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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, 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 24-bit 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 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 CurveDefinite 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 inflectionDefinite 
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 TransformationsDoppler Effect and the Twin Paradox, The
 Length 
Contraction
 Michelson-Morley 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 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." 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 1954-1974, by Race Produced by Bruce Cornwell 
			and David J. Kasik for the Graphic Social Reporting Project .  |  |