From Circle to Hyperbola in Taxicab Geometry

  • From Circle to Hyperbola in Taxicab Geometry

    Ruth I. Berger
    How far is it from Grand Central Station to the Empire State building? A pigeon could fly there in a straight line, but a person is restricted by the street grid. The geometry measuring the distance between points using the shortest path traveled along a square grid is known as taxicab geometry. This topic can engage students at all levels with tasks from plotting points and observing surprising shapes, to examining the underlying reasons for the appearance of these figures. Having to work with a new distance measurement takes everyone out of their comfort zone of routine memorization and makes them think, even about definitions and facts that seemed obvious before. Group discussions can be lively!
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