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On the sums of two cubes
sums two cubes
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2011/2/28
We solve the equation f(x, y)3 + g(x, y)3 = x3 + y3 for homogeneous f, g ∈ C(x, y), completing an investigation begun by Vi`ete in 1591. The usual addition law for elliptic curves and composition give...
Curve Reconstruction in Riemannian Manifolds: Ordering Motion Frames
Curve Reconstruction Riemannian Manifolds Ordering Motion Frames
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2011/3/3
In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds.We prove that the minimal spanning tree, given a sufficiently dense sample set of ...
Transitive Sets and Cyclic Quadrilaterals
Transitive Sets Cyclic Quadrilaterals
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2011/2/28
Motivated by some questions in Euclidean Ramsey theory, our aim in this note is to show that there exists a cyclic quadrilateral that does not embed into any transitive set (in any dimension). We show...