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Abstract

The energy of a smoothly parameterized knot y(t) is defined as rr\ i i lp7 \\dn dsdt Jo Jo \||7M-7(0f (D(t(s),T(t))) 2 j\\ds \\dt where D(y (s), y(t)) is the arc length between the two points y (s) and y(t) on the curve. Simple calculus based arguments are used to locate critical values of the energy functional for torus knots. Explicitly the curves given parametrically by °(«*)W = (V2°iSri).JSSBe V2 C s7nS are CriticalP ° intS ° fthe energy functional whenever a and b are relatively prime.

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