B & K Cornwell
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View Bruce & Katharine Cornwell's Congruent Triangles and Journey to the Center of a Triangle

Bruce and Katharine Cornwell
are primarily known for a series of remarkable animated films on the subject of geometry. Created on the Tektronics 4051 Graphics Terminal, they are brilliant short films, tracing geometric shapes to intriguing music, including the memorable 'Bach meets Third Steam Jazz' musical score in ‘Congruent Triangles.’ Their work, distributed by the defunct International Film Bureau, is now out of distribution.

As a World War II WAC, Katharine Marie Seremal  was involved in investigating the ENIAC computer for bomb survey analysis, which fueled her interest in mathematics.  Bruce Haynes Cornwell, who in WWII set up radio transmitters in the South Pacific, eventually returned to earn a degree in cartography at at University of Wisconsin.  Bruce created graphics for a television station in Madison, Wisconsin, where he was also engaged with the local public radio station. The Cornwells were married in 1956 and eventually moved to Brooklyn, NY. Like many other makers of quality academic film, the Cornwells found it made better financial sense to have additional careers. In New York, he worked in the brand new Geographic Information Services department of an industrial engineering firm, Gibbs & Hill, starting in the late 1970s, working on a 640x480 raster graphics display system with 24-bit color. Later he supervised aspects of computerized mapping for the NYC Department of City Planning, and his last position was with the Brooklyn Botanic Garden doing similar work on a much smaller scale for their plant records department. Katharine became a consultant specializing in executive compensation. Eventually, Bruce taught at the Polytechnic Institute of Brooklyn, the New School, and the School of Visual Arts.

Bruce has stated that his interest in math films was influenced by his seeing Disney’s ‘Donald in Mathmagic Land,’ which prompted his comment "anyone with half a brain and one hand tied behind his back could make a better film." Bruce passed away on January 26, 2012, and Katharine on March 4, 2013, at the age of 93.

Filmography

For the Mathematical Association Of America in conjunction with Stanford University, a number of films of at least fourteen titles were produced at the Cornwells' studio for the MAA Calculus series from 1965-1968, under various directors. This may be an incomplete list (hanks to researcher Greg Javer for contributing many of these titles). We do not have the names of most of these films, but among them are:

Area Under a Curve
Definite integral
Continuity of Mappings
Definite Integral as a Limit
Function is a Mapping
Fundamental Theorem of the Calculus
I maximize
Infinite Acres

Limit (1965) 10m
Newton's Method
Theorem of the Mean Policeman
(1966, dir. H.M. MacNeille), 15m
Volume by Shells
Volume of a Solid of Revolution
(1965, prod. B&K Cornwell), 8m
What is Area?

For Houghton Mifflin, the Cornwells, in conjunction with Duane W. Bailey, made a 1973 series called 'Calculus in Motion,' consisting  of eight 3 minute, color, animated, silent 8mm loops. They were available as either Technicolor Magicartridges or Kodak Cassettes. They are:

Concavity and Points of inflection
Definite Integral, The
Derivatives
Fundamental Theorem
Functions
Limits
Rolle's Theorem and the Mean Value Theorem
Taylor Polynomials

They also made a series for Houghton Mifflin in 1974 called 'Relativity: a Series of Computer animated Films, in conjunction with Robert Ehrlich, again on Super 8mm silent cartridges. All are 4 minutes in length. The films are:

Coordinate Transformations
Doppler Effect and the Twin Paradox, The
Length Contraction
Michelson-Morley Experiment, The
Simultaneity is Relative
Speed of Projectiles. The: Sound and Light, Time Dilation, and World Lines.


Cornwell films distributed by the International Film Bureau (IFB):

bulletCircle Circus (1979) 7m
bulletCongruent Triangles (1976) 7m
bulletDragon Fold - and Other Ways to Fill Space (1979) 7m
bulletHow Do You Count? (1963) 12m
bulletIdea of Numbers, The: An Introduction to Number Systems (1961) 14m
bulletJourney to the Center of a Triangle (1976) 8m. According to son Eric Cornwell, here's how the film was made:
The Tektronics 4051 Graphics Terminal produced only black and green vector images, not even grey scale. The film's scenes were divided into layers in the programming, one layer for each of the colors in the scene, and each was shot separately onto high-contrast fine-grained b&w film stock. The final scene in "Journey" had 5 layers: one for each of the four colored dots, plus one for the white triangle and line. These five clips were then multiple-exposed onto color film on an optical printer, using colored filters to add the desired color to each black&white layer as it was copied. The resulting color was much better than a film of an RGB display would have been because the color filters on the optical printer allowed access to the full range of the color negative film, allowing much more saturated colors. All of that color is pretty much lost now, between prints fading and/or transfers to the VHS, and then viewing them on a computer screen which has a much more limited color gamut. Please imagine it all in bright, brilliant colors.
bulletLondon Of William Hogarth, The (1956) 26m
bulletNewton's Equal Areas (1967) 8m (also a version in Spanish, Areas Iguales de Newton)
bulletPossibly So, Pythagoras! (1963) 14m
bulletSeven Bridges Of Koenigsberg, The  (1958) 4m
bullet Similar Triangles (in Use) (1975) 7m
bulletTrio For Three Angles (1968) 8m (also a version in Spanish, Triangulos

Cornwell films distributed by Film Associates (BFA)

bulletBig Numbers, Little Numbers (1962) 11m
bulletSets, Crows, and Infinity (1962) 12m

 


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