Reciprocation in geometry, an operation with circles that involves transforming each point in plane into its polar line and each line in the plane into its pole
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Reciprocating motion, a type of oscillatory motion, as in the action of a reciprocating saw
She was active in Anglo-Japanese relations, visiting the UK in 1962 (in reciprocation for the first post-war visit by a member of the UK Royal family, Princess Alexandra of Kent, the previous year), and again in 1967, for the 75th anniversary of the Japan Society.
Many employees of the Crown were once required by law to recite an oath of allegiance to the monarch before taking their posts, in reciprocation to the sovereign's Coronation Oath, wherein he or she promises "to govern the Peoples of ... Jamaica ... according to their respective laws and customs".