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Prof. Robert Hazen
Syllabus for Fall Semester 2003
(Also listed under ARTH399, AVT399 and AVT599)
MONDAYS, 1:30-4:10 pm in David King 210PRIVATE
Office: East Building 202
Office Hours: Mon (4:30-5:45 pm; 6:45-7:15 pm)
Phones: 703-993-2163 (GMU)
202-478-8962 (Geophysical Lab)
E-Mail: hazen@gl.ciw.edu
COURSE OBJECTIVES: Symmetry encompasses any aspect of matter or experience that involves the repetition of a pattern in space, in time, or in any other dimension. Sights and sounds and other inputs constantly bombard our senses. The only way that we can make sense of the universe is by learning to recognize patterns and their variations. Symmetry thus affects every characteristic of the natural and artistic world.
Symmetry pervades every subject in science: subatomic particles, electrons in chemical bonds, atoms in crystals, the molecules of life, the external and internal morphologies of all living things, the earth, the solar system, and the universe all have symmetries that follow from physical laws. By the same token, every art form depends on pattern and symmetry. Form and balance, attained by symmetry in two and three dimensions, are essential aspects of painting, sculpture and architecture. Temporal symmetries are integral to all music and poetry, while drama and dance develop symmetry in four dimensions. Many other events and experiences, from habits and daily routine, to sports and board games, legal and political systems, economics and business, and our emotional and physical states, illustrate the far-reaching principles of symmetry. We begin by examining three aspects of symmetry that are common to all of these diverse subjects:
The Motif: The motif is the pattern that is repeated, possibly with modification. A flower design on wallpaper, a series of musical notes, a subatomic particle, or an emotional state are all motifs that provide a starting point for the study of symmetry.
The Dimension: A motif is repeated in one or more dimensions. Wallpaper patterns are repeated on a two-dimensional surface, whereas musical notes are repeated in the dimension of time.
The Symmetry Operator: The symmetry operator defines the relationship between one motif and its repetition in a dimension. Operators such as a translation, a mirror, or a rotation, for example, may repeat a floral motif in wallpaper.
In many instances, these ideas can be systematized using the mathematics of geometry. We will introduce some of those mathematical ideas in two and three dimensions, and we will explore their extension to higher dimensions. Hands-on classroom activities with symmetrical objects will help you think about symmetry in three dimensions.
Once the basic vocabulary of symmetry is introduced, we will investigate a variety of symmetries in the physical world, life, and the arts. We will examine the laws of motion and thermodynamics for symmetries that influence all matter and energy. We will read Shakespeares King Lear and other works to see how authors exploit symmetry in plays and poetry. We will listen to the periodic symmetries of classic rock and roll and compare them to the more subtle repetitive patterns in Beethovens 5th symphony and other music. In addition, each student will prepare a term paper (oral report if the class is small) on an aspect of symmetry relating to his or her major.
COURSE OUTLINE (Details subject to change)
PART I Symmetry Operators and Symmetry Groups: Mirrors, rotations and translations are the basic vocabulary of symmetry. Well explore a variety of symmetric objects and introduce the idea of a symmetry group.
Week 1. What is Symmetry? Hubcaps!!! Plane Point Symmetry (Aug. 25)
Course introduction, introductory lecture, in-class exercise and take-home lab
Week 2. Kaleidoscopes!!! Mirrors in Combination (Sept. 8 -- ***Sept. 1 is a holiday***)
Lecture on symmetry groups and mirror operators and in-class lab
Week 3. Crystals!!! Three-Dimensional Point Groups (Sept. 15)
Lecture on crystals, lattices and 3-D point groups; in-class lab
Week 4. Wallpaper!!! Plane Groups (Sept. 22)
Lecture on the 7 line groups and 17 plane groups, translation and glide plane symmetry operators, and lots of practice.
Week 5. Penrose Tiles, Magnetic Groups, Color Groups and More!!! (Sept. 29)
Lecture on higher symmetry groups, more plane group practice, and the 1st plane group
quiz (first chance of 3).
PART II Symmetry in Everyday Experience: Building on the first 5 weeks, well explore symmetry in many aspects of art, science and daily life.
Week 6. Board Games (Oct. 6)
Well play a variety of board games to explore how symmetry (and asymmetry) can be used to win. Youll play a symmetric game of scrabble and an asymmetric game of Chinese checkers.
Week 7. Take-Home Lab #1 on Team Sports (***Tuesday Oct. 14)
Your assignment will be to watch a team sporting event and to analyze how asymmetries are exploited to win.
