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Leibniz's catenary and logarithmic curves. Diagram showing the geometric construction of catenary and logarithmic curves, drawn in 1691 by the German mathematician Gottfried Leibniz (1646-1716). This was Leibniz's own answer to his challenge to the mathematicians of the day to discover a method to construct these related curves. A catenary curve is the shape formed by a chain or string hanging from its ends under its own weight. A catenary curve is both arithmetically (addition) and geometrically (multiplication) related to the logarithmic curve (itself the inverse function of multiplication of numbers). This is demonstrated here by subdivisions of the vertical and horizontal lines used to construct the curves.
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