
twist (ganeet)

vibhedak bhoomitimadhye, 'ribbon' chaa valank mhanje tyachya aksheey firanyacha darr. fiti sootra _ 1 heey avkash vakr sootra _ 2 neey banalele asoo dya, jethe sootra _ 3 heey sootra _ 4 chee kamani lambi aahe, aanee sootra _ 5 heey eka ekak samanya vector aahe, jeey sootra _ 4 chya pratyek binduvar lumb aahe. fiti sootra _ 1 laa kadaa sootra _ 4 aanee sootra _ 9 asalyane, twist (kinwa "ekoon twist number") sootra _ 10 heey aksheey vakr sootra _ 4 chya bhovati aanee tyachya bajoone asalelya kaath vakr sootra _ 11 chya sarasari valanala mojate. prem (1944) nusar twist paribhashit kele aahe.
jethe sootra _ 14 heey sootra _ 4 chey ekak sparshika vahak aahe.
ekoon valane sankhya sootra _ 10 heey vighatit kele jaau shakate (mofat aanee rika 1992) "samanyikrut ekoon valane" sootra _ 17 aanee "aantarik valane" sootra _ 18 madhye
jethe sootra _ 20 heey avkash vakr sootra _ 4 chey valane aahe aanee sootra _ 22 heey sootra _ 4 sobat sootra _ 23 chaa ekoon firanyacha coone darshavite. sootra _ 25 kinwa sootra _ 10 heey ribbon kshetra sootra _ 23 pasoon swatantra naheet. tyaeivaji, fakt samanyikrut valane sootra _ 28 heey vakr sootra _ 4 chey aparivartaniy aahe (banchoff aanee white 1975).
jevha fiti vikrut kelee jaate jenekarun tee 'pratikshep avasthetun' (i.eae. sootra _ 4 madhye eka vichalan bindu aahe), valanache sootra _ 31 ekvachan banate. ekoon tortion sootra _ 28 sootra _ 33 neey udee marte aanee ekoon coone sootra _ 25 ekach velee sootra _ 35 (mofat aanee rika 1992) chee samaan aanee viruddha udee marte aanee sootra _ 10 akhand rahate. yaa vartanache vidnyanachya anek kshetrantil urjechya vicharansathi anek mahattvache parinam aahet (1997,2005; 2006).
sootra _ 4 chya reith sootra _ 37 saha, twist heey eka bhaumitik praman aahe jeey topological drav gatishilatemadhye (vector kshetrachya gatiman aanee chumbakeey helicityshi tyachya jawalchya sambandhasathi), bhautik gaath siddhant aanee sanrachanatmak jatilata vishleshanamadhye calugrenu-pandhare-purn sootra sootra _ 39 chya vaparat mahattvachi bhoomika bajavate.