References

On this page, we have collected a series of links to other websites dealing with logarithmic spirals and/or its manifestation in nature. Furthermore, quite a few book and article references can be found here, indicating the vaste interest which lay in the study af natural patterns, expecially the logarithmic spiral.

A Pinecone

Other websites dealing with similar subjects:

[3]	Pau ATELA and Christophe GOLÉ Phyllotaxis, An Interactive Site for the Mathematical Study of Plant Pattern Formation http://www.math.smith.edu/~phyllo/

[4]	Unknown author The Nautiloid Network http://www.nautiloid.net/

[14]	M.Alan KAZLEV Cephalopoda Through the Ages http://www.palaeos.com/invertebrates/molluscs/cephalopoda/nautiloidea.htm

[15]	Ron KNOTT Fibonacci Numbers and the Golden Section http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

[20]	Tony PHILLIPS The most irrational number http://www.ams.org/new-in-math/cover/irrational1.html

[24]	Wolfram MathWorld An introduction to logarithmic spirals http://mathworld.wolfram.com/LogarithmicSpiral.html

Selected book and article references:


[2]	Pau ATELA, Chrisophe GOLÉ and Scott G.HOTTON A dynamical system for plan pattern formation : A rigorous analysis 2002 Article available in PDF format at http://www.math.smith.edu/~phyllo/Assets/pdf/dsforplantpattern.pdf

[5]	Samuel COLEMAN Nature’s Harmonic Unity: A Treatise on Its Relation to Proportional Form AyerCoPub, 1913

[6]	Theodore Andrea COOK The Curves of Life Dover Publications, New York, May 1979

[7]	Deborah R.FOWLER, Hans MEINHARDT, and Przemyslaw PRUSINKIEWICZ Modeling seashells Proceedings of SIGGRAPH’92, 1992 Article available in PDF format at http://www.cpsc.ucalgary.ca/Research/bmv/papers/shells.sig92.pdf

[8]	Jens GRAVESEN Differential Geometry and Design of Shape and Motion Department of Mathematics, DTU, 2002

[9]	Alfred GRAY Modern Differential Geometry of Curves and Surfaces CRC Press, 2000

[10]	Istaván HARGITTAI and Clifford A.PICKOVER Spiral Symmetry World Scientific, 1992

[11]	W. HOFMEISTER Allgemeine morphologie der gewasche Handbuch der pages 405–664, 1868

[12]	Scott G.HOTTON Symmetry of plants Ph.D thesis, University of California, Santa Cruz, 1999 Thesis available in PDF format at http://www.math.smith.edu/~phyllo/Assets/pdf/thesis.pdf

[13]	Kamon JIRAPONG and Robert J.KRAWCZYK Case study: Modeling the interior structure of seashells Illinois Institute of Technology, 2002 Thesis available in PDF format at http://www.iit.edu/~krawczyk/shell01/kj01.pdf

[16]	Edward Harrington LOCKWOOD A Book of Curves Cambridge University Press, 1961

[17]	Vagn LUNDSGAARD HANSEN Geometry in Nature A K Peters, Ltd. ,Massachusetts, US, 1993

[19]	Leonardo of PISA (Fibonacci) Liber Abaci 1202

[21]	David M.RAUP Computer as aid in describing form in gastropod shells Science, 138: 150–152, 1962

[22]	David M.RAUP Geometric analysis of shell coiling: general problems Journal of Paleontology, 40: 1178–1190, 1966

[23]	D’Arcy Wentworth THOMPSON On Growth and Form Dover Publications, 1917