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LOGARITHMIC CURVE
Other name: exponential curve. |
Logarithmic version:
Cartesian equation: Transcendental curve. In the case where a = b: Curvilinear abscissa starting from the point with abscissa a: The Cartesian tangential angle is defined by Radius of curvature: |
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Exponential version:
Cartesian equation: Transcendental curve. In the case a = b: Curvilinear abscissa starting from the point with zero abscissa: The Cartesian tangential angle is defined by Radius of curvature: |
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The logarithmic curve is the plot of the logarithmic function (and also that of the exponential function) or its image by a dilatation.
NSC: curve with constant sub-tangent.
The logarithmic curve is also characterized by the fact that translating it along its asymptote is equivalent to scaling it perpendicularly to this asymptote.
![]() Translation equivalent to a scaling in one direction |
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In the case where a = b, its caustic by reflection for rays perpendicular to its asymptote is the catenary.
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The logarithmic curve is the profile a tower (i.e. a solid of revolution) must have in order for the pressure applied on any horizontal section by the upper section to be constant. | ![]() |
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See also the involute of an exponential, the
ballistic curve, the catenary, and the tractrix.
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© Robert FERRÉOL
2017