Ia laua i ka pelane: keʻano a me ka waiwai

Ia laua i ka pelane mea he manaʻo ike mua ia i loko o ka Euclidean anahonua no elua tausani oi aku makahiki aku nei.

Main ano o ka panina anahonua

I ka hanau ana o keia scientific mau pili me ka kaulana hana o kahiko Helene poe akeakamai Euclid, nana i kakau iho i loko o ke kolu o ke kenekulia BC, ka pepelu "hehee wale". Maheleia i heʻumikumamākolu mau buke, "hehee wale" o ka mea kiʻekiʻe loa e piʻi like o nā mea a pau kahiko makemakika, a hoakaka pono aku i ka pono kīvila kanaka tenets pili i ka waiwai o ka pelane huahelu.

Ua ua kālaiʻia panina ke ano o ka laua Kekoa like penei: elua Kekoa i ke kapa ia laua ina ka mea, kela mea keia mea i ole, he pono ole ka papa. Ua heluhelu Euclidean lima o ka postulate hana.

Waiwai o laua Kekoa

Ka Euclidean anahonua o kaʻawale, IeAUPIIe, IAa IOʻelima:

• Ka waiwai o ka mua (a me laua a hiki i ka pelane wehewehe lākou kū hoʻokahi). Ma he hookahi wahi, e waiho nei ma waho o kēia mau pelane, ua hiki ke kauo i kekahi a me kekahi wale laua pelane

• Ka lua o ka waiwai (iʻikeʻia e like me ka waiwai triplicate). Ma ka hihia ma ka Kekoa mau mea ia laua me ka manao i ke kolu, ma waena o lakou iho, ka mea, e hoi laua.

• Kolu o ka waiwai (i loko o nā hua'ōlelo, ka mea, ua kapaʻia he waiwai laina intersecting ia laua i ka pelane). Inā lawe kaawale pololei laina nā keʻa i kekahi o kēia mau laua Kekoa, ka mea, e kapa a me kekahi.

• Ha o ka waiwai (waiwai o ka pololei laina kiʻi kālaiʻia ma luna o Kekoa ia laua i kekahi i kekahi). Ka wā mau laua Kekoa intersect ke kolu (mai kekahi huina), a me kā lākou mau laina o ke kuʻina i ia laua

• Lima o ka waiwai (i ka waiwai e hōʻike ana i nā Hoʻohana likeʻole o laua pololei laina, a moe ma waena o nā Kekoa laua i kekahi i kekahi). Ka Hoʻohana o ka laua laina, a i puni iho la ma waena o elua laua Kekoa pono kaulike.

Ia laua i ka pelane ma ka ole-Euclidean anahonua

Oia i kokoke e hiki aku i ka pau o ka anahonua o Lobachevsky a me Riemann. Inā Euclidean anahonua ua hoʻokō ma ka palahalaha hakahaka, laila Lobachevsky ma negatively uma hakahaka (uma wale i), iā Riemann e loaa kona hoʻi i ikaika uma hakahaka (i loko o nā hua'ōlelo - mau mea). Aia ka he loa, he pono ole stereotypical nānaina i Lobachevsky ia laua i ka pelane, (a me kekahi laina) intersect. Naʻe, i kēia mea,ʻaʻole oiaio. He oiaio o ka hanau ana o hyperbolic anahonua i pili me ka maopopo o Euclid ka lima o ka postulate a me ka hoʻololi 'ike ma luna o laila, akā, no ka nui loa ka wehewehena o laua Kekoa a me ka pololei laina o ia hoʻi, i ka mea hiki ole i kela kapa, aole hoi Lobachevsky aole hoi Riemann, ma na mea a hakahaka ka mea, e hoʻokō. A loli o ka naau a me ka hua'ōlelo mea like penei. I wahi o ka postulate i hoʻokahi wale laua pelane hiki e holo ana ma kekahi wahi,ʻaʻole ma luna o ka haawiia pelane, hele mai la kekahi hoʻomanaʻo: ma kekahi wahi e pili ole moe ma luna o kēia mau pelane hiki ke lawe i elua, ma ka liʻiliʻi loa, pololei, ka mea i loko o kekahi pelane me keia, a mai kela kapa ia.