  In Euclidean relational particle mechanics (ERPM) only relative times,
relative angles and relative separations are meaningful, while in similarity
relational particle mechanics (SRPM) only relative times, relative angles and
ratios of relative separations are. These theories are clearly of interest in
the absolute or relative motion debate. In this paper, ERPM and SRPM are
provided in fully reduced form for 3 particles in 2D, i.e. the classical
dynamics on triangleland in 2D with and without scale. Exact solutions to each
of these are then found, and simple Newton--Coulomb-like and harmonic
oscillator-like SRPM models are studied numerically. The mathematics one
arrives at thus overlaps in many ways with that which arises in the absolutist
approach. The ERPM gives standard mathematics, while the SRPM has standard
small-relative-scale behaviour and an unexpected but in itself standard
universal large-relative-scale behaviour. One way in which SRPM is unusual is
that it is a model in which a symmetry principle underlies an unexpected
departure from standard physical behaviour at sufficiently large relative
scales (interpolation between the abovementioned two behaviours). ERPM and SRPM
are also theoretically interesting at the quantum level, both on their own
merit and as toy models for the development of various approaches to the
problems of time and of observables in quantum general relativity.
