Course:SLU MATH 124: Math and Escher  Fall 2008  Dr. Anneke Bart
Contents
 1 Homework and Reading Assignments
 2 Course Information
 3 Schedule
 3.1 Week 1 (Aug 25  Aug 29) Symmetry and Rozette Patterns
 3.2 Week 2 (Sep 1  Sep 5) Symmetry, Isometries, and Frieze Patterns
 3.3 Week 3 (Sep 8  Sep 12) Frieze Patterns and Intro to Wallpaper Patterns
 3.4 Week 4 (Sep 15  Sep 19) Wallpaper Patterns
 3.5 Week 5 (Sep 22  Sep 26) Tessellations and Isometries
 3.6 Week 6 (Sep 29  Oct 3) Escherlike Tessellations and Geometer Sketchpad
 3.7 Week 7 (Oct 6  Oct 10) Tessellations with Sketchpad
 3.8 Week 8 (Oct 13  Oct 17) Art Project Assignment and intro to Spherical Geometry
 3.9 Week 9 (Oct 20  Oct 24)Spherical Geometry
 3.10 Week 10 (Oct 27  Oct 31)Spherical Geometry
 3.11 Week 11 (Nov 3  Nov 7) Spherical Geometry
 3.12 Week 12 (Nov 10  Nov 14) Hyperbolic Geometry
 3.13 Week 13 (Nov 17  Nov 21) Hyperbolic Geometry
 4 Final Stretch of the Course
Homework and Reading Assignments
 Due Friday, August 29:
Read Visions of Symmetry pg. 115.
Read M.C. Escher and Introduction_to_Symmetry.
Do Rosette Exercises # 15, 812, 14  Due Friday, September 12:
Read Visions of Symmetry pg. 1531.
Read Frieze Patterns.
Do Frieze Exercises # 19  Due Friday, September 19:
Read Visions of Symmetry pg. 3140.
Do Wallpaper Exercises # 1, 3, 8, 9, 10  Homework for Monday Sep 22: Read Fundamental Concepts. You are not responsible for the optional section on reciprocals at the very end.

Cathedral Fieldtrip is scheduled for Friday October 3. (Or on your own time.) We will use this Field trip assignment St. Louis Cathedral Basilica
This assignment is due on Friday October 17.  Exam 1 is scheduled for Friday October 10. Study Guide  Exam 1  BartFall08
Recommended reading: Fundamental Concepts: Classifications. Plane Geometry. (Skip the section on "Sums of Reciprocals" at the end)
 Introduction to Symmetry: Reflections, rotations, and rosette patterns. (skip color symmetry).
 Frieze Patterns: Translations, glide reflections, and frieze patterns.
 Wallpaper Patterns: Lattices. The 17 groups. Classification flow chart. Escher's use of symmetry.
 Introduction to Tessellations
 Tessellations by Polygons (You may skip the section on Archimedean tessellations)
 The Tessellation Project is due Friday October 24. Read Tessellation Art Project. We will follow the following rubric: Course:Art Project Rubric  Bart 2008
 Write up solutions to problems 1  7: Spherical Geometry Exploration (due Monday Oct 27)
 Turn in solutions to Spherical Geometry: Polygons Friday October 31
 Homework assignment #1 for Spherical Geometry  handed out in class. Due Monday November 3, 2007
Course Information
General
Math and the Art of M.C. Escher
MWF 9:00 am  9:50 am
Ritter Hall 316
Prerequisite: 3 years of high school mathematics or MT A 120 (College Algebra).
Course Goals
 Develop an intuitive understanding of geometry by looking at examples and applications in art (mainly Escher’s work, but also some other modern artists).
 Develop a thorough understanding of the concepts and techniques of geometry.
 Further develop the ability to apply your knowledge of geometry to solve unfamiliar problems.
 (Further) develop skills for working effectively with others on mathematics problems.
Math and the Art of M.C. Escher is an inquiry based course. Inquiry based courses depend on a process called Cooperative Learning. Some helpful facts are described on this page that will help you succeed andexcel in this course.
Contact Information
 Office: Ritter Hall 115
 Email: barta@slu.edu
 Phone: (314) 9772852
The best way to contact the instructor is via email.
Office hours:
 Monday, Wednesday, Friday 10:30  11:30 am
 Thursday 10  11 am
 By appointment
 Remember that you can always ask questions via email.
Books
 The online textbook Math and the Art of MC Escher, at http://math.slu.edu/escher
 M.C. Escher: Visions of Symmetry by D. Schattschneider. W.H. Freeman and Company (1990)
 Flatland: A romance of many dimensions by E.A. Abbott, Dover Publ. (1992). Note that Flatland can also be found in its entirety on the internet. You may of course buy a hard copy if you prefer a book.
