what was his contribution to the concept of hyperbola?
He found that the area under a rectangular hyperbola (i.e. a curve given by "xy = k") is the same over [a,b] as over [c,d] when This observation led to the hyperbolic logarithm.
Grégoire de Saint-Vincent
Saint-Vincent found that the area under a rectangular hyperbola (i.e. a curve given by "xy = k") is the same over [a,b] as over [c,d] when

This observation led to the hyperbolic logarithm. 
when are polar coordinates used in real life In spirals who came up with the system? Grégoire de Saint-Vincent and Bonaventura Cavalieri who is the former? He was a Flemish Jesuit and mathematician.
wiki:638960
Grégoire de Saint-Vincent [SEP] Quadrature of the hyperbola
Saint-Vincent found that the area under a rectangular hyperbola (i.e. a curve given by "xy = k") is the same over [a,b] as over [c,d] when This observation led to the hyperbolic logarithm. The stated property allows one to define a function "A"("x") which is the area under said curve from 1 to "x", which has the property that formula_1 This functional property characterizes logarithms, and it was mathematical fashion to call such a function "A"("x") a logarithm. In particular when we choose the rectangular hyperbola "xy" = 1, one recovers the natural logarithm. A student and co-worker of Saint-Vincent, A.