To share the same tangent and curvature and at a given point, as in the case of two osculating curves. For example the curve y = x2 and the x-axis osculate at the origin. Found on http://www.daviddarling.info/encyclopedia/O/osculating.html
osculate, osculating, osculated 1. To touch with the lips or to press the lips (against someone's mouth or other body part) as an expression of love, greeting, etc. 2. To touch with the lips or to press the lips (against someone's mouth or other body part) as an expression of love, greeting, etc.: 'The newly married couple kissed', 'Her grandfathe... Found on http://www.wordinfo.info/words/index/info/view_unit/1524/