Pentagrams, the Golden Ratio & Art
- Maurice OReilly
Here we have used GeoGebra to explore the construction in Raphael Hynes’ “Dehydrating Mandarins” (2008) . The table top is shown in brown; the fruit in pink, purple & red. The entire construction is (or appears to be) based on regular pentagons and inscribed pentagrams/pentacles (the figure derived by drawing the diagonals of each pentagon). Four pentagrams are shown here. Importantly, the ratio between the lengths of a diagonal of a pentagon and its side is the golden ratio. This has been much favoured in geometry throughout the ages, in Greek architecture, in the works of Renaissance artists (such as Luca Pacioli & Leonardo da Vinci) and, more recently, Salvador Dali, as well as (it has been argued) in the construction of the Egyptian pyramids and in the (Saxon & Irish) insular manuscripts (such as the book of Kells).
Check out the following links: http://www.flickr.com/photos/raphaelhynes/7991862637/sizes/l/in/photostream/ http://www.mathsisfun.com/geometry/regular-polygons.html http://www.mathsisfun.com/geometry/pentagram.html http://www.encyclopedia.com/topic/pentacle.aspx http://www.mathsisfun.com/numbers/golden-ratio.html http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html http://plus.maths.org/content/os/issue22/features/golden/index http://www.intmath.com/numbers/math-of-beauty.php http://www.daviddarling.info/encyclopedia/G/golden_ratio.html http://www.dartmouth.edu/~matc/math5.geometry/unit2/unit2.html http://www.usna.edu/AcResearch/2007SummaryPDFsofReports/Hill_English_2007ResearchReport_NARC.pdf http://staff.spd.dcu.ie/oreillym/pages/memi.htm