Rubi Trees/Golden Mean

Pretty strange: I took several hours to carefully count the number and types of trees in the Rubi Woods using an 8×5 grid method, and came up with the following sums. The total number of trees in the woods, counting those bordering Robin Lane in extreme north Rubi, is 199.

These include 123 eucalyptus trees…

… and 76 cypress trees of both green (larger) and brown (smaller) variety.

The amazing part came when I started dividing the total and subtotals to compare percentages. A number very close to the golden mean kept coming up….

199/123 = 1.617886178861789

123/76 = 1.618421052631579

… or the golden mean +1 in this case:

199/76 = 2.618421052631579

What I soon found out is that I’d somehow stumbled upon a succession of what’s called Lucas numbers or Lucas series, closely related to the more famous Fibbonaci series.

Some articles on Lucas numbers:

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/lucasNbs.html

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/lucas200.html

http://milan.milanovic.org/math/english/lucas/lucas.html

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