Animals : Humans : {Creative Manifestations}

Not only is the Golden Ratio, also known as the Divine Proportion, observed in human physiology, it seems to be also evident in our less physical characteristics--in the way we perceive and in what we find beautiful.  Whether through deliberate application or non-rational appeal, the Divine Proportion is exhibited in many human-created manifestations throughout the ages, many of these being works of music, architecture, or visual art that we consider as the most aesthetically-pleasing of all time. 

Parthenon image, <>
The proportions of the Egyptian Pyramids have been linked to Phi, and the Parthenon in Acropolis in Athens has dimensions approximating the Golden Mean (perhaps designed particularly to fit this ratio given the Greeks’ understanding of geometry and a survey of similar architecture leading up historically to the Parthenon’s construction).  During the Renaissance, geometric principles such as the importance of Phi were returned to and used by artists in their creative aims;  Leonardo da Vinci was an artist deeply interested in the form and proportion of the natural world, and the Divine Proportion was a conscious consideration in many of his simplest sketchbook drawings and is evidenced even in the eternal face of the Mona Lisa. 

The Divine Proportion in time has been recognized in such musical works as Mozart’s Sonata in C major (in the first movement the character of the music changes after the 17th of 28 bars, demonstrating the ratio Phi) and in several Preludes by Chopin.

Susan Happersett is one of the many artists inspired by math and the Fibonacci sequence. Happersett's set of books, "Box of Growth," relates directly to the Fibonacci Sequence in nature and was one of our group's inspirations for this project.

"Box of Growth" is a collection of five handmade books, each about a particular occurrence of the Fibonacci sequence in nature. The books use a visual language of characters composed of Fibonacci numbers of lines (1 line, 2 lines, 3 lines, 5 lines), arranged to represent patterns of growth and decay. Every aspect of each book, the colors used, the font, the texture of the paper, the layout of the description on the final page, is connected to the object that book describes, such as a conch shell or a flower.

The books are available for viewing in the John Hay Library and we would suggest that Math 8 students go to see them.

For more information on Susan Happersett's mathematical art, follow this outside link, an article by Ivars Peterson on her work, especially her interest in mobius bands <>

Box of Growth: book of Bloemen
Box of Growth: book of leaf
"Box of Growth" by Susan Happersett, from the Purgatory Pie Press site,  <>

Downwards in the tree: {Humans}

Sources: Parthenon image, <>; 
images of "Box of Growth" by Susan Happersett, from the Purgatory Pie Press website, <>; "Invisible Architecture" website by Bonnie Goldstein DeVarco; "The Divine Proportion" website by George Gruner. See bibliography.