Dynamic rectangle

Jay Hambidge, as part of his theory of dynamic symmetry, includes the root rectangles in what he calls dynamic rectangles, which have irrational and geometric fractions as ratios, such as the golden ratio or square roots.

[4] According to Matila Ghyka, Hambidge's dynamic rectangles can produce the most varied and satisfactory harmonic (consonant, related by symmetry) subdivisions and combinations, and this by the very simple process [...] of drawing inside the chosen rectangle a diagonal and the perpendicular to it from one of the two remaining vertices (thus dividing the surface into a reciprocal rectangle and its gnomon) and the drawing any network of parallels and perpendiculars to sides and diagonals.

ορθος, orthos, "straight"[9] and γονια, gonia, "angle"; "a right angled figure", which, as a consequence, is rectangular and tetragonal[10]) has been used historically by artists, architects and calligraphers to guide the placement and interaction of elements in a design.

[3][11] These orthogons are:[12] Wolfgang von Wersin's book includes an extraordinary copy of text from the year 1558 (Renaissance), with diagrams of seven of the 12 orthogons and an invitation from the passage to pay careful attention as the "ancient" architects believed "nothing excels these proportions" as "a thing of the purest abstraction.

Once an individual Orthogon is constructed, additional related measurements are determined (small, medium, large).

These measurements can then be used to guide the design (painting, architecture, pottery, furniture, calligraphy, auto, etc.).

The artwork of Giorgio Morandi exemplifies how measurements of varying sizes (derived from an Orthogon) can create visual harmony.

Marcus Vitruvius Pollio in Book Three of "De Architectura" (known currently as "The Ten Books of Architecture") explains: "Therefore, since nature has designed the human body so that its members are duly proportioned to the frame as a whole, it appears that the ancients had good reason for their rule, that in perfect buildings the different members must be in exact symmetrical relations to the whole general scheme.

Leonardo's drawing of the Vitruvian Man is an illustration of the concept of parts relating to the work as a whole.

Hambidge's 1920 illustration of the construction of root rectangles. The lengths of the horizontal sides of the original square and the four root rectangles derived from it, are respectively . [ 2 ]
A root-phi rectangle divides into a pair of Kepler triangles (right triangles with edge lengths in geometric progression).
Caskey's 1922 illustration of the property that a root-N rectangle divides into N reciprocal rectangles of the same proportions. [ 8 ]