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Trinity College Dublin

[Self-portrait]

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 Post-primary School Mathematics, the preparation of which was undertaken principally by Anthony O'Farrell, with assistance from Ian Short.
An Overview of Geometry for Post-primary 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.