Week 8. The 230 Space Groups and Crystallography the Gillespite Story (Oct. 20)
X-ray crystallography explores the symmetry of 3-dimensional periodic atomic arrangements. This lecture will examine how the x-ray process works, and some of the surprising changes in symmetry that can result when crystals are subjected to high pressures and temperatures.
Week 9. Symmetry Breaking in King Lear and Particle Physics (Oct. 27)
Certain seemingly identical objects will suddenly appear to be different when subjected to external forces or stimuli. Well examine symmetry breaking as a literary device in Shakespeare and a guiding principle in particle physics. King Lear by Shakespeare is required reading.
Week 10. Take-Home Lab #2 on Art and Architecture (Nov.3)
This take-home laboratory exercise involves a museum visit and an excursion around the GMU campus and downtown Fairfax. You will look at a variety of art works, as well as buildings, and analyze them in terms of their use of motifs and symmetry.
Week 11. Symmetry in Music and Dance (Nov. 10)
Music and dance involve varied symmetries in the dimension of time and frequency (pitch). Well explore a variety of music and dance styles.
Week 12. Symmetry and Asymmetry in Life, Nature and the Universe (Nov. 17)
Natural laws, antimatter, stars, plate tectonics, and lots of aspects of biological systems. Well focus especially on external bilateral symmetry vs. internal asymmetry of multicellular organisms. Ill describe my research on handedness and the origin of life.
PART III Final Projects
Week 13. Final Project Presentations (Nov. 24)
Information to follow, but everyone must write a paper and make a 10-minute presentation on some aspect of symmetry. The best papers draw from your own interests and background.
Week 14. Final Project Presentations (Dec. 1)
More presentations.
* * * * *
EXPECTATIONS AND CLASS ATTENDANCE: Most of the material in this course is not covered in any text. Many of the classes will be primarily laboratory exercises that are not easily made up. Attendance, therefore, is mandatory.
Be sure to come to class prepared by reading any assignments and completing out-of-class work. You are responsible for bringing writing and other materials, as specified week-to-week.
READING: I will hand out reading materials at various points in the course. In addition, Shakespeares King Lear will be required reading.
Useful books, if you can find them, are:
Bryan Bunch, Realitys Mirror
Martin Gardner, The New Ambidextrous Universe
GRADING POLICY: Grades will be based on the following criteria
Attendance 240 pt
Your symmetry notebook (cumulative projects) 200 pt
Pass/Fail Plane Group Quiz (3 chances to pass) 200 pt
Two take-home exercises on art and team sports 200 pt
Final project paper and presentation 200 pt
Other point opportunities 100 pt
Total Possible Points 1140 pt
Your grade will be based on the point totals:
950 or more = A 820-859 = B 700-739 = C
900-949 = A- 780-819 = B- 600-699 = D
860-899 = B+ 740-779 = C+ below 600 = F
* * * * *
Attendance: I will take attendance every week at the beginning and end of class. You get 10 points for being there at the beginning, and 10 points at the end (20 points per week). If an emergency arises and you must miss a class, be sure to call my office (703-993-2163) or leave a message at my Lab answering machine (202-478-8962) prior to the class. However, attendance points cannot be made up.
Your Symmetry Notebook: From time to time I will give you instructions on assembling your symmetry notebook. This notebook is your permanent record of symmetry groups and patterns. Future artists and designers will find it especially useful to maintain and build this reference. I will grade your notebook based on your attention to criteria in the individual assignments, as well as neatness, accuracy, and style. I will exam your notebook formally at midterm and at the end of the semester.
Final Projects: Final projects, which include a written report and oral presentation, are to be on any aspect of symmetry that interests you. Ive had excellent projects on topics as diverse as snowboarding, Navajo religion, the government of Kenya, and bathroom tile. If you are an art major you may choose to develop a studio project related to some aspect of symmetry. You will still be required to write a short paper explaining how elements of symmetry (or asymmetry) have been used in your artwork, and you will have to make a presentation to the class regarding your project.
Pass-Fail Plane Group Quiz: There are 17 distinct plane group symmetries. Everyone must pass a quiz on identifying these plane group of all-over patterns. Well spend a lot of time on this and youll have several chances to pass.
Take-Home Exams and Exercises: Throughout the semester there will be point opportunities, including two take-home labs (100 points each) and various other extra credit assignments.
* * * * *
HONOR CODE: All assignments and projects must be done on your own. All students at GMU are governed by the provisions of the honor code, as given in the catalog.
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