
ET7246  Geometry and Trigonometry
Dr. David R. Wilkins

Material for Hilary Term 2018
 Leaving Certificate Mathematics Syllabus
 The syllabus for Foundation, Ordinary and Higher Level, for
examination from 2015, and incorporating the document
Geometry for Postprimary School Mathematics,
the preparation of which was undertaken principally by
Anthony O'Farrell, with assistance from Ian Short.
 An Overview of Geometry for Postprimary School Mathematics in Ireland
 This document is an evolving document, representing
work in progress, and is likely to be subject to constant
revision whilst teaching of Module ET7246 is in progress.
 Axiomatic Foundations of Planar Geometry
 This document is an evolving document, representing
work in progress, and may be revised
whilst teaching of Module ET7246 is in progress.
 Selected Circle Theorems
 A sequence of presentation slides incorporating circle
theorems, and concluding with a discussion
of “golden sections” and
“golden triangles”
, establishing the theoretical
background underlying the construction of the regular pentagon
using straightedge and compass. (This series of slides stops
short of explaining and justifying the construction of the
regular pentagon itself.
 The Pentagram
 A sequence of presentation slides concerning properties
of the pentagram formed within a regular pentagon, focussing
in particular on the equality of all the small angles in
the figure, and the properties of the various “golden
triangles” that emerge from the construction.
 Trigonometry
 A sequence of presentation slides concerning trigonometry
 A GeoGebra construction of a regular pentagon using straightedge and compass
Resources for the Study of Geometry and Trigonometry
 Resources for the study of Euclid's Elements of Geometry
 Resources for the study of the history of geometry and trigonometry
 Resources concerning the teaching of geometry and trigonometry
 Miscellaneous resources for the study of geometry and trigonometry
 Axiom Systems for Synthetic Geometry
Dr. David R. Wilkins,
School of Mathematics,
Trinity College Dublin.