# Pentagrams, the Golden Ratio & Art

- Author:
- 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