Final answer:
The architectural style that began in the 1980s, featuring a mix of modernism's hard rectangles with eclectic historical elements, is known as Postmodernism. It was a reaction against the minimal and functional design approaches of the International Style and embraced a more decorative and historically referential aesthetic.
Step-by-step explanation:
The style of architecture which began in the 1980s and combines the hard rectangles of modernism with unusual materials and stylistic features from the past is known as Postmodernism. This movement emerged as architects began to explore new forms that incorporated elements from various historical styles and applied them to contemporary designs. Contrary to the purely functional forms of the International Style, Postmodernism embraced ornamentation, mixing past aesthetics with the new.
Postmodern architecture saw iconic buildings just like the Beaubourg Center in Paris, which connected with the deconstructive ideas of philosophers like Jacques Derrida. Renzo Piano and Richard Rogers designed the Beaubourg Center with most of its functional systems exposed externally, reflecting the deconstructionist philosophy. Postmodernism was, in a sense, a cultural reaction against the perceived finality of modernist principles in architecture and other forms of art and philosophy.