Summary: S#ntomh istorik# eisagwg#
H uperbolik# gewmetr#a dhmiourg#jhke sto pr#to mis# tou 19ou ai#na kat# thn pro­
sp#jeia katan#hshc twn eukle#deiwn axiwm#twn thc t#te gnwst#c gewmetr#ac. E#nai #nac
t#poc mh­eukle#deiac gewmetr#ac, dhlad# e#nai mia gewmetr#a pou den ikanopoie# #na ap#
ta ait#mata tou Eukle#dh, to a#thma thc #parxhc twn parall#lwn eujei#n. Oi Einstein
kai Minkowski br#kan sthn uperbolik# gewmetr#a to gewmetrik# up#bajro gia thn kata­
n#hsh tou fusiko# q#rou kai tou qr#nou. Ta pr#ta qr#nia tou 20ou ai#na h uperbolik#
gewmetr#a ejewre#to basik# gn#sh gia touc majhmatiko#c kai touc fusiko#c.
H uperbolik# gewmetr#a e#nai to arqetupik# par#deigma miac gewmetr#ac me arnhti­
k# kampul#thta. Auto# tou e#douc oi gewmetr#ec e#nai exairetik# koin#c kai #qoun so­
bar#c efarmog#c sthn jewr#a twn migadik#n sunart#sewn, sthn topolog#a twn 2­ kai
3­pollaplot#twn, sthn jewr#a twn peperasm#na parast#simwn #peirwn om#dwn, sthn
Fusik# kai se #llec di#spartec perioq#c twn Majhmatik#n.
Ta ait#mata tou Eukle#dh me s#gqronh orolog#a e#nai ta ak#louja :
1. D#o diaforetik# shme#a mporo#n na sundejo#n me #na akrib#c euj#grammo tm#ma.
2. K#je euj#grammo tm#ma mpore# na epektaje# aperi#rista kai proc tic d#o kateu­
j#nseic.
3. Gia k#je shme#o up#rqei akrib#c #nac k#kloc me k#ntro to shme#o aut# kai dedom#nh
akt#na.
4. Olec oi orj#c gwn#ec e#nai #sec.

Source: Athanassopoulos, Konstantin - Department of Mathematics, University of Crete

Collections: Mathematics