arXiv subjects
Publications and source records attributed to Tommy Murphy.
We consider the problem of optimizing the product of the distances from a given point in a triangle to each vertex. There are two possible cases in general. For isosceles triangles, we explicitly show exactly when both cases occur.
The FRACTRAN programs $\sqrt{2}$GAME and NR$\sqrt{2}$GAME are presented, both of which compute the decimal expansion of $\sqrt{2}$. Our $\sqrt{2}$GAME is analogous to Conway's PIGAME program. In fact, our proof carries over to PIGAME to produce a simpler proof of Conway's theorem as well as highlight how the efficiency of the program can be improved. NR$\sqrt{2}$GAME encodes the canonical example of the Newton--Raphson method in FRACTRAN.
We characterize the Archimedean solids among the convex uniform polyhedra via face embeddings into a regular Tetrahedron. This result has been listed without proof in the literature.
We produce an upper bound for the Hausdorff dimension of the graph of a Weierstrass-type function. Whilst strictly weaker than existing results, it has the advantage of being directly computable from the theory of hyperbolic iterated function systems.
In this note we adapt the work of Hall to find quasi-Einstein metrics on sphere bundles over products of Fano Kaehler-Einstein manifolds, as well as bundles where only one end is blown down.