Kū mākou i ka geometry i kēlā me kēia kekona me ka nānā ʻole ʻole iā ia. ʻO nā ana a me nā mamao, nā lauana a me nā alaloa nā mea he geometry āpau. ʻO ka manaʻo o ka helu π ʻike ʻia i nā poʻe geeks ma ke kula mai ka geometry, a ʻo ka poʻe, e ʻike nei i kēia helu, ʻaʻole hiki ke helu i ka ʻāpana o kahi pōʻai. Nui paha ka ʻike mai ka māla o ka geometry ma ke ʻano he kula haʻahaʻa - ʻike nā mea āpau ʻo ke ala pōkole loa ma o ka ʻāpana huinahā aia ma ka diagonal. Akā i mea e hoʻokumu ai i kēia ʻike ma ke ʻano o ka theorem Pythagorean, ua lawe ʻia ke kanaka i mau makahiki he mau makahiki. ʻO Geometry, e like me nā ʻepekema ʻē aʻe, ua ulu kūpono ʻole. Ua kuapo ʻia ka ʻāʻī ʻoi loa ma Helene Helene e ka stagnation o ʻEloma Roma, a ua hoʻololi ʻia e nā wā pouli. Ua hoʻololi ʻia kahi ʻōlapa hou i ka wā waena e ka pahū maoli o nā kenekulia 19 a me 20. Mai kahi ʻepekema noi, ua lilo ka geometry i kahua o ka ʻike kiʻekiʻe, a hoʻomau ʻia kona ulu. Ua hoʻomaka me ka helu ʻana i nā ʻauhau a me nā pyramids ...
1. Maliʻa paha, hoʻomohala ʻia ka ʻike geometrical mua e ko ʻAigupita kahiko. Noho lākou ma nā lepo momona i hoʻopiha ʻia e ka Nile. Ua uku ʻia nā ʻauhau mai ka ʻāina i loaʻa, a no kēia mea pono ʻoe e helu i kona wahi. Ua aʻo ka ʻāpana o ka square a me ka huinahā helu i ka helu empirically, ma muli o nā kiʻi liʻiliʻi like. A lawe ʻia ka pōʻai ma ke ʻano he square, a ʻo nā ʻaoʻao o lākou he 8/9 o ke anawaena. ʻO ka helu o ka π ma kēia hihia ma kahi o 3.16 - kahi pololei kūpono.
2. Ua kapa ʻia ko ʻAigupita e hana ana i ka geometry o ke kūkulu ʻana i kapa ʻia ʻo harpedonapts (mai ka huaʻōlelo "kaula"). ʻAʻole hiki iā lākou ke hana iā lākou iho - pono lākou i nā kauā kōkua, ʻoiai e māka i nā ʻilikai he mea pono e kī i nā kaula o nā lōʻihi like ʻole.
ʻAʻole ʻike ka poʻe kūkulu pyramid i ko lākou kiʻekiʻe
3. ʻO ka poʻe Babulona ka mea mua i hoʻohana i ka mīkini makemakika no ka hoʻoponopono ʻana i nā pilikia geometric. Ua ʻike mua lākou i ka theorem, a ma hope e kapa ʻia ʻo Thethem Pythagorean. Ua kākau nā Babulona i nā hana āpau i nā huaʻōlelo, a hoʻoluhi loa iā lākou (ma hope o nā mea āpau, ʻo ka hōʻailona "+" i hōʻike wale ʻia i ka hopena o ke kenekulia 15). A hana nō naʻe ka geometry Babulona.
4. ʻO Thales o Miletus i ʻōnaehana i ka ʻike geometric o ka manawa liʻiliʻi. Ua kūkulu ko ʻAigupita i nā pyramid, akā ʻaʻole lākou i ʻike i ko lākou kiʻekiʻe, a ua hiki iā Thales ke ana iā ia. Ma mua o Euclid, ua hōʻoia ʻo ia i nā theometric geometric mua. Akā, malia paha, ʻo ka hāʻawi nui a Thales i ka geometry ke kamaʻilio pū me nā ʻōpio Pythagoras. ʻO kēia kāne, i ka wā ʻelemakule, ua hana hou i ke mele e pili ana i kāna hui ʻana me Thales a me kona ʻano no Pythagoras. A ʻo kekahi haumāna a Thales i kapa ʻia ʻo Anaximander i kaha kiʻi i ka palapala ʻāina mua o ka honua.
