Sihlangabezana ne-geometry njalo ngomzuzwana ngaphandle kokukunaka. Ubukhulu namabanga, ubujamo kanye nama-trajectories konke kuyi-geometry. Incazelo yenombolo π yaziwa ngisho nangalabo ababengama-geeks esikoleni kusuka ku-geometry, futhi labo, ngokwazi le nombolo, abakwazi ukubala indawo yombuthano. Ulwazi oluningi oluvela emkhakheni weJiyomethri lungahle lubonakale luyisisekelo - wonke umuntu uyazi ukuthi indlela emfushane kakhulu engxenyeni engunxande iku-diagonal. Kepha ukwenza lolu lwazi ngesimo semfundiso kaPythagoras, kwathatha iminyaka eyizinkulungwane zesintu. IJiyomethri, njengamanye amasayensi, ithuthuke ngokungalingani. Ukwanda okucijile eGrisi lasendulo kwathathelwa indawo ukuma kweRoma lasendulo, okwathathelwa indawo yiNkathi Yobumnyama. Ukuqhuma okusha eNkathini Ephakathi kwathathelwa indawo ukuqhuma kwangempela kwekhulu le-19 - lama-20. IJiyomethri isukile kwisayensi esetshenzisiwe yaya emkhakheni wolwazi oluphakeme, futhi ukukhula kwayo kuyaqhubeka. Futhi konke kwaqala ngokubalwa kwentela kanye nemipiramidi ...
1. Cishe, ulwazi lokuqala lwejometri lwakhiwa ngabaseGibhithe lasendulo. Bazinza enhlabathini evundile ekhukhulwe yiNayile. Izintela zakhokhwa emhlabeni otholakalayo, futhi ngalokhu udinga ukubala indawo yakhona. Indawo yesikwele nonxande ifunde ukubala ngokwamandla, kususelwa kumanani amancane afanayo. Futhi isiyingi sathathwa saba yisikwele, izinhlangothi zaso zingu-8/9 wobubanzi. Ngasikhathi sinye, inani le-π lalicishe libe ngu-3.16 - ukunemba okuhle impela.
2. AbaseGibhithe ababenza i-geometry yokwakha babizwa ngama-harpedonapts (kusuka egameni elithi "intambo"). Abakwazanga ukuzisebenzela ngokwabo - babedinga izigqila ezisizayo, ngoba ukumaka indawo kwakudingeka ukwelula izintambo zobude obuhlukile.
Abakhi bephiramidi babengazi ukuphakama kwabo
3. AbaseBabiloni baba ngabokuqala ukusebenzisa izinsizakusebenza zezibalo ukuxazulula izinkinga zejometri. Babevele beyazi i-theorem, eyayizobizwa kamuva ngokuthi yiPythagorean Theorem. AbaseBabiloni babhala yonke imisebenzi ngamagama, okuyenza ibe nzima kakhulu (ngemuva kwakho konke, uphawu "+" lwavela kuphela ngasekupheleni kwekhulu le-15). Noma kunjalo i-geometry yaseBabiloni yasebenza.
4. IThales of Miletsky yahlela ulwazi oluncane lwejometri ngaleso sikhathi. AbaseGibhithe bakha amapiramidi, kepha babengazi ukuphakama kwabo, kanti uThales wakwazi ukukulinganisa. Ngisho nangaphambi kuka-Euclid, wafakazela ama-theorems wokuqala we-geometric. Kepha, mhlawumbe, umnikelo omkhulu weThales ku-geometry kwakuwukuxhumana nePythagoras encane. Le ndoda, ebisivele igugile, iyiphindile le ngoma emayelana nokuhlangana kwayo noThales nokubaluleka kwayo kuPythagoras. Futhi omunye umfundi waseThales ogama lakhe lingu-Anaximander wadweba ibalazwe lokuqala lomhlaba.
UThales waseMilethu
5. Ngenkathi uPythagoras efakazela umbono wakhe, wakha unxantathu ohlangothini olungakwesokudla onezikwele ezinhlangothini, ukushaqeka nokwethuka kwakhe kwaba kukhulu kangangokuba abafundi banquma ukuthi umhlaba usuyaziwa vele, kwasala ukuwuchaza ngezibalo. UPythagoras akazange aye kude - wadala izinkolelo-mbono eziningi zezinombolo ezingahlangene nakancane nesayensi noma nempilo yangempela.
AmaPythagoras
6. Ngemuva kokuzama ukuxazulula inkinga yokuthola ubude bedayagonali yesikwele nohlangothi 1, uPythagoras nabafundi bakhe babona ukuthi ngeke bakwazi ukuveza lobude ngenombolo enomkhawulo. Kodwa-ke, igunya likaPythagoras lalinamandla kangangokuba wabenqabela abafundi ukuthi badalule leli qiniso. UHippasus akazange amlalele lo thisha futhi wabulawa ngomunye wabalandeli bakaPythagoras.
7. Umnikelo obaluleke kakhulu kwi-geometry wenziwa ngu-Euclid. Ubengowokuqala ukwethula amagama alula, acacile nacacile. U-Euclid uphinde wachaza iziqu ze-geometry ezinganyakazi. Incwadi kaEuclid ethi "Beginnings" (yize ikhuluma ngokuqinile, ayiyona incwadi, kodwa iqoqo lamapapiri) yiBhayibheli le-geometry yanamuhla. Sekukonke, u-Euclid wafakazela ama-theorems angama-465.
