A geodesic dome is a dome that features small triangle shapes over its face, which are created through the intersection of circles throughout what would be the total sphere. These triangles allow for the stress of the building's weight to be distributed over its entire structure, which allowed larger domes to be built in the twentieth century. The innovative architect Buckminster Fuller first demonstrated the architecture was possible, actively sought out opportunities to build domes, and coined the term "geodesic dome."

The Chrysler Building in midtown Manhattan was the tallest building in the world for eleven months, spanning from its completion in May of 1930 to the completion of the Empire State Building. Apart from sheer size, the Chrysler building was also notable as a shining example of Art Deco design. The building's brick artifice, metal crown, and use of modern technological design all were exactly in line with Art Deco's chief features.

"Beaux-Arts Architecture" refers to the style promoted by the École de Beaux-Arts in Paris, but especially as promulgated by Americans who had studied there and produced work in the late nineteenth and early twentieth centuries. The style was a mix of neoclassicism and rococo elements, with the unifying themes being grand spaces, small classical flourishes, flat roofs, arched windows, and fancy embellishments around doors and windows. Any utilitarian spaces were hidden from any obvious views in favor of grand entrances and sweeping hallways.

"Deconstructivism" refers to a style of architecture that seems to break down typical architectural conventions, often by using forms and shapes that curve and bend. Frank Gehry has worked in such a style most of his career, with his work on the Guggenheim Museum in Bilbao and the Walt Disney Concert Hall in Los Angeles being notable examples of his approach. These buildings feature curving lines and non-rectilineal shapes, hallmarks of the deconstructivist approach.

The "International Style" is a term that derives from a 1932 book of that name by Henry-Russell Hitchcock and Philip Johnson. The two men used the term to described the then-contemporary aesthetic that had grown to dominate architecture since 1900. Uniting Bauhaus, Functionalism, and L'Esprit Nouveau styles, Hitchcock and Johnson promoted architecture that valued functionality, clean lines, and use of modern materials such as plate glass and steel.

Art Deco was a thoroughly early-twentieth-century phenomenon in arts and architecture, as it blended machine-age construction with traditional craftwork aesthetics. The designs featured a great deal of metal with rich colors, bold geometric shapes, and distinct ornamentation. One of the most famous Art Deco buildings is the Chrysler Building in New York.

Wright is best associated with the Prairie school. The hint in the question was the eaves and the roofs, as those provide that context.

The answer cannot be brutalism or functionalism as the homes and buildings created by Wright did not follow the simplistic styles of those schools: those schools would have obelisk-like buildings that lacked much detail.

Art Nouveau was a bit too early of a period for Wright to be associated with. Art Deco, though in the same period as Wright, differentiated by its ornate designs, in contradistinction with Wright's minimalist, natural designs.

Provenance is a very specific term to determine the ownership history of artworks. It is similar to lineage, but lineage has to do with people and their family trees.

Filing is not the answer, though many who purchase artworks do file ownership certificates or file such assets.

Apadana is a Persian audience hall and Intonaco is the final layer of plaster in Italian frescos.

The Farnsworth House was built outside of Chicago as a rural retreat for a businessman by the German born architect Ludwig Mies van der Rohe. Mies, his middle name that he preferred to go by in most settings, was a German immigrant who helped pioneer modernist architecture in America. Using glass, steel, and straight lines, the Farnsworth House was a model and template for further explorations of architecture in America.

The Bauhaus was a revolutionary art school, which sought to unite various forms of art under one roof and one set of guidelines based around clean lines, modern techniques, and functionality. The Bauhaus was most influential in the world of architecture, where its modern and simple style inspired achitects around the world. Adolph Hitler and the Nazi Party banned the Bauhaus, and forced its teachers and leaders to find refuge in other nations, which furthered their influence internationally.