The linear search problem rides again

The Linear Search Problem concerns a search for a point in the real line by continuous motion starting at 0. The optimal turning points for such a search under the hypothesis that the location of the target is distributed normally about 0 have been approximated by mechanical calculation, but no proof has been given that there is only a single minimizing strategy or that the numbers calculated do indeed approximate that strategy. Plausible arguments have been made before, both by these authors and others. In this paper, the plausible arguments are supplanted by mathematical proofs. The research of the senior author has been supported by the Wisconsin Alumni Research Foundation. The research of the junior author has been supported by Hewlett Packard, Inc. under a Faculty Development Fellowship at Cornell University.