It looks almost certain that these simple ruler-compass (or only-compass) constructions comply with the spirit, the work practice and work inspiration of medieval builders (particularly master masons), but still also with those of the Baroque architects. And, as Matila C. GHYKA shows in chap. VIII of “Geometry of Art and Life” (1946, since 1977 Dover) clearly demonstrates, with Greek geometry and design patterns for art and architecture. And with still older civilizations, with Indian, Islamic, Buddhist and other East Asian (i.e. Chinese, Japanese, Korean etc.) design patterns that were often strongly based on “square-based” geometric constructions. (The Arabs intensively and repeated used precise translations of Greek math and geometry, particularly of Euclid, and developed these insights for theoretical and practical applications, as we know from Leonardo di Pisa (Fibonacci), who lived and learned years of his childhood in Bougie, Algeria). As mentioned, these figures belong to the square-based proportion figures, and apparently they constitute “bridges” between the Quadrature proportion codes and those of Triangulature and Quinture (Golden Mean, Golden Section). The diagonals of these figures have always irrational lengths (incommensurable lengths), that were used as radiuses of archs drawn with compass. GHYKA quotes PLATO, VITRUVIUS, EUCLID, J. HAMBIDGE (“dynamic symmetry”, a term he derived from Plato’s Theaetetus), MOESSEL, F.M. LUND and others, and shows them on plate XLVI as “Static and Dynamic Rectangles”. I have not yet integrated all these figures in my list of proportion codes according Triangulature, Quadrature, and Quinture (Golden Section), I attached to my Tradarch list posting of Aug 8th, of this year. But undoubtly, they belong to there. My list was developed on base of CAD analyses of traditional vernacular architecture (I call it TVA) in Central Europe (later of all other parts of Europe, the US, Latin America, Japan, Turkey). It would be interesting to check if these angles can be found in these age-old architecture. More than a quarter of more than 1,000 CAD analyses I made of this kind of architecture, clear belong to the Golden Rectangle, being the diagonal of the m:M and M:m rectangles. The flat m:M rectangle can be encountered in regions of Mediterranean TVA, while being almost unknown in non-Mediterranean TVA. I have not had yet access of the whole of the other parts of your temporary file. Dr Joachim Langhein

Another diagram easily found on the web is the Auron (Golden Section). My website has directions for the three you mention and also the Auron. The rest of the 12 total orthogons are somewhat difficult to create electronically. I am in the process of publishing a book on the orthogons and have instructions that can be snail-mailed: http://www.timelessbydesign.org/

The orthogons are amazingly beautiful as an understructure for art and architecture. Walter Valentini's art is a stylization of orthogons--very nice: http://www.galaverni.com/artisti/mostre2.php?id=3

For more info about the orthogons, check out my website (links included--also a good idea to google individual orthogons: hemidiagon, trion, etc.)

VJ