A general rational solution of an equation associated with perfect cuboids

Abstract

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. birationally equivalent over $\mathbb{Q}$ to a plane.

LaTeX, 3 pages

References in corpus (1)

• A biquadratic Diophantine equation associated with perfect cuboids

Cited by in corpus (12)

• Inverse problems associated with perfect cuboids
• On singularities of the inverse problems associated with perfect cuboids
• A note on rational and elliptic curves associated with the cuboid factor equations
• On two algebraic parametrizations for rational solutions of the cuboid equations
• A note on solutions of the cuboid factor equations
• On two elliptic curves associated with perfect cuboids
• A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture
• Asymptotic estimates for roots of the cuboid characteristic equation in the linear region
• Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture
• A note on invertible quadratic transformations of the real plane
• On a pair of cubic equations associated with perfect cuboids
• A fast modulo primes algorithm for searching perfect cuboids and its implementation