Trent University
Mathematics 2260H
Geometry I: Euclidean Geometry
MATH 2260H is an introduction to Euclidean plane geometry, starting from Euclid’s axioms and developing properties of lines, angles, polygons (especially triangles), and circles.
Prerequisite: At least one of MATH 1005H, 1110H, or 1350H, or permission of instructor.
Winter 2025
- MATH 2260H Course Outline
- Euclid's Elements of Geometry, edited and translated by Richard Fitzpatrick.
The textbook for the first half or so of the course.
- Eudlid's Postulates and Proposition I-1 (excerpted from the textbook)
- Euclid’s Postulates Extended - Euclid's five postulates, plus a couple of extra ones filling in some of the gaps in his system.
- Hilbert's Axioms
(excerpted from The Foundations of Geometry by David Hilbert)
- Similar Triangles and Similarity Criteria
- Assignment # 1,
2,
3,
4,
π,
5,
τ,
6,
7,
8,
9,
10,
11
and Solutions to Assignments #
2,
7
- Take-Home Final Examination
- Some of the lectures were recorded, but too many were not. Please see the sets of recordings from Winter 2024 and Winter 2021 below for fairly complete sets of recordings.
Winter 2024
- MATH 2260H Course Outline
- Euclid's Elements of Geometry, edited and translated by Richard Fitzpatrick.
Our textbook for the first half or so of the course.
- Euclid’s Postulates Extended - Euclid's five postulates, plus a couple of extra ones filling in some of the gaps in his system.
- Hilbert's Axioms
(excerpted from The Foundations of Geometry by David Hilbert)
- Similar Triangles and Similarity Criteria
- Assignment # 1,
2,
3,
4,
5,
2e,
6,
7,
8,
9,
10,
11
- Take-Home Final Examination
- Lectures and Notes. Notes contributed by two students wishing to remain anonymous. (Much appreciated by all - thanks! :-) Unfortunately, one had to give it up after an accident. Lecture videos in webm format.
- 2024-01-09 Euclid's Definitions and Postulates, Proposition I-1: Video, Notes 1, Notes 2
- 2024-01-10 Propositions I-2 to I-4, Congruence: Video, Notes 1, Notes 2
- 2024-01-11 Propositions I-5 to I-8: Video, Notes 1, Notes 2
- 2024-01-16 Propositions I-9 to I-12: Video, Notes 1, Notes 2
- 2024-01-18a Propositions I-13 to I-15: Video, Notes 1, Notes 2
- 2024-01-18b Propositions I-16 to I-19: Video, Notes 1, Notes 2
- 2024-01-23 Propositions I-20 to I-22: Video, Notes 1, Notes 2
- 2024-01-25a Propositions I-23 to I-28: Video, Notes 1, Notes 2
- 2024-01-25b What If the Parallel Postulate Fails?: Video, Notes 1, Notes 2
- 2024-02-01a Propositions I-29 to I-32: Video, Notes 1, Notes 2
- 2024-02-01b Proposition I-35: Video, Notes 1, Notes 2
- 2024-02-06 Propositions I-36 to I-40: Video, Notes 1, Notes 2
- 2024-02-08a Propositions I-41 to I-45: Video, Notes 1, Notes 2
- 2024-02-08b Propositions I-46 to I-47 (The Pythagorean Theorem): Video, Notes 1, Notes 2
- 2024-02-13 Proposition III-1 and Corollary, Corollary to Proposition III-16: Video, Notes 1, Notes 2
- 2024-02-15a Thales' Theorem, Intersecting Chords: Video, Notes 1, Notes 2
- 2024-02-15b More on Intersecting Chords: Video, Notes 1, Notes 2
- 2024-02-27 A Bit More on Intersecting Chords, Triangle Centres, Angle-Bisectors and the Incentre and Incircle: Video, Notes
- 2024-02-29a Medians and the Centroid: Video, Notes
- 2024-02-29b Centroid, Altitudes and the Orthocentre, Sallows' Theorem: Video, Notes
- 2024-03-05 The Euler Line, Relations among Centres: Video, Notes
- 2024-03-07a Relations among Centres, The Nine-Point Circle: Video, Notes
- 2024-03-07b The Nine-Point Circle: Video, Notes
- 2024-03-12 The Nine-Point Circle and the Euler Line, Cevians: Video, Notes
- 2024-03-14a Ceva's Theorem: Video, Notes
- 2024-03-14b Menelaus' Theorem: Video, Notes
- 2024-03-19 Pappus' Theorem: Video, Notes
- 2024-03-21a Desargues' Theorem: Video, Notes
- 2024-03-21b Morley's Trisector Theorem: Video, Notes
- 2024-03-26 Tilings, Periodic and Aperiodic: Video, Notes
- 2024-03-28 Playing with Penrose's Kites and Darts Tiles: This lecture was not recorded; we just cut out tiles printed on paper and tried to tile with them.
