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Limits of Golden Constructions (Journal Article)

By: Contributor(s): Material type: TextTextSeries: Mathematics Magazine ; Volume 96: Number 4, October 2023Publication details: Philadelphia, PA :Taylor & Francis Group , September 2023Description: 399-412pISSN:
  • 0025-570X
Subject(s): Online resources:
Contents:
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Summary: Abstract: A golden rectangle is characterized by the fact that if an inscribed square is removed from one end, then the remaining rectangle is similar to the original one. By iterating this process of removing a square, one obtains an infinite sequence of nested golden rectangles which converges to a point. One can construct other sequences of rectangles by starting from arbitrary, not necessarily golden, rectangles. The goal of this paper is to analyze the behavior of these sequences, primarily by modeling the process using linear algebra.
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Abstract: A golden rectangle is characterized by the fact that if an inscribed square is removed from one end, then the remaining rectangle is similar to the original one. By iterating this process of removing a square, one obtains an infinite sequence of nested golden rectangles which converges to a point. One can construct other sequences of rectangles by starting from arbitrary, not necessarily golden, rectangles. The goal of this paper is to analyze the behavior of these sequences, primarily by modeling the process using linear algebra.

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