images-2      Five is my favorite number. Sounds funny, a bit nerdy. You know, to have favorite numbers. But it’s true. I confess a certain affection for all the numbers. After all, they’re all “sacred expressions of the transcendent”. But the five is truly special. Its symmetry is perhaps the richest of all.

The golden proportion phi, rooted in fivefold symmetry, is a phenomenon of great beauty and importance to all living things. Phi — the square root of five minus one/divided by two — or 1.618… images-1the golden proportion, timages-2he proportion most pleasing to the eye. Plants grow using the phi proportion. The DNA molecule is arranged according to five or tenfold symmetry. Seeds are most efficiently packed into a flower using phi. And phi is based on the five.

The pentagram with its pentagon inscribed – which circumscribes another smaller pentagram – which in turn generates another little pentagon – then another pentagram, and so on ad infinitum – will also expand in the same proportions ad infinitum (and if you add all those infinitums together you get an awful lot of infinitums).

The diagonals of the pentagram intersect in phi proportions:images-3 the big piece is to the little piece as the entire piece is to the big piece. It’s the “golden mean”. Artists like Leonardo have used it for ages. Phi’s aestheticly pleasing proportions are apparently wired into us. Our senses are naturally attuned to it, and we find it’s proportion of 5 to 8 or thereabouts a simple way to compose a painting or a building or nearly anything. The Parthenon is so constructed. The Great Pyramid too. The application of the phi principle is fundamental to Cheop’s pyramid; it’s dimensions are laid out in accordance to the golden mean. It’s an ancient piece of knowledge. Expressed algebraically phi is represented as AB/AC= (AB+AC)/AB — which reduces to the square root of five minus one/divided by two.images Phi squared equals phi plus one. The mathematical wonders of phi never cease.

The five pointed star is a universal and elegant symbol of course. Although neither the star nor the pentagon tesselate cleanly like the square or the triangle or hexagon, figures based on phi angles nonetheless create patterns like these – Penrose tilings – a tesselation discovered by the physicist and mathematician Roger Penrose – which is a lucky coincidence because it would have been weird if someone called Moskowitz discovered it and named it Penrose tiling (Sorry ’bout that one).

I’ve included a song I wrote that starts off with the fifth. I wrote the song many years ago back in the Bronx, but still enjoy playing it. It tells a bittersweet story, a love story of course. The song is in D, but it starts off in A, the fifth of D. Now, how the musical fifth ties in with what I’ve been talking about is beyond me, but this song is the first one I thought of. I have a weakness for songs that start off in the fifth. Not to mention my weakness for the number five. OK, I won’t mention it (oops I just did).