SCHOOL SCIENCEAND

MATHEMATICSVOL. LXIIIJANUARY, 1963WHOLE No. 552

Making a Geometry Movie

Raymond Sweet and Peter Dunn-Rankin1702^ Laurel St., Sarasota, Florida

Projects have long been used as a vehicle to stimulate interest andpromote learning. In order to do something slightly different for aclass project, it was suggested to a geometry class that they devoteseveral of their laboratory periods to the making of a movie pertainingto geometric construction. Such a project, if successfully completed,would create an instructional aid for the future, be a motivation forlearning, and constitute a fairly lasting reminder of this particulargeometry class. In addition to the geometry involved in the construc-tion of the model itself, a certain amount of mathematics would beused in determining depth of field, parallax for close-ups, and inmeasuring for correct focus. It was stressed that should the studentsundertake something of this nature, the filming and planning wouldbe entirely their responsibility. The teachers would supervise andmake only those decisions which are necessary in any classroomundertaking.Some questions having to do with the justification for such a project

follow. Should the class time involved be utilized instead for coveringmore subject matter? Would individual projects be better than agroup project? Does the cost involved compared to the benefitsderived make such an undertaking impractical? Will the class beswamped with technical difficulties? Can the time spent upon the

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movie be kept in a proper balance with the rest of the geometry pro-gram? The remainder of this paper will show that these questionswere given proper consideration.The laboratory class was composed of fifty ninth grade students

who were using SMSG geometry material and BSCS biology materialin an accelerated program. They had a seventy-five minute geometrylaboratory each week in addition to five regular fifty-minute periods.In this laboratory each student had already completed two individualprojects and had participated in such other activities as curve stitch-ing, wax paper folding, origami, model making, surveying, and mak-ing truth tables. There was within the group quite a bit of artistic andwriting talent as well as leadership ability.The two teachers had originally intended making an 8mm movie of

the construction of some model such as the octahedron. What withthe abundance of home movie enthusiasts and electric eye cameras inmost communities, it was assumed that there was a good chance for asuccessful end product. When the idea was presented to the class,they were not only interested, but were much more ambitious thantheir instructors. They wanted to make a 16mm sound film in color.A boy in the class volunteered the use of his father’s 16mm equipmentand a committee was appointed to investigate the cost and feasibilityof such a project. It was found that the cost of purchasing and proc-essing silent film would be less than the cost of a commercially pro-duced sound film. The students^ final decision was to produce a six toeight minute 16mm color film and to write a script that could be readorally while the film was being shown. The subject of the film was theMoebius triangle. It was selected because: the construction of its netrequired the use of more of the basic constructions than other sug-gested models; it was more difficult to find a reference that would showhow to construct it; there was a special feature in assembling it thatrequired a twisting of the figure that could be shown in slow motionmuch more effectively than it could ever be described verbally; andalso because of the unusual features of the figure.The following committees were then established: the equipment

committee; the script writers; the layout committee; the modelmakers; and the stage hands. The equipment committee procured thecamera, lights, and film and shot the scenes. The layout committeedescribed the camera scenes to follow the script. The model makersmade several nets of the Moebius triangle in various stages of comple-tion so that the scenes could be cut when the construction becamerepetitious and the action could move on to the next step. They alsomade an octahedron and a dodecahedron. The stage hands were re-sponsible for makeup and props. A director and four actors wereelected. The director coordinated the script and layout, and super-

Making a Geometry Movie 3

vised the filming. The only position not filled by a student,was that ofproducer. The principal accepted this position and provided themoney for the venture. Each student was assigned a task and servedupon at least one committee.

In writing the script and in laying out the scenes, the students weremore imaginative than the producers of many commercial mathe-matics movies that the writers of this paper have viewed. Below isincluded a part of the student’s worksheet to indicate the generalprocedure used in filming the movie.

