On Sandra Boynton‘s Facebook page yesterday:

Today is Pet Photo Day, so here is a recent snapshot of my semi-domesticated Golden Meanie, Fibonacci.

*Golden Meanie* is a bit of complex language play, combining the mathematical term *golden mean* (aka *golden ratio*); a reference to the Blue Meanies of the animated film *Yellow Submarine*; and a reference to the amiable domestic dog breeds the golden retriever and the golden Labrador. Plus, the name of Boynton’s Golden Meanie, Fibonacci, is a reference to the Fibonacci sequence in mathematics, which is intimately related to the golden ratio.

Compare Boynton’s cartoon with this diagram:

(#2) A Fibonacci spiral which approximates the golden spiral, using Fibonacci sequence square sizes up to 34. The spiral is drawn starting from the inner 1×1 square and continues outwards to successively larger squares.

From Wikipedia:

In mathematics, 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.

… [referred to by] the Greek letter phi (𝜑) … It is an irrational number with a value of 1.6180339887…

The golden ratio is also called the golden mean or golden section (Latin:

sectio aurea).… The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.

The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …. [Start the sequence with 1, 1; then the next term in the sequence is the sum of the two previous terms.]

The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence …, as originally shown by Kepler [the ratios are: 1, 2, 1.5, 1.666…, 1.625, 1.615…, 1.619…, 1.617…, 1.618…, …]

(See my 1/18/15 posting “The creatures of Fibonacci” on Fibonacci numbers, with links to earlier postings.)

On Blue Meanies, from Wikipedia:

The Blue Meanies are a fictional army of fierce, if buffoonish, music-hating creatures in the surreal 1968 Beatles film

Yellow Submarine. They allegorically represent all the bad people in the world.

And then the dogs. The golden retriever:

And the golden Labrador, or golden Lab for short, a cross between the golden retriever and the Labrador retriever:

The dogs are sweet, affectionate, and family-oriented. Pretty much the polar opposites of Blue Meanies. So the Golden Meanie is a union of opposites — semi-domesticated, as Boynton says.

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