A geometric interpretation of Ungar's addition and of gyration in the hyperbolic plane

We present a geometric interpretation of the operation a⊕b and the gyration on the unit-disc as defined by A.A. Ungar. Using this geometric interpretation we show that the two known generalizations to the n-dimensional unit ball are identical. The interpretation in the plane leads us to the notion of outer-median of a triangle and we discuss some possible properties of this median.