If anyone doubted the Museum of Modern Art’s consummate excellence in fulfilling its mandate as custodian of the Modern movement, a new show in a new gallery, “Geo/Metric: Prints and Drawings from the Collection,” attests to how wisely and how well its curators have chosen during the past eight decades.

Just by rummaging in a few drawers, they have come up with a substantial narrative of the role of geometric abstraction over a span of very nearly 100 years, from the Synthetic Cubism of Picasso and Braque to the latest attempts of Gabriel Orozco, Mary Heilmann, and Mark Grotjahn.

The modest ambitions of this show, which has been curated by Starr Figura with Kathleen Curry and mounted in new galleries adjacent to Café 2, consist in simply laying several dozen choice prints and drawings before the public, with little commentary. Yet the show provokes in this viewer a far larger question: Why was the 20th century so obsessed with geometric — that is to say, rectilinear — art in the first place, especially in its abstractions? Was it a necessary consequence of the Modern movement itself, or was it a mere accident of art history? Put another way, if the sharp facets of Cubism had not arisen out of Cezanne in the first decade of the last century, would we still have had the Bauhaus and all that that institution begat?

Probably, but not certainly. In what may be one of the few false steps in the present show, the first work one sees is an early painting by Mondrian, “Pier and Ocean,” from 1915. Its sequence of lines and tawny half-tones clearly looks back to the early stages of Cubism, attested on an opposing wall. So, for that matter, do several works by Mondrian’s Russian contemporaries, the avant-guardists Lyubov Popova and El Lissitzky. Why did the curators not choose one of Mondrian’s more typical and better works, from his Neo-Plasticist period several years later? Presumably this choice was intended to provide some sense of evolution from Cubism into the Bauhaus style with which Mondrian would be associated. But in that option lies the crux of the question before us. Surely the young Mondrian (after his first Symbolist forays) was influenced by Cubism. But did he need Cubism to get to the works for which he is best known or is it just a coincidence? Is it just that delectation geometrique, to coin a phrase, that enthralled Modernism for fully half a century?

I incline to the latter proposition. You could argue that the Bauhaus arose out of Cubism, with its general emphasis on angularity. But, more likely, both movements were propelled by the same geometric appetite, the same willful need to reject the organic curvature of all earlier European art, from the cave paintings of Lascaux to the last, absinthial gasps of representation in the studios of the Symbolists. Something about right angles and straight lines seemed so quintessentially modern, so redolent of the machine age, that even Kandinsky, who more or less invented abstract art as expressive gesture back in 1910, soon abandoned subjectivity for the hard purity of a work such as “Orange” (1924), on view in this show.

As for the Bauhaus, with which Kandinsky was associated as well, the mere technological imperatives of its architectural wing, embodied in the glass and steel of the International Style, established the grid, that sacred, blessed grid, as the cornerstone of Western visual culture for much of the 20th century.

Two generations after the invention of Cubism, the Abstract Expressionists attempted to tear down that grid, but by 1960, it had reconstituted itself with a vengeance in the works of hard-edge painters like Barnett Newman and Ad Reinhardt, oddly missing from this show, as well as in the Minimalists whom they inspired and in much of the work of the Conceptualists who came after the Minimalists.

These two later movements are well-represented in the present show. Surely the conceptual underpinnings of Minimalism are entirely different from those of Cubism and of pre-war geometric abstraction. Whereas the latter had emerged, long before, out of representations of reality that had been thoroughly exploded by Cubism, the terminally cool Minimalism of Sol LeWitt’s “Forms Derived from a Cube” (1982) began with the grid, an intellectual abstraction, and that grid served as the essential armature for what he and the other Minimalists went on to create.

In the ever swinging pendulum of Modern and Contemporary art, Minimalists such as Dorothea Rockburne and Robert Ryman, both masters of pallid monochromes, and Agnes Martin in “Tremolo” (1960), reacted not by rejecting the Modernist grid, but by converting it into a living, breathing, textured thing, far more moody and emotive than anyone had previously imagined.

And now the pendulum has swung again, as artists of the latest generation, like Olaf Nicolai and Mark Grotjahn, restore the hard-edge that the Modernist grid had lost, but infuse it with new meanings — an insistent reference to things outside of and beyond what the eye perceives, the allusions to chess, for example, in the dazzling “Samurai’s Tree Invariant,” conceived by Gabriel Orozco in 2006. These artists prove, if proof were needed, that whatever the grid might mean for Postmodernism in general, it has not nearly worn out its welcome among the latest generation of artists.