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Title: Golden Ratio and the Fibonacci Sequence
Book Description: This WorkBook uses Logo style graphics to explore the relations between the Golden Ratio and the Fibonacci sequence. The Greek view of ratio is illustrated. In this view, a ratio of segments is the "shape" of a rectangle whose sides are those segments. Incommensurable segments have rectangles that cannot be filled with equal squares. The Golden rectangle is an example, and it represents the "golden ratio". The incommensurability is disclosed by a reverse process in which, for each natural number, a rectangle is drawn whose sides are in the ratio of two successive terms of the Fibonacci sequence. The construction is illustrated in the WorkBook, where the reader may select the natural number, then view the rectangle, and compare its shape with that of the Golden Rectangle. Decimal approximations to the ratios of successive sides are printed, and these may be seen to converge to the golden ratio, while the geometric limiting process gives another visualization of the same thing.
Author: James White
Suggested Use: Visualization of an irrational number
Topics: golden ratio, fibonacci sequence, Logo graphics
Number of Pages: 3
Animation: Yes
Grade
Level: 