Grading
 Two exams – 15% each
 Tessellation Project – 10%
 Basilica Cathedral Fieldtrip  10%
 Saint Louis Museum Fieldtrip  5%
 Homework, inclass work, attendance – 20%
 Final – 25%
Grades:93100 A, 8992 A, 8688 B+, 8285 B, 8081 B 7779 C+, 7076 C, 6069 D, 059 F
Curve: I do not technically grade on a curve, but your work will of course be compared to that of your classmates, and even to students who have taken the class before you. To give an example: when evaluating answers that require an explanation, I will collect all the answers I consider “Alevel” and then rank them. If the question is worth 20 points, an A is somewhere between 18 and 20 points. The best answers will receive 20 points, the next best group will receive 19 points, and the others 18. They are all awarded an A, but the best answers receive a few more points. If someone writes answers that are truly excellent, then I will award extra credit.
How to do well: Attendance and participation is extremely important. Missing class regularly causes students quite a bit of trouble. It is very hard to make up this material on ones own.
Schedule
Week 1 (Aug 25  Aug 29) Symmetry and Rozette Patterns
Introduction to the course; First topic is "Symmetry"
Wednesday we do the Symmetry of Stars and Polygons Exploration and Rozette Symmetry Groups with Kali Exploration.
On Friday: Rotational and Reflectional Symmetry in Escher’s Sketches
On Friday Homework #1 is due:
Read Visions of Symmetry pg. 115.
Read M.C. Escher and Introduction_to_Symmetry.
Do Rosette Exercises # 15, 812, 14
Week 2 (Sep 1  Sep 5) Symmetry, Isometries, and Frieze Patterns
Monday September 1 is Labor Day: Official University Holiday
Start on Frieze patterns  also known as Borderpatterns. Use examples from earlier work to define reflections and translations. Discuss the difference between a symmetry and an isometry. Define translations and glidereflections.
 Do Frieze Names Exploration (Wednesday)
 On Friday we discussed homework. Some important points to remember:
 The homework prepares you for the exams. You need to solve all the problems assigned.
 Starting early so that you can ask for help is very important.
 Write up nice detailed solutions. Complete sentences should be the rule. Remember that you will be referring to your work when you study for exams. Write down enough so that your answers will be clear to you several weeks from now.
Week 3 (Sep 8  Sep 12) Frieze Patterns and Intro to Wallpaper Patterns
This week read: Frieze Patterns
 Do Identifying Frieze Patterns Exploration (Monday)
 We will start exploring tessellations. As an introduction we will do Tessellations, a first look Exploration (Wednesday)
 Next will be Wallpaper Symmetry Exploration (Friday) This exploration was started in class, but needs to be completed at home. The assignment is due Monday September 15.
 Homework #2 is due on Friday.
Week 4 (Sep 15  Sep 19) Wallpaper Patterns
This week read: Wallpaper Patterns
 Escher's Wallpaper Groups Exploration (Monday) If time permits, start on homework.
 Wednesday: review of some terminology. We discussed some properties of triangles, quadrilaterals. We defined convex and concave polygons. This information and more can be found in Fundamental Concepts
 Tessellation Exploration: The Basics
 Homework: From Wallpaper Exercises do problems 1, 3, 8, 9, 10
Due Friday September 19.
Week 5 (Sep 22  Sep 26) Tessellations and Isometries
Homework for Monday Sep 22: Read Fundamental Concepts. You are not responsible for the optional section on reciprocals at the very end.
Note: there may be a quiz on this reading assignment!
 Angles of Polygons and Regular Tessellations Exploration
 On Wednesday: Discussion of some theorems we now have:
 Theorem 1: All parallelograms tessellate the plane.
 Corollary (result that follows from the theorem): All rectangles and squares tessellate the plane.
 Theorem 2: All triangles tessellate the plane.
 Theorem 3: There are exactly 3 regular tessellations.
 Theorem 1: All parallelograms tessellate the plane.
 Friday: We will start on the Polyominoes Exploration. This exploration is assigned as homework and is due on Monday.
Week 6 (Sep 29  Oct 3) Escherlike Tessellations and Geometer Sketchpad
Recognizable Figure Tessellations: Do the new version:
 Creating Escherlike Tessellations Exploration (Monday)
 Continue with the Escherlike Tessellation exploration.
 Cathedral Fieldtrip is scheduled for Friday October 3. (Or on your own time.)
