All that Glitters is Gold

Aug 9, 2020 | Hinsdale

In March, we talked about the Golden Ratio, which is defined as "two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship."

MathWorld gives us a definition of the Golden Spiral: "Successive points dividing a golden rectangle into squares lie on a logarithmic spiral (Wells 1991, p. 39; Livio 2002, p. 119) which is sometimes known as the golden spiral."

If this sounds a little confusing, adding some examples might help! There are many different shapes and sizes that the Golden Ratio can be found in:

MathWorld gives us an example of a Golden Rectangle:

GoldenRatioEuclid

GoldenSpiral

A Golden Triangle:

GoldenTriangle      GoldenTriangleFigures

 

A Golden Rhombohedron:

GoldenRhombohedra

And even a Golden Rhombus:

RhombicHexecontahedron             RhombicTriacontahedron

So now that we have the shapes figured out, how do we find the Golden Ratio while we're out and about? Luckily, there is a formula, and plenty of real-world examples!

MathIsFun gives us the formula: 

Find examples of the Golden Ratio in nature here!

Find examples of the Golden Ratio in art here!

Now you'll be seeing the Golden Ratio everywhere!

 

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