Geometry:  New Tools for New Technologies II

6 Ten Minute Programs
Grade(s):  7 - 12
Curriculum:  Mathematics

GEOMETRY: NEW TOOLS FOR NEW TECHNOLOGIES II introduces and explains various geometric concepts through animation and on-location illustrations and conversations with practicing professionals. The programs then answer the question of many students, "Why do I have to learn this stuff?" by showing examples of how the concepts are applied to real-life situations:

Program Titles; (All timings are working)

  1. Structures: Will It Fall Down (9:27)
    A short segment showing a variety of buildings opens the video and is accompanied by a narrative that underscores the importance of designing strong structures. Architect Scott Loiselle discusses grid systems and how they are made rigid by bracing individual cells of the grid. Following Scott's presentation, the question of determining the minimum number of braces needed to make a grid system rigid is raised. The video closes with a discussion of the triangular grid systems (trusses) used in the construction of many roofs. Truss designer Jamie Brogdan describes the design of trusses.

  2. Symmetry, Rigid Motions and Patterns (9:59
    The video's opening footage conveys the rich variety of pattern that fill our world. Archaeologist Dorothy Washburn discusses the importance of pattern analysis in her work and shows examples of the four types of rigid motion in designs on pottery from archaeological sites in the American Southwest. Graphic displays are used to show how the four types of rigid motion can be used to form seven classes of strip patterns, and Dorothy Washburn presents pottery examples. Carol Bier, curator of the Textile Museum in Washington D.C., follows with examples of rigid motion in textile design. Dorothy Washburn closes the video with an example of the conclusions she has drawn by applying principles of symmetry to her archaeological research.

  3. Topology: Knot Theory (7:42)
    A short segment at the beginning of the video shows that knots are common and important and introduces topology as the branch of geometry that studies knots. Dr. Nicholas Cozzarelli talks about the importance of knots and topology in DNA research. Graphics and demonstrations with rope are used to introduce basic knot terminology, to show how knots are transformed, and to. give an example of how knots are classified.

  4. The Right Stuff: Space Optimization (7:57)
    The video begins with a silent segment that depicts three students packing a van as they head off to college. Next, Steve Henegar discusses the importance of managing space well when you are in the moving business. Graphics are used to assist Steve's explanation of the design of cartons used by movers. Craig Allgaier goes inside the trailer of a moving van to show how the cartons and other objects are efficiently packed into a van. Steve Henegar then explains that deregulation of the moving industry has produced new sizes of moving vans, resulting in the need for redesign of cartons used in the industry. Finally, a return to the college students shows that they have applied good packaging principles to achieve greater success.

  5. Gridville (7:59)
    The video begins with action shots of the Kensington, Maryland, fire department, with the narrative discussing the importance of fire station location. Kensington fire chief Jim Stanton discusses the process used to identify locations for Kensington's new Glenmont fire station and the criteria used to identify those locations. Chuck Boynton and Murray Hunt discuss community concerns about fire station relocation.

  6. Hidden Connections: Graph Theory (9:55)
    The video depicts a day in the cyberspace life of Jason, who operates GEOnet, a geometry site on the World Wide Web. Jason's callers include a band manager who is trying to find the cheapest way to route the band on a tour, a schedule director for a community center who is trying to avoid conflicts when scheduling the center's activities, and a girl who is trying to arrange dates for her friends. Several other callers, including a secretive caller from the Pentagon, suggest ways to use graphs and matrices to solve the problems.