Geometry, it seems, is still radical. This July sees the Sackler Galleries playing host to Radical Geometry, an exhibition that charts the emergence of abstract art in several key areas across South America during the twentieth century. The exhibition underlines the diversity of this kind of abstraction – from the art-historically connected pieces of Joaquín Torres-García in Uruguay in the 1930s and ‘40s to the more politically motivated works of Arte Mundi in 1940s Argentina.

Such work was not confined to the twentieth century, however. As a recent exhibition at the Museum of Contemporary Art of Buenos Aires (MACBA) makes explicit, geometric approaches to image-making continue to provide artistic strategies of the utmost relevance and fertility. Geometry to its Limits presents a selection of works from the museum’s own collection in order to explore “new approaches to current geometric abstraction”. On show are pieces by 25 artists from the 1990s right up to the present day, and while the focus is exclusively on art from Argentina (in contrast to the RA’s continent-wide survey) a comparable diversity of techniques and conceptual approaches is nonetheless in evidence.

This is particularly clear when it comes to the proliferation of different media. Just as in Rio in the 1950s and ‘60s, artists such as Lygia Clarke made use of unusual materials (like hinges) so the same material curiosity is on display amongst this new generation of artists at MACBA. Industrial and technological developments underpin this embrace of the new: Geometry to its Limits includes, for example, a large-scale installation of vinyl and acrylic (Leila Tschopp’s Sin Título, 2013); a work made of adhesive tape (Andres Sobrino’s Sin Título, 2003-10); and even a wall-mounted sculpture of polychrome steel panels held together with magnets (Carolo Zech’s Magnético 110, 2010).

By and large, the works at MACBA are less explicitly politicised than some of those in Radical Geometry, Instead, this is an exhibition characterised by works of dazzling colour and dynamism. Gabriela Boer’s Disco 4 (2013), for example, echoes the multicoloured concentric circles of a giant gob-stopper. Meanwhile, Ines Raiteri’s Ayer Tambien te vi (2013) bustles with energy and vitality, and Valeria Calvo’s abstracted futurist cityscape (Serie Superficies Aparentes N°3) is a disorientating array of high-key hues.

By contrast, the most successful works take a more understated approach to the power of geometry, using clean lines and repetition to critique contemporary attitudes to urban planning or art itself. Guillermo Kuitca’s Sin Título (1998) is one such highlight. A complex, large-scale grid-like composition in oil and graphite echoes an architectural blueprint for some kind of vast social housing project (a warren of tiny rooms and doors to nowhere). Overlaying this is morass of painted smudges and smears, hinting perhaps at the discrepancy between the architect’s masterplan and the reality of lived experience.

Arguably more pure in approach is Mariano Vilela’s Sin Título (2013). Hung on the stairs to the lower-ground floor, it’s easy to miss this quiet composition of dark paper on aluminium. A complicated pattern of overlapping squares emerges from a painstaking process of graphite hatching – the parallel lines turning on the perpendicular to give a sense of texture at the joins. It’s a delicate, understated work whose exact signification – if any – is unclear. But it demonstrates the adaptability of geometry and its ongoing importance as an artistic strategy not only in twentieth century Modernism but right up to the art of the present day.

Geometry to its Limits was exhibited at the Museum of Contemporary Art of Buenos Aires from 14 December 2013 - 4 May 2014.
Radical Geometry: Modern Art of South America from the Patricia Phelps de Cisneros Collection is at the RA from 5 July - 28 September 2014.

Tom Jeffreys (@tomjeffreys) is a writer, editor and curator.