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Unformatted text preview: Sarah E. Dill Calculus I – 1A Golden Rectangle – Notes **Definition : A rectangle which has its ratio of length to width equal to the Golden Mean. This is supposedly the rectangle which is most pleasing to the eye. This is a rectangle whose side lengths are in the golden ratio, 1: , that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden spiral. Golden Spiral A spiral that can be drawn in a golden rectangle as shown below. The figure forming the structure for the spiral is made up entirely of squares and golden rectangles. According to astrophysicist and math popularizer Mario Livio, since the publication of Luca Pacioli's Divina Proportione in 1509, many artists and architects have proportioned their works to approximate the form of the golden rectangle, which has been considered aesthetically pleasing. Sarah E. Dill Calculus I – 1A The large rectangle BA is a golden rectangle; that is, the proportion b:a is 1: . If we remove square B , what is left, A , is another golden rectangle. Constructing a golden rectangle A golden rectangle can be constructed with only a straightedge and compass by this technique: 1. Construct a simple square 2. Draw a line from the midpoint of one side of the square to an opposite corner 3. Use that line as the radius to draw an arc that defines the height of the...
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- Spring '08
- Calculus, Golden ratio, golden rectangle, Sarah E. Dill Calculus