Titlebook: Euclidean Geometry and its Subgeometries; Edward John Specht,Harold Trainer Jones,Donald H. Book 2015 Springer International Publishing S

ADOPT

Ringworm

Collineations of an Affine Plane (CAP),Collineations are bijections of a plane onto itself which map lines to lines; this chapter explores the elementary properties of collineations on an incidence plane on which the parallel axiom holds. Several types of collineations are studied, among them translations, dilations, and axial affinities.

larder

CHOIR

Dappled

Rotations About a Point of a Neutral Plane (ROT),This chapter defines point rotations and point reflections (about a point .) on a neutral plane, and derives their elementary properties to the extent possible without a parallel axiom. It ends with a classification of isometries of a neutral plane, and proof of the existence of a “square root” of a rotation.

ENNUI

GEAR

會議

Belineations on a Euclidean/LUB Plane (AA),This brief chapter shows that on a Euclidean/LUB plane, any non-identity belineation which has more than one fixed point and is not the identity, is an axial affinity; it concludes with a classification of belineations. To prove the main result of this chapter we need Axiom LUB; this explains its placement after the chapter on real numbers.