Last modified: Tue 7 August 15:15:54 IST 2018

Welcome Study @ MIC St. Patrick's Campus Thurles Faculties & Departments Research & Grad School International Students

MH4749 — Geometry

This module is not taught at the moment


Contact Information

Name Dr. Bernd Kreussler
Office N29
Internal Telephone 4578
Email bernd.kreussler@mic.ul.ie
WWW www.maths.mic.ul.ie/kreussler/

Some Links of interest


Plan of the lecture 2017/18

  1. Pythagoras
    • Area
    • The Theorem of Pythagoras
    • Constructions with Ruler and Compass
  2. Congruence and Similarity
    • The Intercept Theorem
    • Parallel Lines
    • Similar Triangles
    • Congruence Theorems
    • Pons Asinorum
  3. Circles and Triangles
    • Degrees and Radians
    • Inscribed and Central Angles
    • Regular Polygons
    • Tangents and Angles
    • Power of a Point
    • Triangle Centres
  4. Trigonometry
    • Trigonometric Functions
    • Addition Theorems
    • Sine Rule and Cosine Rule
    • Calculating Triangles
  5. Coordinates
    • Cartesian Coordinates
    • Lines and Circles
    • Polar Coordinates
    • Conics
  6. Vectors and Symmetry
    • Dot Product, Length and Angle Measure
    • Cross Product
    • Lines and Planes
    • Orthogonal Projections and Linear Mappings
    • Orthogonal Mappings and Isometries
    • Symmetry
  7. Spherical Trigonometry
    • Spherical Coordinates
    • Spherical Triangles
    • Sine Rule and Cosine Rule
    • Spherical Distance and Area
  8. Non-Euclidean Geometry
    • Euclid's Postulates
    • Modern View on Euclidean Geometry
    • Hyperbolic and Elliptic Geometry

Textbooks

  • OSTERMANN, A., WANNER, G., Geometry by Its History, (Springer) 2012.
  • COXETER, H.S.M., Introduction to Geometry, (John Wiley & Sons) 1961.
  • BYER, O., LAZEBNIK, F., SMELTZER, D., Methods for Euclidean Geometry, (MAA) 2010.
  • GARDINER, A.D., BRADLEY, C.J., Plane Euclidean Geometry: Theory and Problems, (UKMT) 2005.
  • BARKER, W., HOWE, R., Continuous Symmetry, From Euclid to Klein, (AMS) 2007.
  • LANG, S., MURROW, G., Geometry, A High School Course, (Springer) 1983.
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