 Field trip assignment St. Louis Cathedral Basilica
Week 7 (Oct 6  Oct 10) Tessellations with Sketchpad
 Your assignment for this week is to do the following three Geometer Sketchpad Explorations at your own pace. The first part of the Introductions to GSP Exploration is heavily based on and inspired by materials developed by Mike Riedy.
 GSP Introduction Exploration
 GSP Quadrilateral Tessellation Exploration
 GSP Triangle Tessellation Exploration
 Exam 1 is scheduled for Friday October 10
Week 8 (Oct 13  Oct 17) Art Project Assignment and intro to Spherical Geometry
Monday:
 Go over the Art Project assignment.
 Do Sketches for the Art Project Exploration. This exploration will likely not been finished in class. It will become part of the Art project (the sketch component).
Friday: Spherical Easel Exploration
Week 9 (Oct 20  Oct 24)Spherical Geometry
Monday and Tuesday October 21/22: Fall Break
 Wednesday: Lecture about the axioms of geometry. Look at problems 1  7: Spherical Geometry Exploration
 Explore Spherical polygons with Spherical Geometry: Polygons
 The Tessellation Project is due Friday October 24.
Week 10 (Oct 27  Oct 31)Spherical Geometry
Homework: Write up solutions to problems 1  7: Spherical Geometry Exploration (due Monday)
 Worked on assignments in class  including starting the spherical homework assignment.
 Friday: Short session. Explanation of some of the problems on the homework assignment.
Week 11 (Nov 3  Nov 7) Spherical Geometry
 Monday: Q&A session about homework about spherical geometry.
 Monday: Discussed possible topics to be covered at the end of the course. The options are:
 Depth and Perspective. (Including Impossible Figures)
 The 4th dimension and fractals.
 History of Mathematics (Ancient Egypt in particular)
 Spherical Triangles Exploration Demonstration of Kaleidotile in class on Monday.
 Friday: Introduction to Hyperbolic Geometry. Discuss the axioms.
Week 12 (Nov 10  Nov 14) Hyperbolic Geometry
 Monday: Do Escher's Circle Limit Exploration
 Wednesday: Hyperbolic Geometry Exploration
 Friday: Hyperbolic Geometry II with NonEuclid Exploration
Week 13 (Nov 17  Nov 21) Hyperbolic Geometry
 Monday: Discuss Non Euclid Exploration (part II)
 Wednesday:Do Ideal Hyperbolic Tessellations Exploration
 Friday: start on homework Hyperbolic Geometry Fall2008  Bart.
Final Stretch of the Course
During the last two weeks students will explore topics according to their personal interests.
 Depth. perspective and impossible figures
Kate B., Adam C., Michelle E., Katherine J., Amanda K., Tiffany S., Chris W.
 The 4th dimension and Fractals
Albert X., Tom C.
 History of Mathematics
Sarah B., Molly B., Lauren B., Jess D., Cassie H., Lizzy L., Spencer L., Dania S.
Week 14 (Nov 24  Nov 28)
 Monday:
 Depth and Perspective Group: Perspective Exploration
 4th Dimension Group: Dimensions Exploration
 History of Math Group: Egyptian Numbers Exploration
 Wednesday November 26: No class
 Thursday and Friday November 27/28: Thanksgiving: Official University Holidays
Week 15 (Dec 1  Dec 5)
 Monday:
 Depth and Perspective Group: Flatness Exploration
 4th Dimension Group: Flatness Exploration and reading assignment: Flatland
 History of Math Group: The Seqed and Modern Trigonometry Exploration
 Wednesday: Review for Exam 2. Discussion of some topics and concepts from both spherical and hyperbolic geometry.
 Friday: Exam on NonEuclidean Geometry Exam 2 Outline
Week 16 (Dec 8)
 Monday: Last day of Class.
 Depth and Perspective Group: Do problems 2,4,5,6,10, and 11 in Depth and Perspective Exercises
 4th Dimension Group: Flatland and the 4th dimension in Flatland Exploration
 History of Math Group: More ancient geometry. Problems
Week 17 (Dec 15)
 Art Museum Fieldtrip. Due on the day of the final. Details
 Final  Monday December 15 during the first block 8  9:50 in RH 316
The final will consist of two sections:
 An essay question comparing and contrasting Euclidean, spherical and hyperbolic geometry.
 Question(s) about the special topic you chose at the end of the semester.
I will not ask any further questions on the final based on homework or explorations. This was already covered on the two exams. This will hopefully make the study process a bit easier and help with time management.