**Summer 2017**

**Spring 2014**

We will approach this study of geometry from four different directions:

- The classical (Greek) approach.
- The analytic approach using vector geometry and linear algebra.
- The projective approach.
- The geometric transformations approach.

**Required Text**: The four pillars of geometry, by John Stillwell.

- Syllabus Math 325
- Notes on angles and construction of square roots
- Spherical triangle
- Integral solutions to a2=c2+2b2

**Projects**

**Homework**

- Page 6 # 1.2.1, 1.2.2, and Page 9 # 1.3.3, 1.3.5, 1.3.6 Solution
- Homework set 1 Solutions to Homework set 1
- Homework set 2 solutions homework set 2
- Homework set 3 Homework set 3 solutions
- Homework set 4 Homework set 4 solutions
- Homework set 5 #4.3.2, 4.3.3, 4.3.4, 5.1.1, 5.3.1, 5.3.3 Solutions to Homework set 5
- Homework set 6 Homework set 6 solutions
- Homework set 7 Solution Homework set 7
- Homework set 8 with solutions

**Quizzes and Exams**

## Fall 2013

We will begin with a fairly classical approach to Euclidean geometry, discussing fundamental theorems of geometry, constructions with straightedge and compass, and so on. Some of the material might ring a bell from a high school geometry class, although our emphasis will be on the foundations of geometry and the proofs of these results, we will include some computational aspect of geometry as well. Toward the end of the course, we will see a contrast to Euclidean geometry through a study of hyperbolic geometry and if we have time spherical geometry as well. **Text: ***A Survey of Classical and Modern Geometries*, by Arthur Baragar, published by Prentice Hall.

Week 1

Week 2

Week 3

Week 4

Week of October 23rd (Section 1.7 and 1.8)

Week of November 4th

Week of November 19th

- Group work on constructible length
- Solution for the above construction

Week of November 25th

**Spring 2013**

We will begin with a fairly classical approach to Euclidean geometry, discussing fundamental theorems of geometry, constructions with straightedge and compass, and so on. Some of the material might ring a bell from a high school geometry class, although our emphasis will be on the foundations of geometry and the proofs of these results, we will include some computational aspect of geometry as well. Toward the end of the course, we will see a contrast to Euclidean geometry through a study of hyperbolic geometry and if we have time spherical geometry as well. **Text: ***A Survey of Classical and Modern Geometries*, by Arthur Baragar, published by Prentice Hall.

**Syllabus Math 325**- My past notes for the course are here
- Picture proof of the Pythagorean Theorem Pythogorean Theorem
- Isometry and Orientation

**Projects**

**Worksheets**

- Worksheet on the Pythagorean Theorem
- Worksheet on Isometry and Orientation
- Worksheet on Similar Triangles Solutions Worksheet Similar Triangles
- Incenter excicles, incircles worksheet

## —————————

**Fall 2012**

We will begin with a fairly classical approach to Euclidean geometry, discussing fundamental theorems of geometry, constructions with straightedge and compass, and so on. Some of the material might ring a bell from a high school geometry class, although our emphasis will be on the foundations of geometry and the proofs of these results, we will include some computational aspect of geometry as well. Toward the end of the course, we will see a contrast to Euclidean geometry through a study of hyperbolic geometry and if we have time spherical geometry as well. **Text: ***A Survey of Classical and Modern Geometries*, by Arthur Baragar, published by Prentice Hall. My notes for the course are here **Syllabus**

**Worksheet**

**Lecture notes**

- Mathematical Proofs
- Lecture notes Part I contains sections 0.2 , o.3, sections 1.1 and 1.3
- Lecture notes Part II contains sections 1.4, 1.5, 1.6, 1.7
- Vectors and Inner Products
- Lecture notes Section 1.8
- Lecture notes Section 1.10
- Incenter excicles, incircles
- Sections 3.1 3.2 3.3
- Section 3.4
- Chapter 6 and Chapter 7
- Geometrical Transformations

**Mathematica Codes**