45 citations · 101 across the 20 of their papers we have counts for
20 papers
An Upper Bound for Lebesgue's Covering Problem
Philip Gibbs
A covering problem posed by Henri Lebesgue in 1914 seeks to find the convex shape of smallest area that contains a subset congruent to any point set of unit diameter in the Euclide…
The Lebesgue Universal Covering Problem
John C. Baez, Karine Bagdasaryan, Philip Gibbs
In 1914 Lebesgue defined a "universal covering" to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal…
A New Slant on Lebesgue's Universal Covering Problem
Philip Gibbs
Lebesgue's universal covering problem is re-examined using computational methods. This leads to conjectures about the nature of the solution which if correct could provide a bluepr…
An Acataleptic Universe
Philip Gibbs
John Wheeler advocated the principle that information is the foundation of physics and asked us to reformulate physics in terms of bits. The goal is to consider what we know alread…
A Universe Programmed with Strings of Qubits
Philip Gibbs
It has been suggested that reality works like a quantum computer, but such claims are just words if they are not backed up by sound mathematics. In pursuit of the fundamental equat…
Elliptic Curves and Hyperdeterminants in Quantum Gravity
Philip Gibbs
Hyperdeterminants are generalizations of determinants from matrices to multi-dimensional hypermatrices. They were discovered in the 19th century by Arthur Cayley but were largely i…