Few geometrical shapes appear in nature as often and in so many places as the spiral, or helix. Numerous examples of it can be found in the field of physics, chemistry and biology, but perhaps most interesting are those that show up in living organisms.

Look closely at bindweed and you will see how it turns around clockwise on its support, forming a right-handed spiral. Honeysuckle, on the other hand, twists the other way, in a left-handed spiral.

There has been much confusion in past botanical literature about how to define a right-handed and left-handed spiral. To be clear, a right-handed spiral corresponds to a screw that turns clockwise as it enters the wood; a left-handed spiral corresponds to a screw that turns counterclockwise. Think of the spiral as moving away from you, toward a clock on the other end.

Spirals are common in the trunks and branches of trees, which can be seen after the tree dies and the bark falls off. The twist in the wood probably makes the trees stronger and more resilient.

Helices also appear in the arrangement of leaves around the stalks of plants, each leaf twisting either to the right or left of the one below it. This increases the chance the leaves will be exposed to sunlight rather than falling in the shadow of another leaf. The habit of spiral growth is amazing enough, but what’s even more amazing is the leaves on the spiral form a precise numerical arrangement.

Start with a leaf and find the next one that appears on the same side directly above it, noticing that the leaves in between form a spiral of one or more full turns around the twig. Then count the number of leaves from the first leaf to the corresponding leaf above it, and you will come up with a number on the Fibonacci sequence, which is a series of numbers that begins with 1, 2, 3, 5, 8, 13 and so on, each number being the sum of the two preceding.

Every tree has its own unique Fibonacci number. For example, green ash has two leaves in its helix, cottonwood and elm have five, tall goldenrod eight and pussy willow 13. Why the number of leaves in the spiral corresponds exactly to a number on the Fibonacci sequence remains something of a mystery.

The seeds in some flowers and cones are arranged in two overlapping spirals, one curving to the right and the other to the left, and the number of seeds in each spiral corresponds to a number on the Fibonacci sequence. In some pine cones, one of the spirals has eight seeds and the other 13.

Helices also appear in many forms in the animal world, including the tusks of extinct mammals and the horns of rams, goats and antelopes. Many bones of animals have helical twists, the left side mirroring those on the right. Insect antennae sometimes coil in opposite pairs, and the wings of birds, bats and insects have a slight helical twist.

The shells of snails and mollusks provide some of the most striking examples of spiral structure, and thousands of fossil shells have been found with right- or left-handed helices. The cochlea of the ear has a similar snail-like twist.

In the spring, I often have seen migrating geese suddenly break into a chaotic flock and start flying in circles, spiraling upward on a rising air current, and then just as suddenly fall back into a familiar V-formation and continue their northward migration.

A remarkable case of helical flight is demonstrated by the Mexican free-tailed bats of Carlsbad Caverns, N.M. Joseph Wood Krutch describes how the bats invariably swarm out of a cave in a right-handed spiral. The bats apparently have adopted the convention of whirling out of the cave toward the right to prevent head-on collisions.

Spirals are common at the molecular level. Every protein apparently has two kinds of twist, one that spirals to the right and the other to the left, but all the proteins in living things are believed to have a right-handed twist. DNA itself, the genetic material in living cells, is a double right-handed helix.

Dust devils, tornadoes, hurricanes, whirlpools in a stream, water draining down a sink, the orbit of the moon around the earth, all have a helical twist. Driven by the Coriolis effect, tornadoes in the Northern Hemisphere spin clockwise while those in the Southern Hemisphere turn counterclockwise

The curious phenomenon of the helix spans the universe from spiral galaxies to the microcosm of a cell. They are all connected, not by a universal law, but by a curious similarity of shape, a shape that adds beauty to the world and a charming novelty to the lives of plants animals in it.

Nature is full of rabbit holes of adventure, and in the one named “spirals” you enter a world where strangeness becomes normal and the surprises multiply until, like Alice, you become overwhelmed by the sheer wonder of it.

Richard Weber is a nature enthusiast

living in Ellis County.