Golden Ratio

Here’s something to consider when designing your home. In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989. Other names frequently used for the golden ratio are the golden section and golden mean.

Golden ratio expressed algebraically
Golden ratio expressed algebraically

At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.
How to construct a golden rectangle
How to construct a golden rectangle

Construction of a golden rectangle:
1. Construct a unit square (red).
2. Draw a line from the midpoint of one side to an opposite corner.
3. Use that line as the radius to draw an arc that defines the long dimension of the rectangle.

Source: Wiki – Golden Ratio
Lots of interesting reading on how the golden mean can be applied. See The Square, The Circle and the Golden Proportion: A New Class of Geometrical Constructions
Leonardo Squared the Circle! – – Da Vinci’s Secret Solution in the Vitruvian Man Decoded

7 thoughts on “Golden Ratio”

  1. Does anyone out there remember or have any access to plans or the principal architects who had golden mean dome kits in the 1990’s?

    They were from the Northwest and I believe were a young inspired group of architects.

  2. Pingback: The Divine Numbers, Golden Ratio, Sacred Geometry and How It's All Connected… | Jan's Experiments
  3. This isn’t just a mathematical curiosity. I’ve been inside buildings that used this ratio and there’s definitely something unusual or a “special feeling” about the space. I guess that’s why the dimensions of many churches and temples are based on the golden mean.


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