A recent story on Saharan silver ants Cataglyphis bombycina (http://www.newscientist.com/article/dn27748-silver-coat-lets-saharan-ants-withstand-scorching-desert-heat.html#.VZPPM6bDs7A) has set me wondering on the uses of geometry in nature. The silver appearance of the ants is due to a layer of hairs that have triangular cross-section, and which reflect the sun’s rays.
But triangular is by no means the most efficient shape to reflect unwanted light and heat. The best shape by far is the corner cube reflector, shaped like the corner of a cubical box with reflective coatings on all three inner surfaces. Such a reflector will throw light and heat rays back exactly in the direction from which they came – so accurately, in fact, that Earth-based scientists have been able to bounce a laser beam off an array that was set up on the moon by astronauts Neil Armstrong and Buzz Aldrin after the Apollo 11 moon landings, and receive the reflected beam back in their own lab (the basic geometry is described well in http://farside.ph.utexas.edu/teaching/302l/lectures/node133.html. Euclid could have worked it out, but I have unable to find out whether he did).
Corner cube reflectors have many uses, from cat’s eyes in roads to reflecting covers above open-top freezers in supermarkets. So, I wondered, why hasn’t nature developed them?
Well, it has. They occur in the eyes of the Macrura (lobsters, prawns, shrimps, etc) and the weird deep-sea galatheid crabs, and act to focus light by reflection, rather than by refraction through a lens. Just as astronomers have both refracting and reflecting telescopes, so nature has refracting and reflecting eyes. There is indeed nothing new under the sun.
FOR MORE INFORMATION: There isn’t much for the non-specialist, but Gerald Meurant’s The Biology of Crustacea Vol.3: Neurobiology, Structure and Function, pp. 313 – 315 is surprisingly accessible, and you can check it out on Google (https://books.google.co.uk/books?id=y6d7oKo700gC&pg=PA313&lpg=PA313&dq=biological+corner+cube+reflector&source=bl&ots=0yXpw9X819&sig=fqSka5a2T9wt7ynaDkMCIA2UaeA&hl=en&sa=X&ei=qxeVVabqJIr-UOP-hOAH&ved=0CFEQ6AEwCA#v=onepage&q=biological%20corner%20cube%20reflector&f=false)