Contact (mathematics)
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In mathematics, contact of order k of functions is an equivalence relation, corresponding to having the same value at a point P and also the same derivatives there, up to order k. Equivalence classes are generally called jets.
One speaks also of curves and geometric objects having k-th order contact at a point: this is also called osculation (i.e. kissing), generalising the property of being tangent. See for example osculating circle.
Contact forms are particular differential forms of degree 1 on odd-dimensional manifolds; see contact geometry. Contact transformations are related changes of co-ordinates, of importance in classical mechanics. See also Legendre transformation.