The Golden Section And Architecture

The Golden Section and Architecture Do we find it pleasing?

Incorporated into Buildings for Millennia • Egyptians used it in the design of their religious buildings • Had many proponents in Ancient Greece • Explosion in art and architecture during the Renaissance • Psychologists have been examining its aesthetic qualities since the 1870s • Today many architectural firms have it on their web sites • Is it incorporated into Ross

What is the golden section?

Suppose that we were to divide a line such that the ratio of the shorter segment to the longer segment equals the ratio of the longer segment to the entire line.

Mathematically, this can be shown as a/b = b/(a + b) Where a, b represent the lengths of the shorter and longer segments, respectively, and a + b = 1 Phi 1 --------------|-------1 phi phi = 0.618 Phi = 1.618…

In Book 6, Proposition 30, Euclid discusses division of a line to obtain the golden section 1 A G B ------------------------------g 1–g GB = AG , 1 – g = g AG AB g 1

What are some of the properties of Phi? • • • • •

Phi = 1.618…, phi = 0.618… Phi = 1 + phi Phi = 1/phi Phi2 = Phi +1 Phi = (sqr5 +1)/2

How can the golden section be constructed?

Also can be found in ratios of Fibonacci numbers 1,1,2,3,5,8,13,21,… 1/1,1/2,2/3,3/5,5/8,8/13,13/21,… 1,.5,.67,.6,.625,.615,.619,…

Which Structures Have Incorporated It?

Egyptians used the golden section in their pyramids

In Greece, the most famous building incorporating phi is ….

Also popular in medieval and Renaissance architecture

Or Notre Dame in Paris

Many art books talk about centering objects about 1/3 of the way across

Many artists incorporated it into their works

Famous modern day architects discussed its beauty

Incorporated into buildings such as the UN in NYC

Le Corbusier’s Villa Stein in Garches

I.M. Pei’s Bank of China

Is it aesthetically pleasing?

Controversial • Many studies have been done • Conduct of studies has been controversial •

Early Psychological Research • Fechner (1871) “Zur experimentalen Aesthetik” • Subjects given 10 rectangles of equal area and asked to choose most pleasing • 35% expressed a preference for the golden section • 21% expressed a preference for the 1.5:1 rectangle

Criticism • Golden rectangle was in middle of proportion ranges (7th) • Subjects not randomly selected • Subjects may have been cognizant of Fechner’s hypothesis • Preference is a function of associations • Association being the human body which all subjects had

Angier and Division of a Line 1903 • Asked 9 subjects to divide a line 72 times “at the most pleasing place.” • Only two subjects chose the golden proportion with great regularity • Mean proportion was 0.6

E.L. Thorndike 1917 • Subjects given 12 rectangles of varying proportions, but with same height • Height to width ratios varied from 1.3: 1 to 3.75:1 • Asked to rank in terms of “which do you like the looks of most?” • The golden rectangle and the next two most elongated rectangles were ranked 1st, 2nd and 3rd

Similar Studies Kept Being Done • • • •

Studies by age groups Preschoolers had no particular preference 3rd and 6th graders preferred wider triangles Post secondary students preferred rectangles 0.55, 0.60 and 0.65 ratios • Elderly subjects preferred wider rectangles

Studies by Culture • Canadian versus Japanese • 9% of Canadians preferred it versus 5% of Japanese • Americans versus Europeans • Substantial differences showed up between these two groups

Result is a “mass of conflicting data and conclusions.” (Green 1995)

• “It may simply be that the psychological instruments we are forced to use in studying the effects of the golden section are just too crude.” D.E. Berlyne, 1971

According to you folks… Dimensions: A 0.4:1 B 0.5:1 C 0.92:1 D 0.62:1 E 0.85:1

Thank You!