Final Project

Goals and Objectives: The geometry curriculum is continually changing, so in this project, you will research a topic related to geometry and you will communicate your expertise in an oral abstract and poster session. In the process you will experience another aspect of presentations - small group questions and answers. This is to be an individual project and the topic must be pre-approved by Dr. Sarah. Your project must exhibit effort that is appropriate for your background and major. Topics will be assigned on a first come/first served basis (see below for some suggestions, but you can choose any topic related to geometry).

Part 1 Topic and Annotated References (Due Tues Apr 25): Choose a topic (get this pre-approved by Dr. Sarah) and create a list of useful preliminary references and web reference addresses. In addition, after each reference, summarize (in your own words) what is contained within each reference. Dr. Sarah will respond to your references in a bulletin board posting on WebCT.

On Sat Apr 29, you should arrive 10 minutes early in order to set up your poster. We will begin the oral abstract presentations promptly at 3, and the poster sessions will follow afterwards. Poster sessions and evaluations will end at 5:30.

Part 2 Oral Abstract

Writing an abstract is an important part of presentations. An abstract should be thought of as an advertisement that others can read in order to decide whether they wish to attend. At conferences, there are often many talks that occur at the same time. Hence, people use abstracts to decide which talk to attend from among possibly many talks that they are interested in at the given time. While conference abstracts are written, your abstract will be presented orally within a 1-3 minute timeframe. It should include some big picture ideas that discuss the importance and relevance of your final project and place it into the bigger context of related fields. A blackboard and a transparency projector will be available should you wish to use them. The following are some examples of actual conference abstracts:
  • Simpsons Rule: Mathematical Morsels from The Simpsons
  • Using WebCT Instruction in Courses You Never Thought You Could
  • Tracing the Historical Progression of Mathematics and the Changing Roles of Women and Minority Mathematicians with Student Projects
  • Part 3 Poster Your poster will consist of the following portions:

    a) The majority of your poster should relate to the content of your chosen topic. In addition...
    b) Briefly discuss some ways (activities, worksheet ideas, references ...) to bring aspects from your topic into school classrooms.
    c) Briefly reflect on the relationship of your topic to the NCTM Standards for Geometry, Measurement or Reasoning and Proof.

    We will divide up the class into two poster sessions. During your poster session, you must stand by your poster to answer questions (and your answers must demonstrate expertise of your topic). During the other session, you should briefly look over everyone's project, and choose three or four people (who are standing by their poster) to evaluate using the peer review form that will be given to you. A portion of your final project grade will be determined by the depth, quality and clarity of your peer reviews, which will be read by Dr. Sarah, but not by the project presenter. Each peer review must demonstrate that you read the project carefully.

    Part 4 Presentation Notes and Annotated References Your project will be graded based on the depth of the mathematics, the clarity of your explanations, and the quality of your peer reviews. Turn in your presentation notes (on paper or index cards) and a final list of references with a summary of what is in each reference and how you used the reference.

    Some Ideas for Topics

  • Can You Hear the Shape of a Drum?
  • Conic Sections
  • Double Bubble Problem
  • Efficiency and Strength of Regular Polyhedra and Applications to Architecture
  • Fractals
  • Geometry and the Art of M.C. Escher
  • Geometry and DNA
  • Geometry of the Universe
  • History of Geometry
  • Mapping the Brain
  • Number Patterns in Geometry
  • Origami Folding Axioms
  • Packing Problems (Packing Geometric Shapes Into Other Geometric Shapes)
  • Polyhedra
  • Surfaces
  • Symmetry
  • Tessellations
  • Topology
  • Vertex-edge graphs