This version 16 November 2012; first published 2006.
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§1. Introduction. For at least a century, a popular plaything for younger children has been the toy train. With rare exception, the equipment includes miniature locomotives, cars, and track. Crossing gates, signals and buildings are frequently included, and sometimes a roadway system with automobiles is added. Generally, the rolling stock is powered only by the push of the child's hand, although battery-powered units are increasing in popularity.
These sets are usually manufactured of a combination of plastic and wood, with a higher proportion of wood in the higher-priced versions. A limited amount of metal often appears in critical locations, for instance in axles and in the magnetic couplers that hold together the cars within a train.
Among related web sites are those of these hobbyists:
Something approaching an industry standard in track specifications has evolved, and the purpose of this report is to examine the ramifications of that standard on layout geometry. A key feature of this standard is that track is rigid and sectional, a typical train set containing several dozen pieces. They snap together end-to-end, and are easily reconfigured into a variety of patterns.
Principal pages of this site, best viewed in the sequence listed:
Each different number of segments to a circle gives rise to a substantively different outcome. Although the number of segments happens to be even in the cases above, it could also be odd: for instance a 72° system [5 segments] will work.