Spirals

• Belousov's Brew. A recipe for making spiraling patterns in chemical reactions.

• Equiangular spiral. Properties of Bernoulli's logarithmic 'spiralis mirabilis'.

• Fermat's spiral and the line between Yin and Yang. Taras Banakh, Oleg Verbitsky, and Yaroslav Vorobets argue that the ideal shape of the dividing line in a Yin-Yang symbol is formed, not from two semicircles, but from Fermat's spiral.

• Fourier series of a gastropod. L. Zucca uses Fourier analysis to square the circle and to make an odd spiral-like shape.

• The golden bowls and the logarithmic spiral.

• Golden spiral flash animation, Christian Stadler.

• Graphite with growth spirals on the basal pinacoids. Pretty pictures of spirals in crystals. (A pinacoid, it turns out, is a plane parallel to two crystallographic axes.)

• Helical Gallery. Spirals in the work of M. C. Escher and in X-ray observations of the sun's corona.

• Mathematical imagery by Jos Leys. Knots, Escher tilings, spirals, fractals, circle inversions, hyperbolic tilings, Penrose tilings, and more.

• Log-spiral tiling, and other radial and spiral tilings, S. Dutch.

• Looking at sunflowers. In this abstract of an undergraduate research paper, Surat Intasang investigates the spiral patterns formed by sunflower seeds, and discovers that often four sets of spirals can be discerned, rather than the two sets one normally notices.

• Modeling mollusc shells with logarithmic spirals, O. Hammer, Norsk Net. Tech. Also includes a list of logarithmic spiral links.

• Pi curve. Kevin Trinder squares the circle using its involute spiral. See also his quadrature based on the 3-4-5 triangle.

• Pictures of various spirals, Eric Weeks.

• Polyform spirals.

• Ram's Horn cardboard model of an interesting 3d spiral shape bounded by a helicoid and two nested cones.

• Research: spirals, Mícheál Mac an Airchinnigh. Presumably this connects to his thesis that "there is a geometry of curves which is computationally equivalent to a Turing Machine".

• Seashell spirals. Xah Lee examines the shapes of various real seashells, and offers prize money for formulas duplicating them.

• Soddy Spiral. R. W. Gosper calculates the positions of a sequence of circles, each tangent to the three previous ones.

• Spidron, a triangulated double spiral shape tiles the plane and various other surfaces. With photos of related paperfolding experiments.

• Spira Mirabilis logarithmic spiral applet by A. Bogomily.

• Spiral generator, web form for creating bitmap images of colored logarithmic spirals.
  

• Spiral in a liquid crystal film.

• Spiral minaret of Samara.

• A spiral of squares with Fibonacci-number sizes, closely related to the golden spiral, Keith Burnett. See also his hand-painted Taramundi spiral.

• Spiral tea cozy, Kathleen Sharp.

• Spiral tilings. These similarity tilings are formed by applying the exponential function to a lattice in the complex number plane.
  

• Spiral tower. Photo of a building in Iraq, part of a web essay on the geometry of cyberspace.

• Spiral triangles, Eric Weeks.

• Spiraling Sphere Models. Bo Atkinson studies the geometry of a solid of revolution of an Archimedean spiral.

• Spirals. Mike Callahan and Larry Shook use a spreadsheet to investigate the spirals formed by repeatedly nesting squares within larger squares.

• Spirals and other 2d curves, Jan Wassenaar.

• Spring into action. Dynamic origami. Ben Trumbore, based on a model by Jeff Beynon from Tomoko Fuse's book Spirals.

• These two pictures by Richard Phillips are from the now-defunct maths with photographs website. The chimney is (Phillips thinks) somewhere in North Nottinghamshire, England. A similar collection of Phillips' mathematical photos is now available on CD-ROM.
     

• Three spiral tattoos from the Discover Magazine Science Tattoo Emporium.

• The uniform net (10,3)-a. An interesting crystal structure formed by packing square and octagonal helices.

• Wonders of Ancient Greek Mathematics, T. Reluga. This term paper for a course on Greek science includes sections on the three classical problems, the Pythagorean theorem, the golden ratio, and the Archimedean spiral.

From the Geometry Junkyard, computational and recreational geometry pointers.
Send email if you know of an appropriate page not listed here.
David Eppstein, Theory Group, ICS, UC Irvine.
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