ʻO Thales o Miletus
5. I ka hōʻoia ʻana o Pythagoras i kāna theorem, i ke kūkulu ʻana i kahi huinakolu kihi me nā ʻaoʻao ma kona ʻaoʻao, no ka nui o kona pūʻiwa a me ka pīhoihoi o nā haumāna, ua hoʻoholo nā haumāna ua ʻike ʻia ka honua, waiho wale ia e wehewehe me nā helu. ʻAʻole hele mamao ʻo Pythagoras - ua hana ʻo ia i nā manaʻomanaʻo helu he nui i pili ʻole i ka ʻepekema a i ʻole ke ola maoli.
ʻO Pythagoras
6. I ka hoʻāʻo ʻana e hoʻoponopono i ka pilikia o ka loaʻa ʻana o ka lōʻihi o ka diagonal o ka square me ka ʻaoʻao 1, ua ʻike ʻo Pythagoras a me kāna mau haumāna ʻaʻole hiki ke hōʻike ʻia kēia lōʻihi i kahi helu palena. Eia nō naʻe, ikaika loa ka mana o Pythagoras ua pāpā ʻo ia i nā haumāna e hōʻike i kēia ʻoiaʻiʻo. ʻAʻole hoʻolohe ʻo Hippasus i ke kumu a ua pepehi ʻia e kekahi o nā mea ukali ʻē aʻe o Pythagoras.
7. ʻO Euclid ka hāʻawi nui a koʻikoʻi i ka geometry. ʻO ia ka mea mua i hoʻolauna i nā huaʻōlelo maʻalahi, mōakāka a maopopo ʻole hoʻi. Ua wehewehe ʻo Euclid i nā postulate o ka geometry i hiki ʻole ke haʻalulu (kapa mākou iā lākou he axioms) a hoʻomaka i ka hoʻohaʻahaʻa kūpono ʻana i nā mea ʻepekema ʻē aʻe, e pili ana i kēia mau postulate. ʻO kā Euclid puke "Nā Hoʻomaka" (ʻoiai ke kamaʻilio paʻa ʻana, ʻaʻole kēia he puke, akā he hōʻuluʻulu papyri) ka Baibala o ka geometry o kēia au. I ka hōʻuluʻulu ʻana, ua hōʻoia ʻo Euclid i nā moʻolelo he 465.
8. Me ka hoʻohana ʻana i nā moʻolelo a Euclid, ʻo Eratosthenes, ka mea hana ma Alexandria, ka mea mua e helu i ke anapuni o ka Honua. Ma muli o ka ʻokoʻa o ke kiʻekiʻe o ke aka i hoʻolei ʻia e kahi lāʻau i ke awakea ma Alexandria a me Siena (ʻaʻole Italia, akā ʻo ʻAigupita, ke kūlanakauhale ʻo Aswan), ke ana hele wāwae o ka mamao ma waena o kēia mau kūlanakauhale. Ua loaʻa iā Eratosthenes kahi hopena he 4% wale nō ia mai nā ana o kēia manawa.
9. ʻO Archimedes, ʻaʻole malihini ʻo Alexandria, ʻoiai ʻo ia i hānau ʻia ma Syracuse, ua hana ʻo ia i nā mīkini mechanical he nui, akā ua manaʻo ʻo ia ka mea nui i loaʻa i ka helu ʻana o nā puke o ka puʻupuʻu a me kahi sphere i kākau ʻia i loko o ka pahu. ʻO ka leo o ke kone he hapakolu ia o ka nui o ka paukū, a ʻo ka nui o ke kinipōpō he ʻekolu hapakolu ia.
Make o Archimedes. "E neʻe aku, ke uhi nei ʻoe i ka lā noʻu ..."
10. Kupanaha, akā, no ka milenio o ko Roma noho aliʻi ʻana o ka geometry, me ka ulu pono ʻana o nā hana noʻeau a me nā ʻepekema i Roma kahiko, ʻaʻole i hōʻike ʻia kahi theorem hou. ʻO Boethius wale nō ka mea i iho i lalo i ka mōʻaukala, e hoʻāʻo nei e haku i kekahi mea e like me ka māmā, a ʻano ʻokoʻa hoʻi, ka mana o nā "Element" no nā keiki kula.
