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  2. Conical spiral - Wikipedia

    en.wikipedia.org/wiki/Conical_spiral

    Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.

  3. Ruled surface - Wikipedia

    en.wikipedia.org/wiki/Ruled_surface

    Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line.

  4. Helicoid - Wikipedia

    en.wikipedia.org/wiki/Helicoid

    Its name derives from its similarity to the helix: for every point on the helicoid, there is a helix contained in the helicoid which passes through that point. The helicoid is also a ruled surface (and a right conoid), meaning that it is a trace of a line. Alternatively, for any point on the surface, there is a line on the surface passing ...

  5. Spiral - Wikipedia

    en.wikipedia.org/wiki/Spiral

    An Archimedean spiral (black), a helix (green), and a conical spiral (red) Two major definitions of "spiral" in the American Heritage Dictionary are: [5]. a curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point.

  6. Helix - Wikipedia

    en.wikipedia.org/wiki/Helix

    The pitch of a helix is the height of one complete helix turn, measured parallel to the axis of the helix. A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis. [3] A circular helix (i.e. one with constant radius) has constant band curvature and constant torsion. The slope of ...

  7. Conchospiral - Wikipedia

    en.wikipedia.org/wiki/Conchospiral

    In cylindrical coordinates, the conchospiral is described by the parametric equations: = = =. The projection of a conchospiral on the (,) plane is a logarithmic spiral.The parameter controls the opening angle of the projected spiral, while the parameter controls the slope of the cone on which the curve lies.

  8. Parametric surface - Wikipedia

    en.wikipedia.org/wiki/Parametric_surface

    Parametric representation is a very general way to specify a surface, as well as implicit representation. Surfaces that occur in two of the main theorems of vector calculus , Stokes' theorem and the divergence theorem , are frequently given in a parametric form.

  9. Translation surface (differential geometry) - Wikipedia

    en.wikipedia.org/wiki/Translation_surface...

    Any parametric curve is a shifted copy of the generatrix (in diagram: purple) and is contained in the right circular cylinder with radius , which contains the z-axis. The new parametric representation represents only such points of the helicoid that are within the cylinder with the equation x 2 + y 2 = 4 a 2 {\displaystyle x^{2}+y^{2}=4a^{2}} .