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THE GOLDEN RATIO: The Story of Phi, The World's Most Astonishing Number, by Mario Livio, (Broadway Books, New York: 2002), p.85:
“From never-ending expressions let us turn our attention to the Golden Rectangle [below]. The lengths of the sides of the rectangle are in a Golden Ratio to each other. Suppose we cut off a square from this rectangle (as marked in the figure). We will be left with a smaller rectangle that is also a Golden Rectangle. The dimensions of the 'daughter' rectangle are smaller than those of the 'parent' rectangle by precisely a factor phi. We can now cut a square from the daughter Golden Rectangle and we will be left again with a Golden Rectangle, the dimensions of which are smaller by another factor of phi. Continuing this process ad infinitum, we will produce a smaller and smaller Golden Rectangle (each time with dimensions deflated by a factor of phi). If we were to examine the ever decreasing (in size) rectangles with a magnifying glass of increasing power, they would all look identical. The Golden Rectangle is the 'only' rectangle with the property that cutting a square produces a similar rectangle. Draw two diagonals of any mother-daughter pair of rectangles in the series, as in [below], and they will intersect all at the same point. Because of the divine properties attributed to the Golden Ratio, mathematician Cifford A. Pickover suggested that we should refer to the point as the “Eye of God.”
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THE GOLDEN RATIO: The Story of Phi, The World's Most Astonishing Number, by Mario Livio, (Broadway Books, New York: 2002), p.85:
“From never-ending expressions let us turn our attention to the Golden Rectangle [below]. The lengths of the sides of the rectangle are in a Golden Ratio to each other. Suppose we cut off a square from this rectangle (as marked in the figure). We will be left with a smaller rectangle that is also a Golden Rectangle. The dimensions of the 'daughter' rectangle are smaller than those of the 'parent' rectangle by precisely a factor phi. We can now cut a square from the daughter Golden Rectangle and we will be left again with a Golden Rectangle, the dimensions of which are smaller by another factor of phi. Continuing this process ad infinitum, we will produce a smaller and smaller Golden Rectangle (each time with dimensions deflated by a factor of phi). If we were to examine the ever decreasing (in size) rectangles with a magnifying glass of increasing power, they would all look identical. The Golden Rectangle is the 'only' rectangle with the property that cutting a square produces a similar rectangle. Draw two diagonals of any mother-daughter pair of rectangles in the series, as in [below], and they will intersect all at the same point. Because of the divine properties attributed to the Golden Ratio, mathematician Cifford A. Pickover suggested that we should refer to the point as the “Eye of God.”
