▁the ▁tang ent ▁vector ▁( see ▁graph ical ▁illustr ations ). ▁In ▁the ▁animated ▁figure ▁the ▁rotation ▁of ▁the ▁bin ormal ▁vector ▁is ▁clearly ▁visible ▁at ▁the ▁pe aks ▁of ▁the ▁t ors ion ▁function . ▁ ▁Properties ▁▁▁ ▁A ▁plane ▁curve ▁with ▁non - van ishing ▁curv ature ▁has ▁zero ▁t ors ion ▁at ▁all ▁points . ▁Con vers ely , ▁if ▁the ▁t ors ion ▁of ▁a ▁regular ▁curve ▁with ▁non - van ishing ▁curv ature ▁is ▁ident ically ▁zero , ▁then ▁this ▁curve ▁belongs ▁to ▁a ▁fixed ▁plane . ▁ ▁The ▁curv ature ▁and ▁the ▁t ors ion ▁of ▁a ▁hel ix ▁are ▁constant . ▁Con vers ely , ▁any ▁space ▁curve ▁whose ▁curv ature ▁and ▁t ors ion ▁are ▁both ▁constant ▁and ▁non - zero ▁is ▁a ▁hel ix . ▁The ▁t ors ion ▁is ▁positive ▁for ▁a ▁right - hand ed ▁hel ix ▁and ▁is ▁negative ▁for ▁a ▁left - hand ed ▁one . ▁ ▁Altern ative ▁description ▁▁ ▁Let ▁r ▁= ▁r ( t ) ▁be ▁the ▁paramet ric ▁equation ▁of ▁a ▁space ▁curve . ▁ ▁Assume ▁that ▁this ▁is ▁a ▁regular ▁paramet riz ation ▁and ▁that ▁the ▁curv ature ▁of ▁the ▁curve ▁does ▁not ▁van ish . ▁Anal yt ically , ▁r ( t ) ▁is ▁a ▁three ▁times ▁differenti able ▁function ▁of ▁t ▁with ▁values ▁in ▁R 3 ▁and ▁the ▁vectors ▁▁▁▁▁ ▁are ▁linear ly ▁independent . ▁ ▁Then ▁the ▁t ors ion ▁can ▁be ▁computed ▁from ▁the ▁following ▁formula : ▁ ▁Here ▁the ▁pr