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