Main Page | See live article | Alphabetical index 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. 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. Contact forms are particular differential forms of degree 1 on odd-dimensional manifolds. Contact transformations are related changes of co-ordinates, of importance in classical mechanics. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.