14 citations · 53 across the 5 of their papers we have counts for
5 papers
Two and three descent for elliptic curves associated with perfect cuboids
John Ramsden, Ruslan Sharipov
A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. Recently it was s…
On two algebraic parametrizations for rational solutions of the cuboid equations
John Ramsden, Ruslan Sharipov
A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. Its existence is…
On singularities of the inverse problems associated with perfect cuboids
John Ramsden, Ruslan Sharipov
Two cubic equations and three auxiliary equations for edges and face diagonals of a rational perfect cuboid have been recently derived. They constitute a background for two inverse…
Inverse problems associated with perfect cuboids
John Ramsden, Ruslan Sharipov
A perfect cuboid is a rectangular parallelepiped with integer edges, integer face diagonals, and integer space diagonal. Such cuboids have not yet been found, but nor has their exi…
A general rational solution of an equation associated with perfect cuboids
John R. Ramsden
We show by finding an explicit parametrization that a 4th degree surface which arises as a necessary condition for the existence of a perfect cuboid is a rational surface, i.e. bir…