I find the idea of the golden ratio very facinating. Two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is approx. 1.6180339887.
The golden ratio was first studied by the ancient greeks because of its frequent appearance in goemetry. The golden ratio can be seen in architecture such as the Acropolis, Parthenon and Great Mosque of Kariouan. It can be seen in works of art by da Vinci (Mona Lisa) and Dali (The Sacrament of the Last Supper). It is also found in music pieces such as Debussy's Image, Reflections in Water and in nature in such things as starfish, animal skeletons and tree branch distribution.
I like this description of it. Adolf Zeising, mathmetician and philosopher, wrote in 1854 " the golden ratio is a universal law in which is contained the ground-principle of all formative striving for beauty and completeness in realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form". (http://en.wikipedia.org/wiki/Golden_ratio)
What a fun concept to teach to students--nature's grand designs and special ratios.
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In showing the students the use of the golden ratio through master works of construction helps the students understand of this important guideline. Students are intrigued when something of centuries ago is still used today. We can manipulate the golden raio to fit it into our classrooms for this day and age.
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