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Proportion
Proportion,loosely defined, is how the size or magnitude of one thing relates to that of another related thing. Objects have proportional relationships within themselves and with other objects outside themselves.

Proportion and Design
Different proportional relationships can make one thing look important and another thing look unimportant.
Help organize the various elements involved in a design, not only drawing the attention of the viewer, but guiding the viewer's eye throughout that piece of design.

Golden Ratio: equation
Segments of a line divided according to the golden ratio will interrelate to each other as such: The length of a + b is to segment a as the length of a is to segment b.

golden ratio rectangle
constructed by drawing an arch with a line the length of the midpoint of a square to the opposite corner. The farthest point this arch reaches then defines the length of the long side of the rectangle.

root 2 rectangle
The root 2 rectangle,which has proportions of 1:1.41, has the impressive property of being able to be subdivided in half continuously and still have the same aspect ratio If. you begin with a root 2 rectangle, and divide it in half, you’ll have two root 2 rectangles. Repeat the process with one of those rectangles, and you’ll again have two smaller rectangles, and so on.

Other proportions:
 root 2 rectangle
 2:3 rectangle
 3:4 rectangle

3:4 rectangle
3:4 can be found in art, music, dance, and even nature. It has the added benefit of being easily divisible in multiple combinations, which makes it easier and more flexible to work with when constructing grids

3:4 Proportion in nature:
One of the more compelling cases for a proportion such as 3:4 can be found in the very nautilus shell that is normally alleged to relate to the golden ratio.

Proportion in Music:
Guitar (string): If you strum an open guitar string tuned to C, you’ll hear a C note. If you shorten the length of that string to half its original length, you’ll hear another C note, but this time an octave higher (the eighth note in the major scale). If you take that same string and strum it instead at threefourths its original length, you’ll hear an F note (the fourth or subdominant note in the major scale). If you strum the string at twothirds its original length, you’ll hear a G note (the fifth or dominant note in the major scale).

Proportion in Architecture:
Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion.

Proporion in Architecture (DaVinci):
Leonardo Da Vinci: the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture.

Vitruvius
long tradition of Vitruvius, > Roman Architect. where the vitruvian man got his name. Goes back to the golden ratio

Proportion in Dance:
Salsa dancing consists mostly of 3/4 proportions. The lead steps forward and then back within the span of three beats, and then pauses for the fourth beat. The lead then repeats the process, this time stepping backward. The pause on the fourth beat gives an exciting sense of inertia for turns and spins. Also Brachata is a 3/4 dance.

