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The trace (purple) of the tangents of a conical spiral with a hyperbolic spiral as floor plan. The black line is the asymptote of the hyperbolic spiral. The collection of intersection points of the tangents of a conical spiral with the --plane (plane through the cone's apex) is called its tangent trace.
A conical or volute spring (including the spring used to hold and make contact with the negative terminals of AA or AAA batteries in a battery box), and the vortex that is created when water is draining in a sink is often described as a spiral, or as a conical helix.
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The slope of a circular helix is commonly defined as the ratio of the circumference of the circular cylinder that it spirals around, and its pitch (the height of one complete helix turn). A conic helix, also known as a conic spiral, may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of the angle ...
Helix. Tendril perversion (a transition between back-to-back helices) Hemihelix, a quasi-helical shape characterized by multiple tendril perversions; Seiffert's spiral [5] Slinky spiral [6] Twisted cubic; Viviani's curve
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.
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.
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 ...