I have seen some examples of duality. Sometimes applied to theorems, as for example Desargues theorem and Pappus theorem. Sometimes applied to spaces, for example the dual space of a vector space. Sometimes even applied to a method like simplex and dual simplex methods in linear programming.
My question is what is the general meaning behind the term duality and what is its relevance to mathematics. Do we mean the same always when we use the term? Or the examples I have put have no connection whatsoever?
Thanks a lot