Which of the following is least likely to be influenced by curvature of the earth in surveying?

The curvature of the earth has a minimal impact on transportation routes compared to the other options listed. This is because transportation routes, such as roads and railways, are designed primarily for practical use and engineering considerations rather than strict geometric accuracy over long distances. Engineers and planners tend to focus on factors like terrain, accessibility, and cost when designing these routes, which can lead to adjustments and deviations that detour from a perfectly straight trajectory.

In contrast, section lines, parcel dimensions, and water boundaries are all significantly influenced by the earth's curvature. Surveyors must account for this curvature when setting boundaries and establishing legal descriptions due to the precision needed in those areas. In this context, while curvature can affect transportation as well, it does not carry the same degree of significance or stricter requirements for accuracy as it does with the other options. Thus, the influence of the earth's curvature is least likely to be a crucial factor in the establishment of transportation routes.