Georges Vantongerloo, who accepted the De Stijl restriction of line to horizontal and vertical in 1919, based his sculpture on the volumetric translation of this principle. The variation of volume and proportion in his work was determined geometrically, often according to mathematical formulae. Mathematics was for Vantongerloo a convention that established order in the world, a rationalization of nature that could be combined successfully with an aesthetic intention to result in the production of a work of art. In this approach he felt closest to the medieval artist who composed within the constraints of geometric convention, and to the ancient Egyptians, whose solution to the “problem” of the pyramid of Cheops consisted in “the inscribed and circumscribed squares of a circle.”¹
In one of his books Vantongerloo juxtaposed a diagram for the present work with an analytic sketch of the rose window at the cathedral of Amiens.² The asymmetry of the De Stijl image distinguishes it from the medieval subject. As the diagram shows and the title indicates, the extensions of the sculpture are determined by the lines of the inscribed and circumscribed squares of a circle. The relationships of its volumes result as much from the creative selectivity of the artist as from mathematical regulation. The effects of changing light produce subtle coloristic modulation and a relationship with the environment approaching that of architecture.
1. G. Vantongerloo, Paintings, Sculptures, Reflections, New York, 1948, p. 22.
2. Ibid., p. 23.