proportionS Proportion is the relation between elements and a whole.
„proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this result the principles of symmetry. Without symmetry and proportion there can be no principles in the design of any temple; that is, if there is no precise relation between its members as in the case of those of a well shaped man.� vitrivius-the ten books of architecture (III, Ch. 1)
wikipedia
In architecture the whole is not just a building but the set and setting of the site. The things that make a building and its site "well shaped" include the orientation of the site and the buildings on it to the features of the grounds on which it is situated. light, shade, wind, elevation, choice of materials, all should relate to a standard and say what is it that makes it what it is, and what is it that makes it not something else. wikipedia
Architectural practice has often used proportional systems to generate or constrain the forms considered suitable for inclusion in a building. In almost every building tradition there is a system of mathematical relations which governs the relationships between aspects of the design. These systems of proportion are often quite simple; whole number ratios or easily constructed geometric shapes (such as the vesica piscies or the golden ratio). wikipedia
Golden Ratio
Vesica Piscies
Generally the goal of a proportional system is to produce a sense of coherence and harmony among the elements of a building. wikipedia
GOLDEN RATIO
The golden section is a line segment sectioned into two according to the golden ratio. The total length a + b is to the longer segment a as a is to the shorter segment b.
A FIBONACCI SPIRAL that approximates the golden spiral, using Fibonacci sequence square sizes up to 34.
HUMAN BODY
EGYPTIAN CANON
XIX c. Alfred Zeising
POLIKLET CANON
LIZYP CANON
Middle ages-Willard de Lionnecourt
WITRUWIUSZ CANON
LEONARDO DA VINCI’S PREPARATION
MODULE MODULE - A UNIT TO DEFINE PROPORTIONS. IT IS USING IN ARCHITECTURE, SCULPTURE AND PAINTING. SUBORDINATING OF WORK TO MODULARITY RULES PERMIT ACHIEVE AN EFECT OF GRAPHIC ORDER, HARMONY AND RYTHM.
LE CORBUSIER – HUMANISTIC ASPECT OF ARCHITECTURE
BEAUTY AS A RESULT OF PROPOTIONS LE COLBUSIER PREPARED MODULAR SYSTEM OF POROPOTION – MODULOR – HE LINKED SYSTEMATICS OF HUMAN SIZES WITH PHENOMENON OF GOLDEN RATIO.
GOLDEN RATIO CAN BE PRESENT GEOMETRICLY OR AS A ANALYTIC FORMULA. GEOMETRICLY- INTERRELATION BETWEEN SQUARE, CYRCLE AND TRIANGLE. ANALYTIC FORMULA- G = 1+1/G LE COLBUSIER DISPENSE PART OF HUMAN BODY: FEED, SOLAR PLEXUS, HEAD, FINGERS OF ELONGATED HAND. HE TOOK AVERAGE HEIGHT OF EUROPEAN 175 CM – HE DIVIDED THIS MEASUREMENT ON THREE SECTIONS OF GOLDEN RATIO 108,2-66,8-41,45-25,4 CM 25,4 ≈ 10 CAL – ENGLISH CAL RED ROW - AND DOWN – 6 ENGLISH FOOD = 1828,8 MM ≈ HEIGHT OF MAN BLUE ROW – HEIGHT WITH REISED HAND = 226 CM
PROPOTIONS SYSTEM => HARMONY, MODERATION – ANY PART DOESN’T VIOLATE LAWS OF WHOLE.
UNITE D’HABITATION - LE CORBUSIER
PYRAMIDS - EGYPT
THE SAME PROPORTIONS SYSTEM
INDIVIDUAL IMAGE
PANTEON - ROME
PALLADIO’S VILLA