This figure shows an algebraic surface that resembles the sculpture, created by Anish Kapoor, in
Chicago's Millenium Park. The sculpture is also known to local
residents as the Cloud Gate.
Chicago Bean, which has a shiny metallic surface,
is said to have been inspired by liquid mercury.
(Click
here to see a Wikipedia article that contains a daytime photo of the
sculpture.) I have not managed to find specific
documentation about mathematical equations that might have guided the design
of the sculpture, although the book Cloud Gate
(MIT Press,2008) says that computer modeling was essential to the process of
analyzing the complex form.
Anish Kapoor: Past Present FutureI am not the only person to attempt a "reverse engineering" approach to representing Cloud Gate by mathematical equations. Indeed, a Google search on "Cloud Gate math" will produce several online articles about this topic. When I first saw the sculpture, I realized that many of its vertical cross sections resemble a certain type of 4 ^{th} degree plane curve. Rotating this curve
around a vertical axis is a first step in constructing the surface;
this is followed by stretching it in one of the horizontal directions.
The top and bottom are parametrized separately; additional "deformation
factors" are introduced to lift portions of the edge.
In addition to the Wikipedia article, a Google search of images produced some photos posted on Tumblr that show the sculpture under different light conditions. Since I have not been able to reproduce the shiny daytime surface, I tried to imagine how sunset colors might be reflected. |

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*The Java files used in this page were downloaded from the
*Geometry Center* webpage.
I generated the geometric data for this figure in November 2012 and May 2013.
Updates completed on June 5, 2013.*

Prof. Joel Roberts

School of Mathematics

University of Minnesota

Minneapolis, MN 55455

USA

Office: 351 Vincent Hall

Phone: (612) 625-1076

Dept. FAX: (612) 626-2017

e-mail: `roberts@math.umn.edu
http://www.math.umn.edu/~roberts
`