Nistabati du adad

Nistabati du adad, hosili taqsimest, ki dar natijai taqsim kardani adadi yakum ba adadi duyum hosil meshavad. Nisbati du buzurgii yakjinsa adadero memonad, ki hangomi buzurgii duyumro chun vohidi chenkuni qabul karda chen namudani buzurgii yakum hosil shudaast. Agar du buzurgi tavassuti yak vohidi chenkuni chen shuda boshand, Nisbati onho ba Nisbatii qimathoi adadii in buzurgiho barobar ast.

Nisbat-i darozihoi du porcharo bo adadhoi ratsionali yo irratsionali ifoda kardan mumkin ast. Dar mavridi yakum porchaho h a m ch e n a, dar mavridi duyum nohamchena nomida meshavand. Matematikoni qadim adadhoi irratsionaliro namodonistand. Onho nisbati du porcharo bo nisbati du adad ifoda namekardand. Nazariyai geometrii Nisbatii buzurgiho novobasta ba mafhumi adad roli mustaqil mebozid va yak andoza nazariyai adadhoi daqiqiro ivaz me­namud. Dar haqiqat, muvofiqi ta­limoti Evklid, agar baroi har guna adadhoi naturali t va p yake aa ta­nosubhoi ta = nb, ta > nb, ta <  nb muvofiqan bo yake az tanosubhoi ta’ = nb\ ma’>nb’ 8 ta'<,pb’ dar yak vaqt ijro shavand, porchahoi a, b, a’, b’ tanosubi a : b = a’: b’-ro tashkil medihand. Agar, porchahoi a va nohamchena boshand, in chunin mano dorad, ki ba du sinf judokunii majmui hamai adadhoi ratsionali (kh =m/n az rui alomati a > khb yo a < xb ba judokuni az rui alomati a’ > khb yo a’ = xb muvofiqat mekunad; goyai asosii nazariyai muosiri burishhoi dedekindi niz dar hamin ast.

Nisbati duchanda (murakkab yo angarmoniki)-i chor nuqta Mt, LG>, Mz, Mk dar khati rost (rasmi 1) adadest, ki bo simvoli (M M3MaMA) ishorat meshavad va ba M,M. Af,M«M.M, : MtMt barobar ast. Agar samti porchahoi L/|L/E va MMj yakkhela boshad, Nisbati M\M$/MgM2 musbat va agar samti in porchaho gunogun boshad, Nisbat manfi nomida meshavad. Nisbati duchanda ba tartibi numeratsiyai nuqtaho (ki az tartibi joygirshavii nuqtaho dar khati rost farq kardanash mumkin ast) vobasta meboshad. Dar qatori Nisbati duchandai chor nuqta Nisbatii duchandai chor khati rosti az nuqtai 0 guzarandai mi, m^, t3, t« muoina kar­da meshavad. In Nisbatro bo simvoli (to, ls t3 t4) ishorat mekunand. On ba

sin (D|Ya,)      sin (TO,41«)

sin (mm,) 1 sin (m.m,)

barobar ast, dar ayni hol kunji (mi ntj) bayni khathoi rosti m1 va rttj vobasta ba alomat muoina karda toe, to4 khoband, (rasmi 1) (M\ M2MMk) – (to, t2t3t4) act, az in sabab ham, agar nuqtahoi Mlt Mb Af>, Mt

dar natijai burishi chor khathoi rosti To|, toj, toz, t4 hosil shuda boshand (M/M2’M3’M/) = (DitMfM^i) meboshad. Va agar khathoi rosti mi, toz, Toj, to« va to/, l»a#, go3′, t/ chor nukta— AL, M M* Mgro proektironand (rasmi 2), (t/t/t^t/) «= — (^nim2m3^4) ast. Nisbati duchanda hangomi har guna tabdiloti proektivi niz betagyir memonad, yane inva­rianta hamin gula tabdilot meboshad, ki az in ru on dar geometriyai proektivi mavqei kalon dorad.