Spiral Polyskelion

Spiral Types:

(1) Archimedean spiral: r(θ) = a*θ

(1 < number of spiral turns < 2)

(2 < number of spiral turns < 3)

(2) Fermat's spiral (Parabolic spiral): r(θ) = a*sqrt(θ)

(1 < number of spiral turns < 2)

(2 < number of spiral turns < 3)

(3) Hyperbolic spiral (Reciprocal spiral): r(θ) = a/θ

(4) Lituus: r(θ) = a/sqrt(θ)

(5) Logarithmic spiral: r(θ) = a*exp(b*θ)

(b = 0.25)

(b = 0.618)

( Mathematical software used: GeoGebra )

Tiling using Spiral Hexaskelions

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = 0.25.

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = golden ratio ~ 0.618.

The spirals are Archimedean spirals.

(1 < number of spiral turns < 2)

The spirals are Archimedean spirals.

(2 < number of spiral turns < 3)

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = 0.05, 0.1, 0.15, 0.2, ..., 0.8.

( Mathematical software used: GeoGebra )

Spiral Starfish - a logarithmic spiral pentaskelion (螺旋海星)

A pentaskelion with five logarithmic spirals r(θ) = a*exp(b*θ),

b ~ 0.30635 (same as that of the golden spiral).

b = 0.25

b = 0.5

b = golden ratio ~ 0.618

( Mathematical software used: gnuplot )