Spin observables are very useful to improve our insight into themicrosocopic dynamics of exclusive reactions, inclusive reactions andparton distributions.Each spin observable is typically normalised to vary between -1 and +1.Pairs of observables of the same reaction are often constrained to asub-domain of the square [-1,+1]^2, such as the unit disk or a triangle.For triples of observables, the domain inside the cube [-1,+1]^3 canassume a variety of shapes: sphere, cone, pyramid, tetrahedron, etc.The corresponding inequalities can be derived by purely algebraicmethods, or from the positivity of the density matrices describing theinitial or final spin states of the reaction and its crossed channels.Examples will be given for the strangeness exchange reaction antiproton+proton -> antiLambda + Lambda, the photoproduction of pseudoscalarmesons, and the Soffer inequality for transversity distributions insidethe nucleon.
