Functional Surfaces I


Eugene Jahnke (1863-1921) and Fritz Emde’s (1873-1951) Tables of Functions with Formulae and Curves (German: Funktionentafeln Mit Formeln und Kurven) was a landmark of the visual presentation of complex surfaces. Originally published in 1909 and subsequently significantly expanded by Emde after the death of Jahnke, the text proved popular not only with mathematicians and engineers but also with designers and artists. Le Corbusier had a copy in his library when designing the Phillips Pavillion, and Max Ernst produced several collages which integrated the functional drawings into estranging contexts (including those shown below).




The graphed functions in Jahnke and Emde’s Tables include Bessel, Zeta, and Hankel functions, elliptic integrals, as well as several complex-valued periodic functions. These diagrams are excerpts of the 42 exemplary graphs of spatial functions presented in the book. Jahnke and Emde’s Tables of Functions ultimately went through several editions (1909, 1933, 1938, 1945). The remarkable images of surfaces presented here were first added in the 1933 edition. Aesthetically, Tables bears some resemblance to the contemporary Felix Auerbach’s Physik in Graphischen Darstellungen (1912), and certainly both books fall in the broad tendency of a more visual approach to mathematics around the turn of the century.

Max Ernst’s use of mathematical surfaces is well known, and several such collage elements were evidently taken from the Tables, shown by the correspondence below:


At left is Jahnke and Emde’s relief of the Hankel function; at right a collage “La Fable de la Souris de Milo” from Ernst’s 1949 exhibition and catalog Paramythes.


At left is Jahnke and Emde’s relief of the Bessel function; at right, Ernst’s Ausstellungssignet (1948).


Bryant, John. “Max Ernst: Levity and Gravity in his Paintings” in Art Lies, Volume 39, Summer 2003.

Ernst, Max. Paramythes. Paris: Le Point Cardinal, 1967.

Treib, Marc. Space Calculated in Seconds: The Phillips Pavilion. Princeton: Princeton University Press, 1996.

Werner, Gabriele. Mathematik im Surrealismus. Berlin: Jonas Verlag F. Kunst U., 2002.

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