Dotik (matematika)

Dotik je v matematiki določen kot način stika dveh krivulj. Dotik običajno definiramo za posamezne točke v stopnjah reda , ki povedo do katere stopnje so odvodi enaki in kjer ima krivulja isto vrednost. Dotik reda dane funkcije je ekvivalenčna relacija.

Kontaktne forme so posebne diferencialne forme s stopnjo 1 v neparno razsežnih mnogoterostih.

Dotiki med mnogoterostimi se proučujejo v teoriji singularnosti, kjer so dotiki razvrščeni.

Vrste dotikov dveh krivulj

Za dve ravninski krivulji, ki se sekata v točki pravimo, da je njun dotik

  • 1-točkovni, če se krivulji samo sekata
  • 2-točkovni, če sta druga drugi tangenta
  • 3-točkovni, če sta krivulji enaki. Za take krivulje pravimo, da sta pritisnjeni krivulji (oskulatorni).
  • 4-točkovni, če so odvodi obeh krivulj enaki
  • 5-točkovni, če so drugi odvodi obeh krivulj enaki

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