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.

- 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

- 2024-01-09

- 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

- 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,
2
*e*, 6, 7, 8, 9, 10, 11, Extra

and Solutions to Assignment # 1, 2, 3, 4, 5, 2*e* - 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

- 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.

- MATH 2260H Course Outline
- Assignment # 1,
2,
3,
π,
4,
5,
6

and Solution to Assignment # 3 - Quizzes and Solutions to the Quizzes
- 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)

- MATH 2260H Course Outline
- Assignment # 1, 2, 3, π, 4, 5, 6
- Quizzes and Solutions to the Quizzes
- Take-Home Final Examination

- Assignment # 1, 2, 3, 4, 5, 6
- Quizzes and Solutions to the Quizzes
- Take-Home Final Exam

- 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

- 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

- 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

- 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.