Dynamic rectangle
Geometric shape
A dynamic rectangle is a right-angled, four-sided figure (a rectangle) with dynamic symmetry which, in this case, means that aspect ratio (width divided by height) is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books. These dynamic rectangles begin with a square, which is extended (using a series of arcs and cross points) to form the desired figure, which can be the golden rectangle (1 : 1.618...), the 2:3 rectangle, the double square (1:2), or a root rectangle (1:√φ, 1:√2, 1:√3, 1:√5, etc.).
Root rectangles
A root rectangle is a rectangle in which the ratio of the longer side to the shorter is the square root of an integer, such as √2, √3, etc.
The root-2 rectangle (ACDK in Fig. 10) is constructed by extending two opposite sides of a square to the length of the square's diagonal. The root-3 rectangle is constructed by extending the two longer sides of a root-2 rectangle to the length of the root-2 rectangle's diagonal. Each successive root rectangle is produced by extending a root rectangle's longer sides to equal the length of that rectangle's diagonal.
Properties
When a root-N rectangle is divided into N congruent rectangles by dividing the longer edge into N segments, the resulting figures keep the root-N proportion (as illustrated above).
The root-3 rectangle is also called sixton, and its short and longer sides are proportionally equivalent to the side and short diameter (height) of a hexagon.
Since 2 is the square root of 4, the root-4 rectangle has a proportion 1:2, which means that it is equivalent to two squares side-by-side.
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