Hi Luke, It was raining earlier today so I pursued your gnomonic thread to spirals and Fibonaccidentally stumbled upon the very instructive: http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#spiral
There a click on Equiangular Spiral led to: http://www.best.com/~xah/SpecialPlaneCurves_dir/EquiangularSpiral_dir/equiangularSpiral.html where a click on Table of Contents led to A Visual Dictionary of Special Plane Curves at: http://www.best.com/~xah/SpecialPlaneCurves_dir/specialPlaneCurves.html All wonderful stuff. On the other hand a click on Logarithmic Spiral led to: http://www.notam.uio.no/~oyvindha/loga.html with its beautifully generated "shells". Thank goodness the return of sunshine has inspired me to search for some water snails outside rather than spiralling further along the branches of these beautifully diverging series. I wonder if Mathematica has been tried for generating sundial information. Cheers, Tom Semadeni