11'2: Taxicab Geometry

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11.2 Taxicab Geometry

• Alex, Caroline, Hunter,
• and Sarah Hunter

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Vocabulary

• Taxicab geometry- points are located on a special
  kind of map or coordinate grid where the
  coordinates are always integers.
• Taxidistance- the distance between two points in
  taxicab geometry smallest number of grid units
  that a taxi must travel to get from one point to
  the other
• Blocks- grid units

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Main Points

• Points are located on a map or coordinate grid
• Horizontal and vertical lines of the grid
  represent streets
• Points can only be at intersections of two
  streets
• Therefore, the coordinates are always integers.
• Unlike Euclidean geometry, taxicab geometry can
  have more than one minimum distance.

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Guided Example

• Answer- 8

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Taxicab Circles

• In Euclidean geometry, a circle is a set of
  points that are a fixed distance from a given
  point.
• In taxicab geometry, the points are all plotted
  one block away from the center of the circle.
• The result is that taxicab circles look more like
  squares.

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Taxicab Circles Continued
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Examples

• For points A(0,1), B(2,3), and C(-2,1), find the
  taxidistance below.
• AB
• BC
• AC

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Examples Continued

• Plot the taxicab circle with the given center and
  radius
• Center (3,2) radius 2
• Center (-1,4) radius 4

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Example Answers

• 1- 4
• 2- 6
• 3- 2
• 4- on board
• 5- on board

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Activity

• http//www.learner.org/teacherslab/math/geometry/s
  hape/taxicab/taxicab_2.phtml
• Youre going to look for treasure!

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Works Cited

• Pringle, Cori, Doug Davis, and Allen Walton.
  "Taxicab Geometry." University of Georgia. 15
  May 2007 lthttp//jwilson.coe.uga.edu/EMT668/EMAT66
  80.F99/DDavis/Taxicab/t axicab.htmlgt.
• Braun, Linda W., and Jeffrey Braxton. "Taxicab
  Treasure Hunt." The Annenberg/CPB Math and
  Science Project. 2007. Annenberg Media. 15 May
  2007 lthttp//www.learner.org/teacherslab/math/geom
  etry/shape/taxicab/ta xicab_1.phtmlgt.
• Schultz, James E., Kathleen A. Hollowell, Wade
  Ellis, and Paul A. Kennedy. Geometry. Austin
  Holt, Rinehart, and Winston, 2004. 706-711.