Hi all
To link to my previous post and the importance of the openings on this vernacular architectures of Southern Europe, I'll write a bit now on common proportions for the openings on traditional construction.
This all makes sense when you think that in most cases, the tools available would be rather simple like ropes and plumb lines, so simple geometric methods were developed for them.
A very surprising one is the tool to make a Pythagorean (right) triangle with rope.
People would take a rope and make 12 equally-spaced knots on this. Then, by folding the rope so that the segments would have 5+4+3 knots, they'd get a right triangle and so would be able to set things at right angles.
So, for example, to make a square, they would nail down a rope and draw a circle, its radius being the desired square side. Then they would drop the plumb line from the center of the circle till it met the circle itself, finding the vertical side of the square; and from it they could apply the 12-knot rope to determine the horizontal side.
Another simple construction is what I am calling the root-of-2 rectangle, as I don't know what it is called in English. It is constructed by drawing an arc of circle through the diagonal of the square. If you take a square of side=1, then the diagonal of that square is √2. This rectangle has a proportion approximately 1:1.41 -- handier to know the numbers when you are working in SL
The root-of-2 rectangle is often called the golden rectangle, but that's not correct! The true golden rectangle is more elongated. Its proportion is the Gold Ratio or φ (Phi), so about 1:1.62.
The construction is a bit more complicated: you find the median point of the side (which you can do easily with a rope; in the drawing, the dash-dotted line with the symmetry sign marks it), and from that median point you draw an arc of circle to a new diagonal and extend the side.
The golden rectangle is considered specially pleasing, and you can find it everywhere -- for example, the A-format paper-sheet is a golden rectangle, as the golden rectangle is infinitely recursive. You can also draw the logarithm spiral from it, and that spiral exists in nature from the arms of galaxies to sunflowers and mollusc shells.
Then, you have the Double Square proportion, or 1:2. This is the proportion of a 512*1024px texture It is just two equal squares
This used to be a common proportion for doors, as a 2m-tall door would be 1m-wide, making for a very comfy door to go through (most human bodies will occupy a width of 0.80m when carrying something in their arms, like a tray or a pot). Nowadays, most mass-produced doors for domestic settings will typically be produced in increments (for example, widths of 0.65, 0.70, 0.75...) and so will miss proportions altogether.
And you can have Triple Square, so three equal squares, or 1:3.
BTW, I have shown here tall rectangles, because on my other post I was talking about the vertical expression of the vernacular architecture in Tuscany, but obviously you can have wide proportional rectangles too.
I am having issues placing more pictures in this post, so I am going to finish it and do a reply to go on