Archimedes' spiral

E156204

Archimedes' spiral is a classical mathematical curve that winds outward from a fixed point at a constant rate as it revolves around that point.

All labels observed (2)

Label Occurrences
Archimedean spiral 4
Archimedes' spiral canonical 1

How this entity was disambiguated

Statements (44)

Predicate Object
instanceOf mathematical curve
plane curve
spiral
appearsIn classical Greek mathematics
category curves defined by polar equations
spiral curves
contrastedWith logarithmic spiral
definedIn polar coordinates
hasCoordinateRepresentation x(θ) = (a + bθ) cos θ
y(θ) = (a + bθ) sin θ
hasIndependentVariable θ (polar angle)
hasParameter a (radial offset)
b (growth rate of radius with angle)
hasPolarEquation r = a + bθ
r = kθ
hasProperty angle between radius vector and tangent varies with θ
can be traced by a point moving with constant linear speed in radial direction and constant angular speed
curvature varies with angle
distance between successive turns equals 2πb
distance between successive turns is constant
equidistant spiral
not self-intersecting for θ in a monotone interval
passes through origin when θ = 0 for r = kθ
radius increases linearly with angle
unbounded curve
hasSpecialCase r = θ
hasSymmetry rotational symmetry about its pole
liesIn Euclidean geometry
surface form: Euclidean plane
namedAfter Archimedes
surface form: Archimedes of Syracuse
relatedConcept Fermat's spiral
equiangular spiral
hyperbolic spiral
studiedBy Archimedes
usedFor squaring the circle (classical constructions)
trisecting an angle (classical constructions)
usedIn cam design
graphical design and art
mathematical analysis of spirals
mechanical engineering
optical devices
path planning and motion control
phonograph recording technology
scroll compressors
spiral antennas

How these facts were elicited

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Archimedes knownFor Archimedes' spiral
Archimedes hasConceptNamedAfter Archimedes' spiral
this entity surface form: Archimedean spiral
On Spirals defines Archimedes' spiral
this entity surface form: Archimedean spiral
Parker spiral model geometricType Archimedes' spiral
this entity surface form: Archimedean spiral
Vogel spiral relatedConcept Archimedes' spiral
this entity surface form: Archimedean spiral