The Golden Mean

The Golden Mean (also known as the Golden Section, Golden Ratio, or Divine Proportion) is a mathematical ratio. When a line is divided into two parts and the longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a), which equals 1.618… (This ratio is what is known as an irrational number. The ellipsis or the three dots at the end of the ratio, tells us that the sequence of decimal digits has no end.) The ratio is expressed mathematically as the Greek letter phi (φ).

The Golden Mean can be applied to shapes. Take a square and multiply one side of by 1.618 and you create the Golden Rectangle (as seen in the images below). If you add a square inside that whose dimensions are the short side of the rectangle, the remainder of the shape is another golden rectangle which can itself subdivided to create another, though much smaller golden rectangle. The Golden Spiral that I use to create the images below is a visualization of the ratio.

While this is a mathematical concept, it often appears to be represented in nature. The pattern of seed on a sunflower or the chambers of the Nautilus mollusk form in very similar proportions, though not mathematically the same as the Golden Mean

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