Spirale

Spirale is the term used in several languages, notably French and Italian, for the geometric concept of a spiral: a curve that winds around a central point while moving away from or toward it. In mathematics, a spirale is usually described in polar coordinates by a radius r that depends on the angle θ, written as r = f(θ).

Several standard spirals are widely studied. The Archimedean spiral, r = a + bθ, has roughly constant spacing between successive turns. The logarithmic spiral, r = a e^{bθ}, expands so that the angle between the tangent to the curve and the radial line is constant. Other forms include Fermat’s spiral, r^2 = a^2 θ, and the hyperbolic spiral, rθ = a^2.

Spirales occur in nature and human-made objects. The nautilus shell and many plant patterns resemble logarithmic spirals; spiral galaxies often display arms that follow similar patterns. Weather systems can form spiraling rainbands. In technology and design, spirales appear in springs, spiral staircases, antennae, and various innovations that exploit rotational symmetry or controlled radial growth.

Etymology traces spirale to Latin spiralis from Greek speira, meaning “coil” or “twist.” The concept appears across disciplines, from pure geometry to biology, astronomy, and engineering, to describe curves that maintain a rotational flow while changing their distance from a center.