ClipArt ETC

This mathematics ClipArt gallery offers 31 images of spirals, including logarithmic and hyperbolic spirals.

A cylindrical helix is a curve generated by a point moving uniformly around a cylinder and uniformly lengthwise of the cylinder at the some time. The hypotenuse of a right triangle will form one turn of a helix if it is wrapped around a cylinder. The base of the triangle is equal to the circumference of the cylinder and the altitude is the pitch of the helix.

Helix

A cylindrical helix is a curve generated by a point moving uniformly around a cylinder and uniformly…

Illustration showing how a rolling logarithmic spiral can be constructed by taking successive values of theta, starting from oc. The values of r can be calculated and then the curve can be plotted.

Construction of Logarithmic Spiral

Illustration showing how a rolling logarithmic spiral can be constructed by taking successive values…

Illustration showing the rolling of two logarithmic spirals of equal obliquity.

Rolling of Logarithmic Spirals

Illustration showing the rolling of two logarithmic spirals of equal obliquity.

An illustration of a coin shell.

Coin Shell

An illustration of a coin shell.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral.

Spiral

Illustration of spiral.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral.

Spiral

Illustration of spiral.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of a spiral curve.

Spiral

Illustration of a spiral curve.

Illustration of a spiral curve.

Spiral

Illustration of a spiral curve.

In this illustration, "the driven surface of the slide coincides with the tangent to the spiral, the line of centres being from o through c to infinity and perpendicular to the direction of motion of the slide.""

Logarithmic Spiral Sector

In this illustration, "the driven surface of the slide coincides with the tangent to the spiral, the…

Illustration showing an Archimedean Spiral.

Archimedean Spiral

Illustration showing an Archimedean Spiral.

A spiral of Archimedes.

Archimedes spiral

A spiral of Archimedes.

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.

Illustration showing a lituus spiral/curve.

Lituus Spiral

Illustration showing a lituus spiral/curve.

Illustration showing a logarithmic spiral.

Logarithmic Spiral

Illustration showing a logarithmic spiral.

Illustration showing a logarithmic spiral/curve.

Logarithmic Spiral

Illustration showing a logarithmic spiral/curve.

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…