8. Esebenzisa imibono ka-Euclid, u-Eratosthenes, owayesebenza e-Alexandria, waba ngowokuqala ukubala ukuzungeza koMhlaba. Ngokuya ngomehluko wobude besithunzi esenziwe yinduku emini e-Alexandria naseSiena (hhayi eyase-Italy, kepha eyaseGibhithe, manje eyidolobha lase-Aswan), isilinganiso sabantu abahamba ngezinyawo sebanga eliphakathi kwale mizi. U-Eratosthenes uthole umphumela ohluke kuphela ngama-4% kuzilinganiso zamanje.
9. U-Archimedes, i-Alexandria ayengamazi, yize azalelwa eSyrause, wasungula imishini eminingi, kepha wabheka impumelelo yakhe enkulu njengokubalwa kwamavolontiya wesigaxa nembulunga ebhalwe kwisilinda. Umthamo wesigaxa uyingxenye eyodwa kwezintathu yevolumu yesilinda, futhi ivolumu yebhola yizingxenye ezimbili kwezintathu.
Ukufa kuka-Archimedes. "Suka, ungimbozela iLanga ..."
10. Ngokumangazayo, kodwa eminyakeni eyinkulungwane yokubusa kwamaJiyomethri amaRoma, nakho konke ukuchuma kwezobuciko nesayensi eRoma lasendulo, akubanga khona neyodwa inkolelo-mbono entsha. NguBoethius kuphela owangena emlandweni, ezama ukuqamba into efana ne-lightweight, futhi ehlanekezelwe kakhulu, inguqulo ye- "Elements" yezingane zesikole.
11. Iminyaka yobumnyama eyalandela ukuwa koMbuso WaseRoma nayo yathinta iJiyomethri. Umcabango wabonakala sengathi uzoba amakhaza amakhulu eminyaka. Ngekhulu le-13, u-Adelard waseBartheskiy wahumushela okokuqala isiQalo esiLatin, kwathi eminyakeni eyikhulu kamuva uLeonardo Fibonacci waletha izinombolo zesi-Arabhu eYurophu.
ULeonardo Fibonacci
12. Owokuqala ukudala izincazelo zesikhala ngolimi lwezinombolo waqala ngekhulu le-17 leFulentshi uRene Descartes. Ubuye wasebenzisa uhlelo lokuxhumanisa (uPtolemy wayazi ngekhulu lesi-2) hhayi kumamephu kuphela, kodwa kuzo zonke izibalo ezisendizeni futhi wenza izibalo ezichaza izibalo ezilula. Ukutholwa kukaDescartes ku-geometry kwamvumela ukuthi enze izinto eziningi ezitholakele ku-physics. Ngasikhathi sinye, esaba ukushushiswa yisonto, isazi sezibalo esikhulu kuze kube yiminyaka engama-40 asizange sishicilele umsebenzi owodwa. Kuvele ukuthi ubenza into efanele - umsebenzi wakhe onesihloko eside, esivame ukubizwa nge- “Discourse on Method,” wagxekwa hhayi kuphela ngabantu besonto, kodwa nangabanye abasebenza ngezibalo. Isikhathi sikhombisile ukuthi uDescartes wayeqinisile, noma ngabe kuzwakala kukuncane kangakanani.
URené Descartes wesaba ngokufanele ukushicilela imisebenzi yakhe
13. UKarl Gauss waba nguyise we-non-Euclidean geometry. Njengomfana, wafunda ngokuzimela ukufunda nokubhala, futhi wake washaya uyise ngokulungisa izibalo zakhe zokubalwa kwezimali. Ekuqaleni kwekhulu le-19, wabhala imisebenzi eminingi esikhaleni esigobile, kepha akazange ayishicilele. Manje ososayensi babengesabi umlilo Wokuqulwa Kwamacala Ezihlubuki, kodwa izazi zefilosofi. Ngaleso sikhathi, umhlaba wajabula nge-Kant's Critique of Pure Reason, lapho umlobi anxusa ososayensi ukuthi balahle amafomula aqinile futhi bathembele ku-intuition.
UKarl Gauss
14. Khonamanjalo, uJanos Boyai noNikolai Lobachevsky nabo bathuthukisa izingcezu ezifanayo zemfundiso yesikhala esingesona se-Euclidean. UBoyai naye wathumela umsebenzi wakhe etafuleni, ebhala kuphela ngokutholwa lokhu kubangani. ULobachevsky ngo-1830 washicilela umsebenzi wakhe kumagazini othi "Kazansky Vestnik". Ngawo-1860s kuphela lapho abalandeli kwakudingeka babuyisele ukulandelana kwezikhathi zemisebenzi yothathu emunye. Kungaleso sikhathi lapho kwacaca khona ukuthi uGauss, uBoyai noLobachevsky basebenza ngasikhathi sinye, akekho owebela umuntu noma yini (futhi uLobachevsky wake wabizwa ngalokhu), kanti owokuqala wayesenguGauss.
UNikolay Lobachevsky
15. Ngokombono wempilo yansuku zonke, ubuningi bamajometri adalwe ngemuva kukaGauss ubukeka njengomdlalo wesayensi. Kodwa-ke, akunjalo. Ama-geometri angewona ama-Euclidean asiza ukuxazulula izinkinga eziningi kwi-mathematics, physics kanye ne-astronomy.
