Osculate is a formal or humorous word for kiss: The couple osculated briefly before parting.
In mathematics and geometry, osculate describes curves or surfaces that touch at a point and share the same tangent and curvature there—an "osculating circle" kisses a curve at exactly one point.
The connection is the Latin root meaning mouth or kiss.
1. kiss — peck, Dry measure or quick kiss; smooch (Informal term for kissing); buss (Affectionate lip press); lip-lock (Prolonged romantic kiss); canoodle · necking · pucker · French-kiss · nuzzle · embrace · lips · affection · tenderness · fondness
2. geometry — tangent, Line touching curve once; curve (Smooth, angleless line); contact (Communication or physical touch); circle (Curved closed shape); ellipse · parabola · hyperbola · conic · intersection · point · arc · touching · tangency · curvature