Handout: Penrose's Kites and Darts Tiles
- 2024-04-02 Penrose's Kites and Darts Tilings, Barlow's Theorem: Video, Notes
Handouts: Kite and Dart Tile Definitions and Inflation/Deflation, The Infinite Sun and Infinite Star Tilings
- 2024-04-04 Tiling the Plane With Kites and Darts and Logic: Video, Notes
Winter 2023
- MATH 2260H Course Outline
- Euclid's Elements of Geometry, edited and translated by Richard Fitzpatrick.
Our textbook for the first half or so of the course.
- Euclid’s Postulates Extended - Euclid's five postulates, plus a couple of extra ones filling in some of the gaps in his system.
- Hilbert's Axioms
(excerpted from The Foundations of Geometry by David Hilbert)
- Assignment # 1,
2,
3,
4,
5,
6,
7,
8,
Bonus,
9,
10,
11
- Take-Home Final Examination
Winter 2021
- MATH 2260H Course Outline
- Euclid's Elements of Geometry, edited and translated by Richard Fitzpatrick.
Our textbook for the first half or so of the course.
- Euclid’s Postulates Extended - Euclid's five postulates, plus a couple of extra ones filling in some of the gaps in his system.
- Hilbert's Axioms
(excerpted from The Foundations of Geometry by David Hilbert)
- Assignment # 1,
2,
3,
4,
5,
2e,
6,
7,
8,
9,
10,
11,
Extra
and Solutions to Assignment #
1,
2,
3,
4,
5,
2e
- Take-Home Final Examination
- Lectures and Notes
- Euclid's Postulates (& Proposition I-1) -
video,
notes
- Proposition I-2 -
video,
notes
- Propositions I-3, I-4, and I-15 [done early] -
video,
notes
- Propositions I-5 to I-8 -
video,
notes
- Propositions I-9 to I-12 -
video,
notes
- Propositions I-13 to I-16 -
video,
notes
- Propositions I-17 to I-22 -
video,
notes
- Propositions I-23 to I-26 -
video,
notes
- Propositions I-27 to I-29 -
video,
notes
- Propositions I-30 to I-32 -
video,
notes
- Some Equivalents of Postulate V -
video,
notes
- Propositions I-33 to I-36 -
video,
notes
- Propositions I-37 to I-40 -
video,
notes
- Propositions I-41 to I-43 -
video,
notes
- Propositions I-44 to I-48 -
video,
notes
- Circles, Angles, Lines -
video,
notes
- Circles, Angles, Lines II -
video,
notes
- Circles, Angles, Lines III -
video,
notes
- Triangles and Their Centres -
video,
notes
- Triangles and Their Centres II -
video,
notes
- Triangles and Their Centres III -
video,
notes
- Triangles and Their Centres IV -
video,
notes
- Triangles and Their Centres V -
video,
notes
- Triangles and Their Centres VI -
video,
notes
- Ceva's Theorem -
video,
notes
- Menelaus' Theorem -
video,
notes
- Pappus' Theorem -
video,
notes
- Desargues' Theorem -
video,
notes
- Desargues' Theorem II -
video,
notes
- Morley's Theorem -
video,
notes
- Bolyai-Gerwein Theorem -
video,
notes
- Bolyai-Gerwein Theorem II -
video,
notes
- Bolyai-Gerwein Theorem III -
video,
notes
Fall 2018
- MATH 2260H Course Outline
- Assignment # 1,
2,
3,
4,
5,
6,
2π,
7,
8,
9,
10,
11,
12,
and Solutions to Assignment # 1,
2,
3,
4,
5,
6,
7,
8
- Take-Home Final Examination
- Euclid's Axioms
(excerpted from Euclid's Elements in Greek by Richard Fitzpatrick)
- Hilbert's Axioms
(excerpted from The
Foundations of Geometry by David Hilbert)
- Euclid's Postulates and More - The extended set of postulates we'll be using for the most part.
Fall 2016
Fall 2015
Winter 2014
Winter 2013
- Assignment # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11
and Solutions to Assignment # 1,
2,
3,
4,
5,
6,
7,
8,
9
- Quizzes and Solutions to the Quizzes
- Take-Home Final Exam
Winter 2012
- Assignment # 1,
α,
2,
3,
4,
5,
6,
7,
8,
9,
10
and Solutions to Assignment #
1,
2,
3,
4,
5,
6
- Quizzes and Quiz Solutions
- Take-Home Final Exam
Winter 2011
- Problem Set # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11
- Quizzes and Quiz Solutions
- Take-Home Final Exam
Winter 2008
- Problem Set # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11
Solutions to Problem Set #
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11
- Quizzes and
Solutions to Quizzes
- Take-Home Final Exam
- Some sources on the foundations of geometry
Fall 2006
- Problem Set # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11 & 12
Solutions to Problem Set #
1,
2,
3,
4,
5,
6,
7
- Quizzes and Quiz Solutions
- Final Exam
Maintained by Stefan Bilaniuk. Last updated 2025-05-14.