyana ta da lambobi. Pythagoras bai yi nisa ba - ya kirkiro ra'ayoyin adadi da yawa wadanda basu da wata alaka da kimiyya ko rayuwa ta zahiri.
Pythagoras
6. Bayan sun yi kokarin warware matsalar gano tsayin dutsen wanda yake da gefe guda 1, Pythagoras da dalibansa sun fahimci cewa ba zai yuwu a bayyana wannan tsawon a adadi mai yawa ba. Koyaya, ikon Pythagoras yana da ƙarfi sosai har ya hana ɗaliban bayyana wannan gaskiyar. Hippasus bai yi biyayya ga malamin ba kuma ɗayan ɗayan mabiyan Pythagoras ya kashe shi.
7. Euclid ne ya ba da gudummawa mafi mahimmanci ga ilimin lissafi. Shi ne farkon wanda ya gabatar da kalmomi masu sauƙi, bayyanannu kuma marasa tabbas. Euclid ya kuma bayyana ma'anar yanayin girgizar kasa (muna kiran su axioms) kuma ya fara hango dukkan wasu tanade-tanaden kimiyya, bisa ga wadannan bayanan. Littafin Euclid "Farkon farawa" (kodayake ana magana sosai, wannan ba littafi bane, amma tarin papyri) shine Baibul na ilimin zamani. Gabaɗaya, Euclid ya tabbatar da ka'idoji 465.
8. Amfani da ka'idojin Euclid, Eratosthenes, wanda yayi aiki a Alexandria, shine farkon wanda ya fara kirga kewayen Duniya. Dangane da bambanci a tsayin inuwar da aka sanya ta sanda a tsakar rana a Alexandria da Siena (ba Italiyanci ba, amma Misirawa, yanzu garin Aswan), ma'aunin masu tafiya na nisa tsakanin waɗannan garuruwan. Eratosthenes ya karɓi sakamakon da yakai 4% kawai daga matakan yau.
9. Archimedes, wanda Alexandria ba bakuwa ba ce a wurin, duk da cewa an haife shi a Syracuse, ya ƙirƙira na'urori da yawa, amma ya ɗauki babbar nasarar da ya samu a matsayin lissafin adadin mazugi da wani fanni da aka rubuta a cikin silinda. Ofarar mazugi shine sulusi ɗaya na girman silinda, kuma ƙarar ƙwallon ƙwal biyu ne cikin uku.
Mutuwar Archimedes. "Kaura, kana rufa min Rana ..."
10. Ba daidai ba, amma ga karnin mulkin mallaka na mulkin mallaka na Rome, tare da dukkanin fasahar kere-kere da ilimin kimiyya a tsohuwar Rome, ba wata sabuwar ka'ida da aka tabbatar. Boethius ne kawai ya shiga cikin tarihi, yana ƙoƙarin tsara wani abu kamar saukakke, har ma da kyakkyawar gurɓatacciyar sigar "Abubuwa" don 'yan makaranta.
11. Zamanin duhu wadanda suka biyo bayan rugujewar Daular Rome suma sun shafi ilimin lissafi. Tunanin, kamar yadda yake, ya daskare na ɗaruruwan shekaru. A cikin karni na 13, Adelard na Bartheskiy ya fara fassara "Ka'idoji" zuwa Latin, kuma bayan shekaru dari Leonardo Fibonacci ya kawo lambobin larabci zuwa Turai.
Leonardo Fibonacci
12. Wanda ya fara kirkirar sararin samaniya a cikin yaren lambobi ya fara ne a karni na 17 Bafaranshe Rene Descartes. Ya kuma yi amfani da tsarin daidaitawa (Ptolemy ya san shi a cikin karni na 2) ba wai kawai ga taswirori ba, amma ga dukkanin adadi a cikin jirgin sama kuma ya kirkiro lissafin da ke kwatanta adadi mai sauki. Binciken da Descartes yayi a cikin ilimin lissafi ya bashi damar yin bincike da yawa a kimiyyar lissafi. A lokaci guda, saboda tsoron tsanantawa daga cocin, babban masanin lissafi har zuwa shekara 40 bai buga ko da aiki daya ba. Ya nuna cewa ya yi abin da ya dace - aikinsa tare da dogon take, wanda galibi ake kira "Tattaunawa kan Hanyar," ba kawai daga malamai ne kawai suka yi suka ba, har ma da takwarorinsa masu ilimin lissafi. Lokaci ya tabbatar da cewa Descartes yayi daidai, ko yaya yaranta shi.
René Descartes ya ji tsoron buga ayyukansa
13. Karl Gauss ya haifi mahaifin ba Euclidean geometry. Yayinda yake yaro, ya koya wa kansa karatu da rubutu, kuma sau ɗaya ya buge mahaifinsa ta hanyar gyara lissafin lissafinsa. A farkon karni na 19, ya rubuta wasu ayyuka a sararin samaniya, amma bai buga su ba. Yanzu masana kimiyya basa tsoron wutar binciken bincike, amma na masana falsafa. A wancan lokacin, duniya ta yi farin ciki da sukar da Kant na Dalilin Dalili, wanda marubucin ya roƙi masana kimiyya da su yi watsi da tsauraran dabaru su dogara da hankali.
Karl Gauss
14. A halin yanzu, Janos Boyai da Nikolai Lobachevsky suma sun ci gaba a cikin gutsuttsurar gutsuren ka'idar sararin da ba Euclidean ba. Boyai kuma ya aika aikinsa zuwa tebur, kawai yana rubutu game da ganowa ga abokai. Lobachevsky a 1830 ya buga aikinsa a cikin mujallar "Kazansky Vestnik". Kawai a cikin 1860s ne mabiyan suka sake dawo da tsarin aikin na ɗayan ɗayansu. A lokacin ne ya bayyana cewa Gauss, Boyai da Lobachevsky sunyi aiki a layi ɗaya, babu wanda ya saci komai daga kowa (kuma Lobachevsky a wani lokaci an danganta wannan), kuma na farko shine Gauss.
Nikolay Lobachevsky
15. Daga mahangar rayuwar yau da kullun, yawan geometries da aka kirkira bayan Gauss yayi kama da wasan kimiyya. Koyaya, wannan ba haka bane. Abubuwan da ba na Euclidean ba suna taimakawa warware matsaloli da yawa a cikin ilimin lissafi, lissafi da ilimin taurari.
