Catenoid-Helicoid is the family of a minimal surface consists of continuous and isometric deformation of a catenoid to a helicoid such that every member of the deformation family is minimal.
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A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.
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The Paracylindrical, also called parabolic cylindrical, coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional parabolic coordinate system in the perpendicular z-direction.
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The Spiral of Archimedes (polar) is a plane curve.
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The Seifferts spherical spiral is a curve in three-dimensional space.
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A Conical helix is a curve in three-dimensional space. The Conic helix may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of the angle indicating direction from the axis.
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Tschirnhaus's cubic is the negative pedal of a parabola with respect to the focus of the parabola. The caustic of Tschirnhaus's cubic where the radiant point is the pole is Neile's parabola.
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