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cheersdup
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Homework Statement
Let m : [0,L] --> ℝ2 be a C2 regular closed curve parametrized with arc length, and define, for an integer n > 0 and scalar ε > 2
μ(u) = m(u) + εsin(2nπu/L)Nm(u)
where Nm is the unit normal to m
(1) Determine a maximum ε0 such that μ is a closed regular curve for any ε < ε0
(2) Assume that m is a circle centered at 0 with radius r > 0
Prove that μ is non intersecting for any ε < r
Compute its interior area as a function of r and ε
Homework Equations
See above
The Attempt at a Solution
I think μ(u) is like some scalar of a sine function moving around the original curve. Essentially I need to find a large enough amplitude ε such that μ(u) intersects itself in the middle of m(u).
It also seems that ε0 must be smaller than the radius of the bitangent circle of m(u)
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