Editing Medial magma (section)

== Nonassociative examples ==
A particularly natural example of a nonassociative medial magma is given by collinear points on [[elliptic curves]]. The operation {{math|1=''x'' • ''y'' = −(''x'' + ''y'')}} for points on the curve, corresponding to drawing a line between x and y and defining {{math|''x'' • ''y''}} as the third intersection point of the line with the elliptic curve, is a (commutative) medial magma which is isotopic to the operation of elliptic curve addition. 

Unlike elliptic curve addition, {{math|''x'' • ''y''}} is independent of the choice of a neutral element on the curve, and further satisfies the identities {{math|1=''x'' • (''x'' • ''y'') = ''y''}}. This property is commonly used in purely geometric proofs that elliptic curve addition is associative.