Kites: An interdisciplinary experience melding math, science, and art

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KitesAn interdisciplinary experience melding
math, science, and art

• Ken King
• Northern Illinois University

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Why Interdisciplinary?

• Advantages of interdisciplinary instruction
• Challenges of interdisciplinary instruction

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Kites Science

• Your kite will be creating an obstacle to the
  normal air flow which will cause the air to
  change direction and speed. When the air flows
  across the objects surface it moves faster over
  the kite while the flow across the lower surface
  of the kite moves more slowly. Air pressure could
  be altered due to the changing air speed and
  results in the kite being pushed higher producing
  lift and flight.

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Kites Science

• Basic forces
• lift
• drag
• gravity
• thrust
• To fly, a kite needs to have enough lift to
  overcome gravity and drag.

thrust
gravity
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Kites Math

• Important skills (from NCTM standards)
• Analyze characteristics and properties of two-
  and three-dimensional geometric shapes
• Specify locations and describe spatial
  relationships using coordinate geometry and other
  representational systems
• Apply transformations and use symmetry to analyze
  mathematical situations
• Use visualization, spatial reasoning, and
  geometric modeling to solve problems

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Mathematics Example

• For example, observe the overlapping pairs of
  triangles in the design of the kite in the
  figure. The overlapping triangles, which have
  been disassembled in the figure, can be shown to
  be similar. Students can measure the angles of
  the triangles in the kite and see that their
  corresponding angles are congruent.

They can measure the lengths of the sides of the
triangles and see that the differences are not
constant but are instead related by a constant
scale factor. With the teacher's guidance,
students can thus begin to develop a more formal
definition of similarity in terms of
relationships among sides and angles.
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The Tetrahedron
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The Tetrahedron

• The tetrahedron is theoretically the strongest,
  most rigid symmetrical structure that can exist
  in nature.
• Using tetrahedron cells to construct a kite has a
  number of advantages.
• A kite can be built to almost any size simply by
  connecting several tetrahedron cells together
• The cells are rigid, and don't need extra bracing
  to maintain their shape
• No need for thicker and stronger sticks as the
  kite grows in size, which produces an
  exceptionally strong and stable kite

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Kites Art

• Elements of art
• Line, shape, value, texture, color
• Harmony involving rhythm and repetition
• Variety involving contrast and elaboration
• Employing
• Balance, movement, proportion, dominance, economy
  and space
• To produce unity

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Steinberg The Discovery of America
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Matisse
Van Gogh
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Andrew W. Tuer Japanese Stencil Designs
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M. C. Escher, Encounter Lithograph, 1944
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Rembrandt, Saskia Asleep
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Constructing a Kite

• Repetition of tetrahedral cells
• select design
• create appropriate number of cells
• High-end approach
• graphite rods, ripstop nylon, etc.
• More modest approach
• soft drink straws, fishing line, tissue paper

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Sample Variations
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This kite is composed of multiple sets of four
tetrahedron cells
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This structure is composed of multiple
repetitions of four-cell structures--similar to
the previous image--but with a different overall
unifying configuration (16 cell Sierpinsky
arrangement x 4)
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Another view of multiple sets of tetrahedral
cells ( 64 cells)
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Bell built gargantuan man-carrying kites made of
thousands of interlocking tetrahedron cells. One
was made of 3,393 cells! The town near Bell's
laboratory gained a new industry as workmen and
seamstresses turned out thousands of silk covers
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Using Kites in an Environment Education/Physical
Science Class
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Our task

• Constructing a series of tetrahedral cells
• Organizing them into a larger overall structure
• Testing our kite

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References

• Interdisciplinary Unit
• http//www.cedu.niu.edu/scied/courses/tlci525/samp
  le_unit.htm
• Art
• http//www.dartmouth.edu/matc/math5.pattern/lesso
  n1art.html
• Math
• http//mathworld.wolfram.com/Tetrahedron.html
• http//www.melbpc.org.au/pcupdate/9902/9902article
  5.htm (Sierpienskys Tetrahedron)
• http//standards.nctm.org/document/chapter5/geom.h
  tm
• Science
• http//www.win.tue.nl/pp/kites/fak/science/scienc
  e.html
• Kites
• Bell, A. G. "The Tetrahedral Principle in Kite
  Structure." National Geographic, 44, 219-251,
  1903.
• Eden, M. (1998). The Magnificent book of kites.
  New York Black Dog and Leventhal.
• Hosking, W. (1992). Kites in the classroom.
  Rockville, MD American Kiteflyer's Association
• Pelham, D. (1976). Kites. Woodstock, NY
  Overlook Press.