order of contact
Suppose that and are smooth curves in which pass through a common point . We say that and have zeroth order contact if their tangents at are distinct.
Suppose that and are tangent at . We may then set up a coordinate system in which is the origin and the axis is tangent to both curves. By the implicit function theorem, there will be a neighborhood of such that can be described parametrically as with and can be described parametrically as with . We then define the order of contact of and at to be the largest integer such that all partial derivatives of and of order not greater than at are equal.
Title | order of contact |
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Canonical name | OrderOfContact |
Date of creation | 2013-03-22 16:59:49 |
Last modified on | 2013-03-22 16:59:49 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 4 |
Author | rspuzio (6075) |
Entry type | Definition |
Classification | msc 53A04 |
Synonym | order contact |