Spirals in Nature

The very numerous examples of spiral conformation which we meet with in our studies of organic form are peculiarly adapted to mathematical methods of investigation. But ere we begin to study them we must take care to define our terms, and we had better also attempt some rough preliminary classification of the objects with which we shall have to deal.

In general terms, a Spiral is a curve which, starting from a point of origin, continually diminishes in curvature as it recedes from that point; or, in other words, whose radius of curvature continually increases. This definition is wide enough to include a number of different curves, but on the other hand it excludes at least one which in popular speech we are apt to confuse with a true spiral. This latter curve is the simple screw, or cylindrical helix, which curve neither starts from a definite origin nor changes its curvature as it proceeds. The ‘spiral’ thickening of a woody plant-cell, the ‘spiral’ thread within an insect's tracheal tube, or the ‘spiral’ twist and twine of a climbing stem are not, mathematically speaking, spirals at all, but screws or helices. They belong to a distinct, though not very remote, family of curves.

Of true organic spirals we have no lack. We think at once of horns of ruminants, and of still more exquisitely beautiful molluscan shells —in which (as Pliny says) magna ludentis Naturae varietas.