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 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 2024-05-01.