- Belousov's Brew.
A recipe for making spiraling patterns in chemical reactions.
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
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.
spiral flash animation, Christian Stadler.
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.
mollusc shells with logarithmic spirals, O. Hammer, Norsk
Net. Tech. Also includes a list of logarithmic spiral links.
curve. Kevin Trinder squares the circle using its involute spiral.
See also his quadrature
based on the 3-4-5 triangle.
of various spirals, Eric Weeks.
- 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.
a triangulated double spiral shape tiles the plane and various other
surfaces. With photos of related paperfolding experiments.
Mirabilis logarithmic spiral applet by A. Bogomily.
generator, web form for creating bitmap images of colored
- Spiral in a liquid crystal film.
minaret of Samara.
- A spiral of squares with
Fibonacci-number sizes, closely related to the golden spiral,
See also his hand-painted Taramundi
- 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.
tower. Photo of a building in Iraq, part of a web essay on the
geometry of cyberspace.
triangles, Eric Weeks.
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.
and other 2d curves,
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,
and recreational geometry pointers.
Send email if you
know of an appropriate page not listed here.
from a common source file.