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Is the Curve Rectifiable?
Is the Curve Rectifiable?
James H. Sterling••6 min read
A rectifiable curve
rectifiable curve
Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment is also called rectification of a curve. The advent of infinitesimal calculus led to a general formula that provides closed-form solutions in some cases.
is a curve having finite length (cf. Line (curve)). ... We can think of a curve as an equivalence class of continuous maps γ:[0,1]→X, where two maps γ and γ′ are equivalent if and only if there is an homeomorphism φ of [0,1] onto itself such that γ′=γ∘φ.
What is the meaning of rectifiable?
: capable of being rectified especially : having finite length a rectifiable curve.
What is a non rectifiable curve?
As mentioned above, some curves are non-rectifiable. That is, there is no upper bound on the lengths of polygonal approximations; the length can be made arbitrarily large. Informally, such curves are said to have infinite length.