11. ʻO nā makahiki ʻeleʻele i ukali i ka hāʻule ʻana o ka Emepaea Roma e hoʻopili pū i ka geometry ʻO ka manaʻo, me he mea lā, ua paʻa i nā haneli mau makahiki. I ke kenekulia 13, ua unuhi mua ʻo Adelard o Bartheskiy i ka Beginnings i ka Lākina, a hoʻokahi haneli mau makahiki ma hope mai ua lawe ʻo Leonardo Fibonacci i nā helu ʻAlapia i ʻEulopa.
Leonardo Fibonacci
12. ʻO ka mea mua i hana i nā wehewehe ʻana o ke ākea i ka ʻōlelo o nā helu i hoʻomaka ʻia i ka kenekulia 17 o French Rene Descartes. Ua noi ʻo ia i ka ʻōnaehana hoʻohui (ʻike ʻo Ptolemy iā ia i ka kenekulia 2) ʻaʻole wale i nā palapala ʻāina, akā i nā kiʻi āpau ma kahi mokulele a hana i nā kaulike e wehewehe ana i nā kiʻi maʻalahi. ʻO nā ʻike a Descartes i ka geometry i ʻae iā ia e hana i nā ʻike i loko o ka physics. I ka manawa like, makaʻu i ka hoʻomāinoino ʻia e ka hale pule, ʻaʻole hoʻolaha ka makemakika nui a hiki i ka makahiki 40 i kahi hana hoʻokahi. Ua ʻike ʻo ia e hana ana i ka mea kūpono - kāna hana me kahi poʻo inoa lōʻihi, i kapa pinepine ʻia ʻo "Discourse on Method," ʻaʻole i hoʻopiʻi wale ʻia e nā mea pule, akā na nā hoa makemakika. Ua hōʻoia ka manawa pono ʻo Descartes, no ke ʻano o ke kani.
Ua makaʻu ʻo René Descartes e hoʻopuka i kāna mau hana
13. ʻO Karl Gauss ka makua kāne o ka non-Euclidean geometry. I ke keikikāne, ua aʻo kūʻokoʻa ʻo ia i ka heluhelu a me ke kākau ʻana, a hahau ʻia kona makuakāne i ka hoʻoponopono ʻana i kāna helu helu helu. I ke kenekulia 19 mua, ua kākau ʻo ia i nā hana he nui ma kahi ākea, ʻaʻole naʻe i paʻi ʻia. ʻAʻole makaʻu ka poʻe ʻepekema i ke ahi o ka Inekuisitio, akā no nā akeakamai. I kēlā manawa, ua hauʻoli ka honua me ka Critique a Kant no ke Kumu Maʻemaʻe, kahi a ka mea kākau i koi aku ai i nā ʻepekema e haʻalele i nā hana koʻikoʻi a hilinaʻi i ka naʻau.
Karl Gauss
14. I kēia manawa, ua hoʻomohala pū ʻo Janos Bolyai a me Nikolai Lobachevsky i nā ʻāpana like o ke kumumanaʻo o ka wahi non-Euclidean. Ua hoʻouna pū ʻo Boyai i kāna hana i ka papaʻaina, kākau wale nō e pili ana i ka ʻike i nā hoa aloha. Ua hoʻopuka ʻo Lobachevsky i ka makahiki 1830 i kāna hana ma ka makasina "Kazansky Vestnik". I nā makahiki 1860 wale nō e hoʻihoʻi ai ka poʻe i ka papa manawa o nā hana o ke kolu holoʻokoʻa. ʻO ia ka manawa i hoʻololi ʻia ua hana like ʻo Gauss, Boyai a me Lobachevsky, ʻaʻohe mea i ʻaihue i kekahi mea mai kekahi (a ʻo Lobachevsky kekahi manawa i manaʻo ʻia), a ʻo Gauss ka mea mua.
ʻO Nikolay Lobachevsky
15. Mai ke kuanaʻike o ke ola o kēlā me kēia lā, ʻo ka nui o nā geometry i hana ʻia ma hope o Gauss e like me ka pāʻani o ka ʻepekema. Eia naʻe, ʻaʻole kēia ka hihia. Kōkua nā geometry Non-Euclidean i ka hoʻoponopono ʻana i nā pilikia he nui i ka makemakika, ke kālaikūlohea a me ka hōkū.
