Oscar Niemeyer (1907–2012) was a modernist concrete poet. But most of all he was king of the curve. The curves in his buildings were attempts to show his devotion to the female form. They call the Oscar Niemeyer Museum in Curitiba (1967-2003) "The Eye", but it speaks with the sinuous slither of a hip, a thigh or a breast.

The Ministry of Education and Health in Rio de Janeiro (1936-43) is the building that dragged Brazil into the modern age. It was used as offices for civil servants, but it was also symbolically for the people. Raised on piloti (pillars) and boasting brise-soleils (sun blinds), it aimed to counter Rio's summer sweat.

Niemeyer was a lifelong Marxist. Not much of a church-goer then – but he had no trouble designing buildings for believers, like the Sao Francisco de Assis catholic church near Belo Horizonte (1943). He got the painter Portinari to add some striking murals in ochre and blue as he sought to stir fine art into his architectural pot.

The Edificio Copan (1952-66) is a beast – it swerves like a giant wave, obliterating your sense of scale and perspective, and stamps its huge footprint in São Paulo's gritty Downtown. Street life ebbs and flows in and out of the amazing atrium, with its Mad Men bars and wood-panelled barber shops seemingly unchanged since the 1960s.

Niemeyer was at the heart of the establishment when president Juscelino Kubitschek asked him and fellow Brazilian architect Lúcio Costa to whip up a new capital in Brasília in just a few years (1957-64). Niemeyer designed the National Congress building, seat of the government, in futuristic shapes at the end of a monumental avenue.

Brasília's Catedral Metropolitana Nossa Senhora Aparecida (1970) shares some characteristics with Frederick Gibberd's spiky one in Liverpool. It rains less in Brasília though – those huge blue skies flood light on to white concrete and pick out the space-age shapes that Niemeyer loved to play around with.

Samba and football are central to Brazilian life. As a boy, Niemeyer used to go to the beach and play football every day. He also loved dancing and watching carnival queens. His Sambadrome on Rio's Marquês de Sapucaí Street (1984) is lit with a million bulbs during the culmination of carnival. It will also be a venue for the 2016 Olympics in Rio.

The Latin American Memorial and Parliament in São Paolo (1989) is an odd complex but manna from heaven for anyone who loves the cool, lucid effect that deliciously curved concrete shapes can have on the brain. A fire ravaged some of the site – which was supposed to encourage co-operation between South American nations – last year.

Some of Niemeyer's early works are concentrated in Ibirapuera Park, São Paulo's green lung, which he built in 1950 for the city's 400th anniversary celebration. He returned later in his life to co-author the Ibirapuera Auditorium (2002-5) – which looks like a gigantic wedge of Wensleydale with a red tongue poking out of the front.

The most stunning location for a Niemeyer building is this promontory in Niterói, overlooking Guanabara Bay in Rio. He designed the Niterói Arts Centre (1996) at the age of 89 – though he continued working well past his 100th birthday, and in total produced more than 500 buildings. Niemeyer gave Brazil a visual voice and a fresh language.