conispiral

Conispiral is a geometric term used to describe a spiral curve that lies on the surface of a cone. In mathematics, a conispiral can be described as the image on a cone of a straight line drawn on the cone’s developed surface, the circular sector obtained by unrolling the cone. When the cone is rolled back, that line becomes a curve that winds around the axis as it ascends toward the base. The resulting curve is commonly called a conical spiral or conical helix. The tightness and pitch of the spiral depend on the cone angle and the slope of the line on the unrolled sector.

In practical contexts, conispirals appear in decorative design and architectural elements, as well as in models of spiral patterns on conical surfaces in materials science. They can be generated computationally by mapping a straight line on the developed surface back to the cone, or equivalently by defining a curve on the cone that maintains a constant relation between rotation around the axis and ascent along it.

Related terms include spiral, helix, and conical surface. The term conispiral is not universally standardized; some sources use conical spiral or conical helix as synonyms.