First of all I should start with an apology as this posting is straying rather from the subject matter of Gordon but it does finish with a reference to Toronto.
Talking about the golden rule reminded me how taken I was when I first read as a maths student (yes in the UK we studied "maths" that being a more appropriate abbreviation for mathematics than the American "math") about the golden number that I now see is also known as the "The golden ratio",and/or also known as the divine proportion, golden mean, or golden section or by the symbol phi defined eloquently and mathematically on:-
http://mathworld.wolfram.com/GoldenRatio.html
where it states that " It is also a so-called Pisot Number"
(don't tell me to pis. o..!!)
But to put it simply in the manner I first heard of it if you have a rectangle whose sides are that ratio then mark off a square at one end the remaining rectangle's sides are in the exact same ratio as the original rectangle's and so on ad infinitum
"successive points dividing a golden rectangle into squares lie on a logarithmic spiral. This figure is known as a whirling square."
These diagrams might help you get your tonsils around the concept
A rather more direct definition and explanation is at:-
http://en.wikipedia.org/wiki/Golden_ratio
"The golden ratio is an irrational number, approximately 1.61803..., that possesses many interesting properties. Shapes defined by the golden ratio have long been considered aesthetically pleasing in Western cultures, reflecting nature's balance between symmetry and asymmetry and the ancient Pythagorean belief that reality is a numerical reality, except that numbers were not units as we define them today, but were expressions of ratios. The golden ratio is still used frequently in art and design. The golden ratio is also referred to as the golden mean, golden section, golden number, divine proportion or sectio divina."
The value of this ratio can of course be computed
as wikipedia says:
The golden ratio value
is the only positive number that is exactly 1 less than its own square.
Note the reference above to "aesthetically pleasing"
and the value 1.61803
Actual examples of the occurrence of this ratio are listed on:-
http://www.php-deluxe.net/wiwimod,in...lden-ratio.htm
and include:-
"Credit cards are generally 3 3/8 by 2 1/8 inches in size, which is less than 2 percent from the golden ratio."
"The Acropolis, including the Parthenon, is often claimed to have been constructed using the golden ratio."
"It is also claimed that the human body has proportions close to the golden ratio"
The number even has its own website
http://www.goldennumber.net/
where you can read amongst a plethora of items:-
Including the main example I remember
Nature (Life)
"The spiral growth of sea shells provide a simple,
but beautiful, example . . ."
A real logarithmic spiral
Architecture
"Its use started as early as with the Egyptians in the design of the pyramids:"
and the architects "used it in the design of Notre Dame in Paris"
In our time
"Its use continues in modern architecture, as illustrated in the United Nations building"
and even:-
"The CN Tower in Toronto, the tallest tower and freestanding structure in the world,contains the golden ratio in its design. The ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of Phi!"
However for a long time I have had in my mind the misconception that this ratio is in fact close to the 4:3 common television screen and digital camera pictures dimensions but obviously that is incorect
John Fowles
Here endeth today's art. history and mathematics lessons boys and girls
Class dismissed
"wake up at the back there" Steve
[ September 27, 2005, 11:21: Message edited by: johnfowles ]