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Natural Logarithm Catacaustic

المؤلف:  Lawrence,

المصدر:  J. D. A Catalog of Special Plane Curves. New York: Dover

الجزء والصفحة:  p. 207

24-6-2019

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Natural Logarithm Catacaustic

 

The catacaustic of the natural logarithm  specified parametrically as

			(1)
			(2)

is a complicated expression for an arbitrary radiant point.

However, for a point , the catacaustic becomes

			(3)
			(4)

Making the substitution  then gives the equivalent parametrization

			(5)
			(6)

which is the equation of a catenary.

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REFERENCES:

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, p. 207, 1972.