The Multi-Media Performance ‘987’ Based on the Golden Ratio

Leonnrdo, Vol. 9, pp. 130-132. Pergamon Press 1976. Printed in Great Britain THE MULTI-MEDIA PERFORMANCE ‘987’ BASED ON THE GOLDEN RATIO Jeffrey B. Havill* 1. Introduction On the evening of 19 February 1974 a performance, entitled ‘987’, was staged by students of the advanced design course given in the Department of Art, California State University, Humbolt, Calif., U.S.A. The primary purpose of the project was to produce multi-media presentations through which the ratio called the Golden Mean or Golden Section might be experienced directly rather than understood by the usual didactic explanation . The project was carried out by 30 students under my general direction. Faculty members of the departments of mathematics, of physics and of music participated as advisors. J. E. Householder of the Department of Mathematics through his adventurous spirit and patience contributed greatly to the execution of the project. A student, selected as technical director, was responsible for delegating jobs to be done, arranging for the procurement of materials and overseeing the construction of special devices. Since only seven weeks were available for the completion of the project in the form of a performance, the initial plan prepared had to be carried out as scheduled. The performance was conceived in terms of a ritual to last for about 16.5 minutes in a darkened room. It began slowly and quietly with simple effects, speeded up and became more complex until a climax was reached and then subsided to a calm ending. At the climax, some spectators said that they suffered from sensory overload as features of the performance multiplied and intensified. The performance began and ended in the darkened room with only the sounds produced by two metronomes. One spectator commented at the end: ‘I feel as though I had been taken somewhere and then safely brought back.’ The spectators at the performance sat on chairs arranged in the shape of a pentacle or five-pointed star. The result was that from some chairs, viewing was awkward, but, since the spectators were told that the arrangement was made to be in harmony with the mathematical basis of the performance, few actually moved their chairs. A poster for publicizing the performance was printed with a design based on the Golden Ratio. 2. The Golden Section or Ratio The name Golden Section was given in the 19th century to the proportion called by Euclid the ‘extreme * Artist and teacher, Department of Art. Clack Art Center, Alma College, Alma,-MI48801, U.S.A. (Received 24 March 1975.) and mean ratio’. In the case of a line made up of a shorter part of length u and a longer part of length 6, the Ratio is given by a/b = b/(a + b). The Golden Rectangle is one in which the Ratio applies to its sides of lengths n and 6. The numerical value of the Ratio is the irrational number (&-1)/2 = 0.618033 . . .,and its reciprocal is 1.618033 .... It is interesting to note that the ratios of successivenumbers in the Fibonacci series approach 0.618033 . . . as a limit. Thus, for 1, 1, 2, 3, 5, 8, 13, 21, 34, .. .610, 987, .. .,in which each number is the sum of its two predecessors, the ratios 8/13 = 0.615384 . . . , 13/21 = 0.619047 . . . , 21/34 = 0.617647 . . . oscillate rapidly to the limiting vaIue 0.618033.. .. This and other information on the Golden Ratio was provided to the students [I]. 3. Planning the project A multipurpose room (54 X 54 X 23 ft) in the Student Union Building was chosen for the performance . The vertical from the center of the floor was taken as the axis or meridian from which measurements were made in feet. A pentagon with sides of about 21 ft and within it a pentagram or pentacle were marked on the floor with white tape. The following comment on these shapes is found in Ref. 2: ‘It is traditionally held that Plato began the study of “The Section” as a subject in itself. The construction of the pentagon by means of the isosceles triangle having each of its base angles double the vertical angle (72”, 72”, 36”) was due to the Pythagoreans (Euclid, Bk. 4...