Topology, a 1961 Eames film for IBM’s Mathematica Exhibit

Topology is one of the five films made by Charles and Ray Eames for the 1961 opening of IBM’s Mathematica: A World of Numbers… and Beyond exhibit at the California Museum of Science and Industry in Los Angeles.

The math short explores the Jordan curve theorem, first proposed by French mathematician Camille Jordan in 1887. From Wolfram Mathworld:

“A Jordan curve is a plane curve which is topologically equivalent to (a homeomorphic image of) the unit circle, i.e., it is simple and closed.”

Plus, an expanded definition of topology from Wikipedia:

“In mathematics, topology (from the Greek words τόπος, ‘place, location’ and λόγος, ‘study’) concerns with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.”

“The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together. For example, the square and the circle have many properties in common: they are both one dimensional objects (from a topological point of view) and both separate the plane into two parts, the part inside and the part outside.”

And when these simple, closed spaces don’t look very simple, there’s still a way to determine which domain a given point is located within. From the film’s narration:

“If a line is drawn from that point to the area beyond and it crosses the curve an odd number of times we find that the point lies inside; an even number of times, it lies outside.”

Watch more from the 1961 Mathematica exhibition:
• Symmetry
• 2ⁿ, a story of the power of numbers

And more from Charles and Ray Eames on TKSST:
• The Solar Do-Nothing Machine
• Tops (1969)
• Making Eames fiberglass shell chairs
• Powers of Ten (1977)