Exploring the Fourth Dimension
Unmasking Mathematical Concepts Found in the Work of Emeagwali

Overview of Lesson Plan: In this lesson, students investigate the role of mathematics in the programming of 65,000 processors. They then discover, through reading an essay and listening to a lecture by Emeagwali and through constructing and de-constructing a hypercube, that mathematics exists on a deeper level in the design of computers and the Internet.

Suggested Time Allowance: 45 minutes

Objectives:
Students will:

  1. List and discuss other applications that involve higher dimensional spaces, such as string theory, parallel universes, hyperball computers, hypercube computers, hyperspace, etc.
  2. Read and discuss
  3. Relate higher-dimensional universes metaphorically to our three-dimensional universe

Resources / Materials:
paper
pens/ pencils
Each student should print copies of

  1. Lyrics of the Rain Forests
  2. The Ways of Counting
  3. SuperBrain
Activities / Procedures:

WARM-UP/DO NOW: Students list all scientific topics they know that involve higher dimensions. The list is shared with other students and the teacher writes them on the blackboard. Students then brainstorm for additional examples.

READ THE ARTICLES, ESSAYS & TRANSCRIPTS

  • Explain what inspired Emeagwali to contest for the Gordon Bell Prize.
  • Summarize the twenty most diificult problems in the computing field compiled by the United States government. Explain what made these problems difficult.
  • Explain what inspired Emeagwali to use 65,000 processors.
  • Summarize the mathematical problem the cause the Austrian Paul Fillunger and his wife to committ suicide. Describe Emeagwali's solution of that problem.
  • Explain why a supercomputer is needed to discover and recover oil.
  • Using a full class discussion, ask the students to brainstorm the different geometrical techniques they can take to subdivide the Earth's atmosphere into 65,000 different regions. How can those 65,000 regions be mapped to 65,000 processors within a supercomputer? Within the Internet?

    WRAP-UP/ HOMEWORK: Students search for mathemetical metaphors in Emeagwali's work. Students write about the mathematical concept or theory in that specific work. Younger students may receive help from teachers in making the metaphoric comparisons.

    Further Questions for Discussion:

    1. What are some examples of stereotypes about mathematicians?
    2. Why did Thomas Jefferson argue that Africans cannot understand advanced mathematical concepts?
    3. Are the greatest mathematicians of ancient times such as Euclid & Fibonacci Africans?
    4. How do television promote these stereotypes?
    5. Do you need mathematics in your future career?
    6. How is mathematics used to discover and recover petroleum?
    7. How is mathematics used to forecast the weather?
    8. How is mathematics used to design supercomputers? The Internet?
    9. How is mathematics used in your daily life?
    10. Why are some people love mathematics?
    11. Why do some people hate mathematics?

    Evaluation / Assessment:
    Students will be evaluated based on participation in classroom discussion and "mathematical metaphors in Emeagwali's Work" project.


    Vocabulary:
    supercomputer, Internet, network, parallel computers, calculus, partial differential equations, hypercubes, topology, geometry, linear algebra,



    Extension Activities:

    1. Study a famous mathematical discovery? Present the latter discovery to your class.
    2. Find an article dealing with mathematics in Emeagwali's work and discuss it with your classmates.

    Interdisciplinary Connections:
    Science: Relate perceptions and stereotypes of scientists to those of mathematicians. How are scientists portrayed in movies and on television? How are these media stereotypes similar? How are they different?

    Language Arts: Study the "mathematics of poetry" (specifically, meter and rhyme schemes).




    Academic Content Standards:
    McRELThis lesson plan may be used to address the academic standards listed below. These standards are drawn from Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education: 2nd Edition and have been provided courtesy of the Mid-continent Research for Education and Learning in Aurora, Colorado.

    AchieveIn addition, this lesson plan may be used to address the academic standards of a specific state. Links are provided where available from each McREL standard to the Achieve website containing state standards for over 40 states. The state standards are from Achieve's National Standards Clearinghouse and have been provided courtesy of Achieve, Inc. in Cambridge Massachusetts and Washington, DC.

    Grades 6-8
    Mathematics Standard 9- Understands the general nature and uses of mathematics. Benchmark: Understands that mathematicians often represent real things using abstract ideas like numbers or lines- they then work with these abstractions to learn about the things they represent.
    Art Connections Standard 1- Understands connections among the various art forms and other disciplines. Benchmark: Knows how various concepts and principles are used in the arts and disciplines outside the arts (e.g., balance, shape, pattern)

    Grades 9-12
    Mathematics Standard 9- Understands the general nature and uses of mathematics. Benchmarks: Understands that theories in mathematics are greatly influenced by practical issues- real-world problems sometimes result in new mathematical theories and pure mathematical theories sometimes have highly practical applications; Understands that mathematics provides a precise system to describe objects, events, and relationships and to construct logical arguments; Understands that mathematics often stimulates innovations in science and technology
    Art Connections Standard 1- Understands connections among the various art forms and other disciplines. Benchmarks: Knows ways in which various art media can be integrated; Understands how elements, materials, technologies, artistic processes, and organizational principles are used in similar and distinctive ways in the various art forms