I am fascinated by interesting numbers, like the “Golden Proportion”, or ratio. However, in researching the number phi φ, or Phi Φ, I have found the usage of these Greek characters, in mathematics, to be completely confused and inconsistent. Sometimes they are BOTH used to represent the number 1.618…, the Golden Mean, Golden ratio, Golden Proportion, Golden Egg (popped out by the Golden Goose). Sometimes one (OR the other) is used to represent the “golden ratio conjugate”, or 0.618… Please, mathematicians, get your act together, and settle on one usage or another, but please be consistent!
Lenny (Leonardo Fibonacci) is probably rollin’ in his grave over this! (purely conjecture on my part – don’t ask me for a “proof”).
I propose that it is logical for (capital) Phi, Φ, to symbolize the Golden Proportion, 1.618…, and (small) phi, φ, to symbolize 0.618… That makes perfect sense in mathematical terms, doesn’t it? Since 0.618… is the smaller number (and geometrically the smaller portion, 0.618…, usually added to 1 to get the larger golden proportion, 1.618…)? Quit confusing young, budding mathematicians with inconsistent usage. On some sites, I have seen the usage confused on the SAME website, and sometimes in the same sentence (or maybe I just imagined that last one).
Don’t ask me for references, I don’t have the energy right now. Just “Google” it and you will quickly see what I am talking about.
“Rant for the day”.