74 citations · 190 across the 73 of their papers we have counts for
5 papers · 1 filter
The Logarithmic Spiral Conjecture
Steven R. Finch
When searching for a planar line, if given no further information, one should adopt a logarithmic spiral strategy (although unproven).
Searching for a Shoreline
Steven R. Finch, Li-Yan Zhu
Logarithmic spirals are conjectured to be optimal escape paths from a half plane ocean. Assuming this, we find the rate of increase for both min-max and min-mean interpretations of…
Lost at Sea
Steven R. Finch, John A. Shonder
What is the path of minimum expected length for escaping a planar convex region Omega? We rigorously obtain best 2-segment and 3-segment solutions when Omega is an infinite strip,…
A Convex Maximization Problem: Continuous Case
Steven Finch
We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this…
A Convex Maximization Problem: Discrete Case
Steven Finch
We study a specific convex maximization problem in n-dimensional space. The conjectured solution is proved to be a vertex of the polyhedral feasible region, but only a partial proo…