Dini's Surface:  a surface of constant negative curvature obtained by twisting a pseudosphere, 2004

Quick return mechanism, 2004

Two hyperbola tangent to one another, 2004


Conceptual Forms



The study of mathematics is thought have begun in ancient India and China. The concept of zero and infinity were not so much discoveries as human inventions. The notion of length with no width is very curious indeed, the pencil line I draw being only an approximation of an invisible mathematical line. Endeavors in art are also mere approximations, efforts to render visible unseen realms. 

Among the notes Marcel Duchamp left in his Green Box are various mathematical notations. The Large Glass attempted to throw projections of the unseen fourth dimension onto our three-dimensional experience, much in the same way that three- dimensional objects cast shadows onto two-dimensional surfaces. 

While not wholly subscribing to the post-Renaissance rational scientific regard on the natural world, I do appreciate those eighteenth- and nineteenth-century optical devices and experimental implements that gave visible form to unseen hypotheses. I have photographed suites of "stereometric exemplars," fabricated in Germany in the late nineteenth and early twentieth century, and now owned by the University of Tokyo. The mathematical models are sculptural renderings of trigonometric functions; the mechanical models were teaching aids for showing the dynamics of Industrial Revolution-age machinery. Art resides even in things with no artistic intentions.



- Hiroshi Sugimoto