Proving the Existence of Infinitely Many Quadruplets of Points that Form a Parallelogram on Every Smooth, Simple, Plane Curve
By DRIPTO BISWAS, Kolkata, India
In this article, I attempt a semi rigorous proof of a particular property of simple, closed, smooth plane curves. We consider a closed, simple, plane curve C(x,y) ε R^2, which is smooth and well-behaved. We shall prove that there exists infinitely many quadruplets (A,B,C,D) of points A,B,C,D which form a parallelogram. We shall also prove a claim, which shall show that these infinitely many parallelograms are found in infinitely many orientations as well.
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