Spirals and Helices
A spiral is any plane curve that winds around a point in successive convolutions, the curve receding more and more from the point that is called the center. A helix is a kind of three-dimensional spiral. Formally, a helix is a curve that lies on the surface of a cylinder or cone with a constant distance between adjacent coils.
Examples
There are many examples of spirals and helices. Spirals are found in the shells of snails and of Nautilus, a type of marine mollusk. They are also found in spiral galaxies. Sunflower seeds are arranged in a spiral in the center of the flower. Helices are even more common, both in natural and artificial situations. A coiled spring is an example of a helix that could be wrapped around a cylinder while the vortex caused by water going down a plughole is an example of a helix that could be wrapped around a cone. Perhaps the best known helix of all is the double helix of DNA. It is called a double helix because it has two strands wound around each other, each of which is a helix. Some bacteria, such as spirochetes, are helical in shape and move due to a helical wave moving along their length, and some bacteria have helical flagella to move them forward. The filamentous green algae Spirogyra has a helical chloroplast running the length of each cylindrical cell.


From Eyewitness Encyclopedia of Science 2.0.
DK Multimedia.

Spiral shapes

in Nature...

Spirals are found in the shells of snails and marine mollusks. Andromeda galaxy is the nearest spiral galaxy beyond the Milky Way. Horns of Mountain goat display a good example of natural helix. Double helix structure of the DNA molecule.

...in science and art.

Spiral of Progress Monument,
Cameroon
M.Escher.
Bond of Union.
Computer generated fractal.
Mandelbrot Set.
The Solomon R. Guggenheim Museum, New York City,
designed by
Frank Lloyd Wright.

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Sources:
Grolier The 1996 Multimedia Encyclopedia
Eyewitness Encyclopedia of Science 2.0. DK Multimedia.