Scene I. Title. Making the Moebius Triangle. Time�7 seconds.Scene II. (Close-up) Sign: Brookside Math Fair. Time�5 seconds.Scene III (Long shot) Bonna, Mike and Terrie stand behind their

models. Terrie and octahedron, Mike and dodecahedron,Bonna and Moebius triangle. Judge enters stage left to evalu-ate the projects. Judge moves to Terrie, Mike, and Bonna inturn. Time�30 seconds.

Narrator: Terrie, Mike and Bonna have reached the finals of theBrookside Math Fair. The judge looks at Terriers project,which is an octahedron. Mike^s project is a dodecahedron.

Scene IV. (Close-up) Bonna and her project. Time�45 seconds.Then blur scene and fade.

Narrator: Bonna shows the judge that her project, a Moebiustriangle, has only one edge and one side. The judge seems per-plexed and asks Bonna to tell him how she made it.

Scene V. Outside shot of library and library sign. Time�5 seconds.Scene VI. Inside library under number 500 Bonna looks for a book,

finds it, opens to the index and finds page. Time�35 seconds.Narrator: The first thing Bonna did was to go to the library and

get a book with the model of the figure she wanted to make.Scene VII. (Close-up�28 inches from tagboard over Bonna’s left

shoulder) Bonna seated at a desk with tagboard and instru-ments laid out in front of her. Book open to picture of net ofmodel. Time�25 seconds.

Narrator: Bonna drew a straight line segment AB. Next shebisected AB.

Scenes VIII to XII consisted of all the steps necessary to the con-struction of the net of the model. The narration accompanied eachstep. The time was one minute and thirty-five seconds.

Scene XIII. Bonna starts to cut out the net. Time�7 seconds.Scene XIV. Bonna scores the lines with a compass point and folds

them. Time�20 seconds.Narrator: Next came the hardest part. Every line had to be

folded the right way; the first one down, the next four up, thenext four down, and the last one up.

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Scene XV. (Slow motion) Bonna twists model into shape and dis-plays it. Time�15 seconds.

Narrator: Then the model was twisted into shape.Scene XVI. (Long shot) Brookside Math Fair. Judge awards the

ribbons. Time�25 seconds.Narrator: After seeing the unusual features of the model and its

construction, the judge decides Bonna’s Moebius triangleshould win the grand prize.

After devoting a portion of several periods to preliminaries, theactual filming took three periods, including retakes. The studentsreadily adopted the language and actions associated with such anenterprise. Commands like: "Lights! Camera! Action!"; "Cut!"; and"This is a take!", while trite sounding, took on real meaning and werethe only phrases that seemed to adequately handle the situation. Forbackground props, the stagehands used projects made this year andsome actually left over from the past two years science and mathe-matics fairs.The greatest hazard to this sort of project is the cost. Even after

the trial runs have been made and the actual filming begins, there is achance that some little thing will go wrong and the scene will beruined.

In filming this movie, the cameraman aimed too low for some ofthe long shots and these had to be taken again. The camera used wasequipped with an electric eye that only controlled the lens openingand insured proper exposure. Thus the close-up shots, which con-stituted the most important part of the movie, required fairly precisemeasurement to achieve correct focus and depth of field. If a fullyautomatic camera had been used, the risk of failure would have beengreatly reduced. The final cost, including a reel and canister, was only$38.79. Black and white movies of this length cost $5.00 to rent andmost purchase prices range from $30.00 for black and white up to$60.00 or more for color.Any teacher who wished to undertake the production of their own

movie should find it fairly easy to do and quite rewarding for the class.Although such a movie probably lacks certain professional touches, itmore than makes up for these by imparting a local flavor.

BIBLIOGRAPHYCOOKE, DAVID C., Behind the Scenes in Television. New York: Dodd, Mead andCompany, 1958.

GARDNER, MARTIN, Scientific American Book of Mathematical Puzzles andDiversions. New York: Simon and Schuster Inc., 1959, p. 66.