On a property of plane curves
نویسنده
چکیده
Let γ : [0, 1] → [0, 1] be a continuous curve such that γ(0) = (0, 0), γ(1) = (1, 1), and γ(t) ∈ (0, 1) for all t ∈ (0, 1). We prove that, for each n ∈ N, there exists a sequence of points Ai, 0 ≤ i ≤ n + 1, on γ such that A0 = (0, 0), An+1 = (1, 1), and the sequences π1( −−−−→ AiAi+1) and π2( −−−−→ AiAi+1), 0 ≤ i ≤ n, are positive and the same up to order, where π1, π2 are projections on the axes.
منابع مشابه
Contributions to differential geometry of spacelike curves in Lorentzian plane L2
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