Spiral

spiralsspherical spiralwhorlplane spiralspiral patternsspiral shapedspiro-formswirly
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.wikipedia
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Phonograph record

vinyl7LP
The first definition describes a planar curve, that extends in both of the perpendicular directions within its plane; the groove on one side of a record closely approximates a plane spiral (and it is by the finite width and depth of the groove, but not by the wider spacing between than within tracks, that it falls short of being a perfect example); note that successive loops differ in diameter.
A phonograph record (also known as a gramophone record, especially in British English), often simply record, is an analog sound storage medium in the form of a flat disc with an inscribed, modulated spiral groove.

Archimedean spiral

spiralspiral of ArchimedesArchimedes spiral
In the side picture, the black curve at the bottom is an Archimedean spiral, while the green curve is a helix.
The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes.

Logarithmic spiral

equiangular spiralmiraculous spiralSpira mirabilis
In another example, the "center lines" of the arms of a spiral galaxy trace logarithmic spirals.
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve which often appears in nature.

Spiral of Theodorus

In geometry, the spiral of Theodorus (also called square root spiral, Einstein spiral or Pythagorean spiral) is a spiral composed of right triangles, placed edge-to-edge.

Lituus (mathematics)

Lituus
In mathematics, a lituus is a spiral with polar equation

Helix

helicalheliceshelically
In others it follows a skew path forming a helico-spiral pattern.
A conic helix may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of the angle indicating direction from the axis.

Angle

acute angleobtuse angleoblique
A rhumb line (also known as a loxodrome or "spherical spiral") is the curve on a sphere traced by a ship with constant bearing (e.g., travelling from one pole to the other while keeping a fixed angle with respect to the meridians).
In other contexts, such as identifying a point on a spiral curve or describing the cumulative rotation of an object in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.

Horn (anatomy)

hornhornshorned
Thompson also studied spirals occurring in horns, teeth, claws and plants.
Horns usually have a curved or spiral shape, often with ridges or fluting.

Helianthus

sunflowersunflowersHelianthus annuus
A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel.
Further, the florets of a sunflower are arranged in a natural spiral.

Patterns in nature

da Vinci branching rulepatternsnatural patterns
Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.

Celtic maze

Celtic mazes are straight-line spiral patterns that have been drawn all over the world since prehistoric times.

Spirangle

In geometry, a spirangle is a figure related to a spiral.

Stairs

staircasespiral staircasestairway
Spiral stairs, sometimes referred to in architectural descriptions as vice, wind around a newel (also the central pole).

Mathematics

mathematicalmathmathematician
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.

Curve

closed curvespace curvesmooth curve
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.

The American Heritage Dictionary of the English Language

American Heritage DictionaryAmerican HeritageAmerican Heritage Dictionary of the English Language

Plane (geometry)

planeplanarplanes
The first definition describes a planar curve, that extends in both of the perpendicular directions within its plane; the groove on one side of a record closely approximates a plane spiral (and it is by the finite width and depth of the groove, but not by the wider spacing between than within tracks, that it falls short of being a perfect example); note that successive loops differ in diameter.

Spiral galaxy

spiral galaxiesspiral armspiral
In another example, the "center lines" of the arms of a spiral galaxy trace logarithmic spirals. The spiral is also found in structures as small as the double helix of DNA and as large as a galaxy.

DNA

deoxyribonucleic aciddouble-stranded DNAdsDNA
The spiral is also found in structures as small as the double helix of DNA and as large as a galaxy.

Two-dimensional space

Euclidean planetwo-dimensional2D
A two-dimensional, or plane, spiral may be described most easily using polar coordinates, where the radius r is a monotonic continuous function of angle \varphi:

Radius

radiiradialradially
A two-dimensional, or plane, spiral may be described most easily using polar coordinates, where the radius r is a monotonic continuous function of angle \varphi:

Continuous function

continuouscontinuitycontinuous map
A two-dimensional, or plane, spiral may be described most easily using polar coordinates, where the radius r is a monotonic continuous function of angle \varphi: