An illustration showing how to construct a spiral with compasses and four centers. "Given the pitch of the spiral, construct a square about the center, with the four sides together equal to the pitch. Prolong the sides in one direction as shown by the figure, the corners are the centers for each arc of the external angles."

Construction Of A Spiral

An illustration showing how to construct a spiral with compasses and four centers. "Given the pitch…

Illustration of a double spiral with unequally spaced intervals.

Double Spiral

Illustration of a double spiral with unequally spaced intervals.

"If B and C are points in the spiral and the ratio of AC to AB be given, the intermediate point D may be obtained by describing a semicircle on BC as a diameter and erecting a perpendicular at A." —Anthony, 1904

Drawing Equiangular or Logarithmic Spiral

"If B and C are points in the spiral and the ratio of AC to AB be given, the intermediate point D may…

A graph showing a logarithmic or equiangular spiral. The spiral is created in polar coordinates (r,Θ) based on the natural log function.

Equiangular or Logarithmic Spiral

A graph showing a logarithmic or equiangular spiral. The spiral is created in polar coordinates (r,Θ)…

A helix spiral generated by revolving about an axis at an angle less than 90 degrees. This generates a cylindrical or coned shape as the tip meets.

Helix Spiral

A helix spiral generated by revolving about an axis at an angle less than 90 degrees. This generates…

A logarithmic spiral.

Hyperbolic spiral

A logarithmic spiral.

A hyperbolic spiral.

Hyperbolic spiral

A hyperbolic spiral.

"This class of spirals may be generated by unwinding a perfectly flexible but inextensible chord from a polygon of any number of sides, the names of the involutes being derived from the polygons which determine their form. The curves consist of radii increasing by an amount equal to the length of the sides." —Anthony, 1904

Involute Spiral

"This class of spirals may be generated by unwinding a perfectly flexible but inextensible chord from…

Lituus spiral.

Lituus spiral

Lituus spiral.

Spiral with lines AB and CD drawn on piece of paper shown flat.

Spiral Drawn on Piece of Paper Shown Flat

Spiral with lines AB and CD drawn on piece of paper shown flat.

Spiral with lines AB and CD drawn on piece of paper and rolled into a cylinder to form spiral running from A to D.

Spiral Drawn on Piece of Paper and Rolled

Spiral with lines AB and CD drawn on piece of paper and rolled into a cylinder to form spiral running…

A long, spiral spring.

Spring

A long, spiral spring.

The evolute spiral stove tile is a painting during the German Renaissance. It is a wavelike pattern that mimics the waves of the sea. The interstices (small opening) between the lines is decorated with leaves and flower buds.

Evolute Spiral Stove Tile

The evolute spiral stove tile is a painting during the German Renaissance. It is a wavelike pattern…

"An ornament or kind of chain, of gold, twisted spiraly, and bent in a circular form, which was worn around the neck." — Anthon, 1891

Torques

"An ornament or kind of chain, of gold, twisted spiraly, and bent in a circular form, which was worn…

The evolute spiral trellis (garden frame) is made out of wrought iron. It is a wavelike pattern that mimics the waves of the sea.

Evolute Spiral Trellis

The evolute spiral trellis (garden frame) is made out of wrought iron. It is a wavelike pattern that…