Fermat's spiral

E620680

mathematical object plane curve spiral

Fermat's spiral is a plane curve whose radius grows with the square root of the angle, often used to model naturally occurring spiral patterns such as those in sunflowers and other phyllotactic arrangements.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (1)

Surface form	Occurrences
Fermat spiral	1

Statements (48)

Predicate	Object
instanceOf	mathematical object ⓘ plane curve ⓘ spiral ⓘ
belongsTo	family of spirals with power-law radius-angle relation ⓘ
classification	algebraic spiral ⓘ
comparedTo	Archimedean spiral ⓘ logarithmic spiral ⓘ
coordinateRelation	x = r cos θ, y = r sin θ with r = a√θ ⓘ
definedInCoordinateSystem	polar coordinates ⓘ
differsFrom	Archimedean spiral where radius grows linearly with angle ⓘ logarithmic spiral where radius grows exponentially with angle ⓘ
field	differential geometry ⓘ geometry ⓘ mathematical biology ⓘ
hasAlternativeName	parabolic spiral ⓘ
hasApplication	computer graphics phyllotaxis algorithms ⓘ procedural generation of plant-like patterns ⓘ visualization of uniform point distributions in a disk ⓘ
hasAsymptoticBehavior	radius tends to 0 as θ tends to 0 ⓘ radius tends to infinity as θ tends to infinity ⓘ
hasBranch	branch for θ ≤ 0 ⓘ branch for θ ≥ 0 ⓘ
hasCurvatureBehavior	curvature decreases as θ increases ⓘ
hasEquation	r = a·√θ ⓘ r^2 = a^2·θ ⓘ
hasIndependentVariable	θ (polar angle) ⓘ
hasParameter	a (scale parameter) ⓘ
hasProperty	arms are equally spaced in angle for constant increments of θ ⓘ can generate nearly uniform density of points when combined with golden angle increments ⓘ often combined with golden angle for realistic phyllotaxis models ⓘ two symmetric branches with respect to the origin ⓘ
hasSelfIntersection	no self-intersections for θ ≠ 0 ⓘ
hasSymmetry	point symmetry about the origin ⓘ
namedAfter	Pierre de Fermat NERFINISHED ⓘ
passesThroughPoint	origin ⓘ
powerLawExponent	1/2 ⓘ
radiusGrowthLaw	radius grows with the square root of the angle ⓘ
relatedToConcept	Fibonacci numbers NERFINISHED ⓘ golden angle ⓘ phyllotactic spirals ⓘ
usedInConstruction	low-discrepancy point sets on the plane ⓘ sunflower seed packing models ⓘ
usedToModel	arrangement of leaves ⓘ cactus spine patterns ⓘ phyllotaxis ⓘ pinecone scale patterns ⓘ spiral patterns in plants ⓘ sunflower seed patterns ⓘ

Referenced by (2)

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

Archimedes' spiral → relatedConcept → Fermat's spiral ⓘ

Vogel spiral → relatedConcept → Fermat's spiral ⓘ

this entity surface form: Fermat spiral