 
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, these brilliant short films
trace geometric shapes to intriguing music, including the memorable 'Bach
meets Third Steam Jazz' musical
score in ‘Congruent Triangles.’ Much of 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,
operating a 640x480 raster graphics display system with 24bit color. Later he
supervised aspects of computerized mapping for the NYC Department of City
Planning. 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 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
Cornwell films distributed by Film Associates (BFA)
 Big Numbers, Little Numbers (1962) 11m 
 Sets, Crows, and Infinity (1962) 12m 
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 19651968, 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
MichelsonMorley Experiment, The
Simultaneity is Relative
Speed of Projectiles. The: Sound and Light
Time Dilation
World Lines
Cornwell films distributed by the International Film Bureau (IFB):
 Axioms in Algebra, (1960) 13m, Produced by Robert Longini 
 Circle Circus (1979) 7m 
 Congruent Triangles (1976) 7m 
 Dragon Fold  and Other Ways to Fill Space (1979) 7m 
 Formulas in Mathematics, 10m, Produced by Robert Longini
(1960) (also a Spanish version, Formulas en Matematicas) 
 How Do You Count? (1963) 12m 
 Idea of Numbers, The: An Introduction to Number Systems (1961)
14m, Produced by RobertLongini, script by Katharine Cornwell 
 Journey 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 highcontrast finegrained 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 multipleexposed 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." Guy
Ross notes that "the Bach preludes featured on the soundtrack to
Triangle were from a recording by The Classicats on the Orion label."

 Language of Algebra, The (1956), from the series 'Mathematics in
Our World.' Copyright 1960 Visual Educational Films, Inc. Katharine
Cornwell: Script, Bruce Cornwell: Production Design. Robert Longini,
Producer. 
 London Of William Hogarth, The (1956) 26m 
 Newton's Equal Areas (1967) 8m (also a
Spanish version,
Areas Iguales de Newton) 
 Possibly So, Pythagoras! (1963) 14m 
 Proportion at Work (1960) 12 m 
 Seven Bridges Of Koenigsberg, The (1958) 4m 

Similar Triangles (in Use) (1975) 7m 
 Trio For Three Angles (1968) 8m (also a version in Spanish,
Triangulos 
Miscellaneous films
 Batch Mode Square Dance (1974)" Unknown director, but
credited on the leader is the handwritten date 9/12/74 and
"Cornwell/Siegel" 

Unemployment 19541974, by Race Produced by Bruce Cornwell
and David J. Kasik for the Graphic Social Reporting Project
. 
