Static Tops To Bc Avoided Ee Plate

flg*28* unity-og? a cube kvlth pace. ratio5 of i • dynamic quality low" .static *

EACH 5IPL 1-73*0*. A SQUARE. PLU5 -IS'1' OF A SQUARE.

FlG-2£>- JSOOT 2 VOLUME. - RATIO OF EACH SIDE. l-A-i* OR A «SQUARE. PLUS .^rOF A 5QUACC.

EACH 5IPL 1-73*0*. A SQUARE. PLU5 -IS'1' OF A SQUARE.

FlG-2£>- JSOOT 2 VOLUME. - RATIO OF EACH SIDE. l-A-i* OR A «SQUARE. PLUS .^rOF A 5QUACC.

fig.<31 . root 4 voluric.« sides have ratios of 2 . least KUHLTIC OF SEJÇJES •

FIG A NEST OF THE

ROOT VOLUMES WITH ROOT 5• RATIO Z.Z3+ OUTSIDE . nOTt ATTRACTIVE. RtLATiON-5H»PS AHP SCi5UErtCt.

Plate 3

lion series of numbers, 3-5-8-13-21- and so on, each number representing the sum of the two preceding numbers, is the basis for the ionic curve or the spiral, Figure 138, page 133, the most attractive of all curves. Well-known arithmeticians assert that beauty in proportioning may be reduced to a mathematical basis, while designers claim that the beauty in modern design rests mainly in its proportions. These points are potent reasons for the following approach, with the distinct reservation that any mathematical theory is a good servant but a poor master; while a sensitivity to proportioning frees one from all forms of mathematical or geometrical approaches.

The Hambidge Rectangles

Through many years of careful research in the design methods of the early Greeks and Egyptians, Jay Hambidge, among other discoveries, found a large number of Greek vase forms which fitted exactly in certain rectangles—rectangles which possessed interesting relations to each other. Five of these rectangles are outstanding and are of value to us as representing dynamic areas used by the best of all proportionists, the Greeks.

Full explanation of the Hambidge theory is not adapted to the objectives of this text; consequently, ratios alone are considered. Omitting the square with its ratio of 1, the parent rectangles rediscovered by Mr. Hambidge are termed the Root Two Rectangle, with its ratio of 1.41+, shown volu-metrically in Figure 29, Plate 3; the Root Three Rectangle, with a ratio of 1.73+, Figure 30, Plate 3; the Root Four Rectangle, with a ratio of 2, Figure 31 (this seems to be the least satisfactory of the series); the Root Five Rectangle, with its ratio of 2.23+, Figure 32, Plate 3; and the Whirling Square Rectangle, or XM Rectangle, with a ratio of 1.618-f, Figure 27a. For comparative purposes and excepting the whirling square, these rectangles have been assembled into

Dynamic Proportions andVolumes

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