A prolonged, quiet unfolding of genius is what Jane Livingston, chief curator of the Corcoran Gallery of Art, calls the first century of National Geographic photography. Striving to portray our planet's remarkably diverse people, creatures, and landscapes, four generations of Geographic photographers have made their work an indelible part of our culture. When the Corcoran Gallery of Art, one of the nation's leading photographic museums, decided to organize an exhibition celebrating the…