Mathematics Education and Early Abstract Art

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Stephen Luecking: Mathematics Education and Early Abstract Art. In: Bridges 2013. Pages 35–42



As a group, the artists educated near the turn of the 19th and 20th centuries possessed greater mathematical knowledge than expected of artists today, especially regarding constructive skills in Euclidean geometry. Educational theory of the time stressed such skills for students in general, who needed these to enter the workplace of the time. Mathematics teaching then emphasized the use of manipulatives, i.e., visual and interactive aids thought to better fix the student’s acquisition of mathematical skills. This visual training in mathematics significantly affected the early development of abstraction in art. This paper presents examples of this visual mathematics education and samples its effects on the development of abstract art in the first decades of the 20th century.

Extended Abstract


Used References

[1] O. Byrne, The First Six Books of the Elements of Euclid, William Pickering, London, 1847. Available at

[2] M. Droste, Bauhaus 1919-1933, Bauhaus Archiv Museum für Gestaltung, Berlin, 1990.

[3] A. Dürer, Unterweisung der Messung mit dem Zirkel und Richtscheit, Nuremburg, 1526.

[4] T. H. Eagles, Constructive Geometry of Plane Curves, MacMillan and Company, London, 1885.

[5] F. Froebel (W. N. Hailmann, Translator), The Education of Man, Dover Publications, Mineola, NY, 2005.

[6] Froebel Web, Influence of Friedrich Froebel on Frank Lloyd Wright, 1999-2000. Available at

[7] Getty Museum, The Collections (website), The J. Paul Getty Trust, 2000. Available at

[8] M. Gough, In the Laboratory of Constructivism: Karl Ioganson's Cold Structures, October, Vol. 84. (Spring, 1998), pp. 90-117

[9] W. Kandinsky, From Point and Line to Plane, Solomon Guggenheim Foundation, (H. Dearstyne and H. Rebay, translators) New York, 1947. Republished by Dover, New York, 1979. Originally published as Punkt und Linie zu Fläche, Bauhaus, Dessau, 1926.

[10] P. Kidwell, Slates, Sliderules and Software - Teaching Math In America, Smithsonian Institution, 2002. Available at

[11] C. Lodder, The VKhUTEMAS and the Bauhaus in The Avant-Garde Frontier: Russia Meets the West 1910-1930, University Press of Florida, Gainesville, 1992.

[12] S. Luecking, A Man and His Square: Kasimir Malevich and the Visualization of the Fourth Dimension, Journal of Mathematics and the Arts, Vol.4, No. 2, June 2010

[13] A. Miller, Insights of Genius: Imagery and Creativity in Science and Art , The MIT Press, Cambridge, MA, 2000.

[14] W. Mueller, Mathematical Wunderkammern, American Mathematics Monthly, November, 2001. Available at

[15] A. Rodchenko, “Slogans” of the Workshop for the Study of Painting in State Art Colleges in Art in Theory 1900-2000, C. Harrison and P. Wood, eds., Blackwell Publishing, Oxford, UK, 2003.

[16] W.W. Ross, Mensuration Taught Objectively, with Lessons on Form, published by the author, Fremont, OH, 1891.

[17] M. Rowell, ew Insights into Soviet Constructivism: Painting, Constructions, Production Art in Art of the Avant-Garde in Russia: Selections from the George Costakis Collection, A.K. Rudenstine cataloger, Simon R. Guggenheim Foundation, New York, 1981

[18] K. Wellhousen, J. E. Kieff, A Constructivist Approach to Block Play in Early Childhood, Delmar, lifton Park, NY, 2000.

[19] E. Wiebe, Paradise of Childhood: A Practical Guide to Kindergartners, edited by Milton Bradley, Springfield, MA, 1907.


Full Text

intern file

Sonstige Links