21 x 27 cm
Collection Museum Haus Konstruktiv
Donated by Sammlung Rolf und Friedel Gutmann
L'angle d'incidance = l'angle de réflexion [Angle of incidence = angle of reflexion]
The Belgian artist Georges Vantongerloo (born 1886 in Antwerp, Belgium, died 1965 in Paris, France) created art that was defined by universal thought. This earned him the reputation of a visionary artist within the geometric and Constructivist avant-garde. His early work was characterized by figuration, but after he began reading mathematical and philosophical works while living in Holland in 1917, he became inspired to explore space as an expansive and integrative phenomenon of a higher order. From this time forward, he rigorously reduced his artistic means. He created a new type of sculpture called “Constructions dans la sphere,” on the basis of which he began an ongoing exchange of ideas with Theo van Doesburg. He was also one of the artists to sign the first manifesto of De Stijl. While living in Brussels (1918–1920) and Menton (1920–1927), he continued to hone his neo-plasticist approach in his orthogonal “Rapports de volumes” while also applying his new insights – which were also inspired by the new field of non-Euclidian geometry and its idea of converging parallels – to articles of daily use and an imposing architectural style.
Vantongerloo moved to Paris in 1928, where he soon assumed a leading role in the artists associations Cercle et Carré and Abstraction-Création. At this time, he began to emphasize the mathematical premises of his art by integrating algebraic formulas in his picture titles. He also expanded his field of reference, which consisted of squares, circles, and ellipses, to include parabolas and hyperbolas, thus highlighting his deep interest in infinite space. They constitute the second major group of works in his mature style and include a gouache from 1931 that seems to be based on intuition alone, with its red, yellow, and green highlights (SK08027). This work is now part of the collection of the Museum Haus Konstruktiv in 2007, together with an accompanying study (SK08028) and two other works by the artist through a generous gift from Rolf and Friedel Gutmann. In the formula in the title of this work, a quadratic function is described in the numerator. As indicated by the negative sign, the graph of this function is a parabola with its legs pointing downward. Its width and horizontal and vertical placement is determined by the parameters a, b, and c. The denominator describes the derivative, or tangential equation, of the same function, making the quotient an important value when looking for the roots of the parabola using Newton’s method. This in turn creates graphs in the form of hyperbolas. Based on these many options, Vantongerloo defines the corner points of the two-dimensional structure. He also used the same method to create a wooden sculpture painted uniformly in light gray with the same title (GV 69) as a way of visualizing the interaction of different “groupes” [groups] in space.
In 1937, the importance of the dynamic curve in Vantongerloo’s artistic approach in terms of form also became apparent when he used curved elements to replace the principle of right angles dictated by De Stijl. This turn, which he revisited in his reference to the cosmos in his late work, is also exemplified in “L’angle d’incidence = l’angle de réflexion” (1942). As the title indicates, the composition is structured around the angle of incidence equal to the angle of reflection according to the law of optical reflection. The radically reduced, fragmented form in this a black and white woodcut (SK08084) can also be found in a color version rendered in oil paint (GV 162), as well as an accompanying study. Three further studies, however, show a bustle of curved lines that create a spatial relation between the seemingly isolated pictorial elements, while also defining spherically vaulted domes. This group of works represents the introduction of light – though only implicit at first – as another important component through which Vantongerloo was able to explore the charged relationship between space, matter, movement, and time in a scientific and rational manner, as well as according to the freer standards of art striving for harmony.