  The time dilation of non-inertial travelers in circular and polygonal closed
paths are well known. In both cases observers completing a round trip will age
less than an observer at rest with respect to the circle / polygon. This rapid
aging is contrary to the slow aging that would be documented by temporarily
comoving inertial observers who might also move along each edge of the polygon.
A detailed description of what the non-inertial observer might actually see
that would explain their own slow aging is presented. It is also argued that
the non-inertial observer will disagree with the comoving inertial observers
about the size of the diameter of the polygon. In particular, the non-inertial
traveler will observer a Lorentz-like contraction of distances measured
perpendicular to the direction of relative motion. As a result, the traveler
will obtain a value of for the ratio of circumference to diameter, in
contradiction to recently published work that predicts a measured ratio less
than and a non-Euclidean geometry for the polygon traveler.
