### (1) Archimedean spiral

### (2) Fermat's spiral (Parabolic spiral)

### (3) Hyperbolic spiral (Reciprocal spiral)

### (4) Lituus

### (5) Logarithmic spiral

( Mathematical software used: gnuplot )

Making Art with Mathematical Equations, Inequalities and Functions (Mappings, Transformations)

( Mathematical software used: gnuplot )

(1 < number of spiral turns < 2)

(2 < number of spiral turns < 3)

(1 < number of spiral turns < 2)

(2 < number of spiral turns < 3)

(b = 0.25)

(b = 0.618)

( Mathematical software used: GeoGebra )

Spirals (green, magenta) around a Spiral Dodecaskelion (grey)

(GIF animation)

A spiral of spirals of spirals.

The spirals are logarithmic spirals: r(θ) = a exp(bθ), b = 0.2.

Spirals of spirals of spirals of ..... (b = 0.2)

A spiral of spirals of spirals.

The spirals are logarithmic spirals with b = 0.30635.

Spirals of spirals of spirals of ..... (b = 0.30635)

Logarithmic spirals

The pair of big spirals: b = 0.1

The small spirals: b = 0.2

The small logarithmic spirals: b = 0.5

The small logarithmic spirals: b = 0.2, 0.5

The small logarithmic spirals: b = 0.5, 0.8

The spirals are Archimedean spirals.

Small spirals: 1 < number of spiral turns < 2

The spirals are Archimedean spirals.

Small spirals: 2 < number of spiral turns < 3

( Mathematical softwares used: GeoGebra, gnuplot )

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 )

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 )

Subscribe to:
Posts (Atom)