
leanier space (jyaamiti)

leanier space anedi insidence jyaamitiloo praathamika nirmaanam. oka sarala sthalamlo paayintlu anie piluvabade muulakaala samiti mariyu panktulu anie piluvabade muulakaala samiti untaayi. prati pankthi paayintla yokka pratyaekamaina upasamiti. oka rekhaloni paayintlu rekhatho sanghatanagaa cheppabadataayi. prati rendu paayintlu oka linelo untaayi, mariyu edainaa rendu linelu oka point kante ekkuva ummadigaa undakapovachhu. antarbodhagaa, eee niyamanni rendu sarala rekhalu ennatikee okati kante ekkuvasaarlu kalusukoni lakshanamgaa chudavachu. 
leanier spacelanu projective mariyu affine plains yokka saadhaaraneekaranagaa chudavachu, mariyu marinta vistrutamgaa, 2-formula _ 1 block designla yokka saadhaaraneekaranagaa chudavachu, ikkada prati block oke sankhyalo paayintlanu kaligi undaalsina avasaram tagginchabadutundi mariyu avasaramaina nirmaana lakshanam emitante 2 paayintlu sarigga 1 line thoo sanghatana. 
leanier space" anae padaanni 1964loe paal libois roopondinchaaru, ayithe leanier space gurinchi aneka phalitaalu chaalaa paatavi.
nirvachanam.
l" = ("p", "g", "i") anedi oka insidence structure, dheeni kosam "p" looni elements nii points anie mariyu "g" looni elements nii lines anie pilustaaru. "eee krindi moodu suutraalu kaligi unte "l" anedi "leanier space":
kontamandi rachayitalu leanier spacelanu nirvachinchetappudu (l3) nuu vadulutaaru. atuvanti paristhitiloo (l3) kuu anugunamgaa unde sarala khaaliilu "chinnavi kaavu" mariyu laenivi "chinnavi" gaa pariganinchabadataayi.
udaaharanalu.
daani binduvulu mariyu rekhalatho saadhaarana euclidean plain oka sarala sthalaanni kaligi untundi, antekakunda anni anubandha mariyu prakshepaka pradaesaalu kooda sarala pradaesaalu.
diguva pattika aidu paayintla saadhyamayye anni chinna sarala khaaliilu chooputundi. edainaa rendu paayintlu ellappuduu oka rekhatho sanghatanagaa untaayi kabatti, rendu paayintlatho matrame sanghatanagaa unna rekhalu sampradaayam prakaram geeyabadavu. chinna vishayam kevalam aidu paayintla dwara oka rekha.
modati drushtaamtamlo, padhi jatala paayintlanu kalipe padhi panktulu geeyabadaledu. rendava drushtaamtamlo, edu jatala paayintlanu kalipe edu panktulu geeyabadaledu. 
n"-1 paayintlatho oka rekhanu kaligi unna "n" paayintla yokka sarala sthalaanni "nier pensil" antaaru. (pensil chudandi)
aastulu.
dii bruyne-erdos siddhaantam, yea parimita sarala antariksha suutram _ 2 loe, idhi okka binduvu ledhaa oke rekha kaadu, manaku suutram _ 3 undani choopistundi.