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 |
---|---|
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 |