Root rectangles Dynamic rectangle

hambidge s 1920 illustration of construction of root rectangles. lengths of horizontal sides of original square , 4 root rectangles derived it, respectively






1


,


2


,


3


,


4


,


5





{\displaystyle \scriptstyle {\sqrt {1}},{\sqrt {2}},{\sqrt {3}},{\sqrt {4}},{\sqrt {5}}}

.

a root rectangle rectangle in ratio of longer side shorter square root of integer, such √2, √3, etc.

the root-2 rectangle (acdk in fig. 10) constructed extending 2 opposite sides of square length of square s diagonal. root-3 rectangle constructed extending 2 longer sides of root-2 rectangle length of root-2 rectangle s diagonal. each successive root rectangle produced extending root rectangle s longer sides equal length of rectangle s diagonal.

properties

when root-n rectangle divided n congruent rectangles dividing longer edge n segments, resulting figures keep root-n proportion (as illustrated above).


the root-3 rectangle called sixton, , short , longer sides proportionally equivalent side , diameter of hexagon.


since 2 square root of 4, root-4 rectangle has proportion 1:2, means equivalent 2 squares side-by-side.
the root-5 rectangle related golden ratio (φ). longer side equal 1 plus 2 times 1/φ (0.618...).




^ cite error: named reference hambidge invoked never defined (see page).
^ jay hambidge. (1926, 1948, 1967)the elements of dynamic symmetry. courier dover publications. pp. 9–10.
^ andrew haslam (2006). book design. laurence king publishing. pp. 48–49. isbn 1-85669-473-9. 
^ wim muller (2001) order , meaning in design. lemma publishers, p. 49.
^ kimberly elam (2001). geometry of design: studies in proportion , composition. princeton architectural press. pp. 34–41. isbn 1-56898-249-6.