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Taxicab Geometry A Study Into Non-Euclidean Geometry Using Geometer Sketchpad

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## Taxicab Geometry A Study Into Non-Euclidean Geometry Using Geometer Sketchpad

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**Taxicab Geometry A Study Into Non-Euclidean GeometryUsing**Geometer Sketchpad Tyler Roell Studied under Dr. R. Talbert Franklin College Math Day November 21, 2009**The Beginning of Taxicab Geometry?**Hermann Minkowski (1864-1909) Teacher of Einstein Also known as Manhattan Distance Karl Menger (1952)**What is Taxicab Geometry?**Assumptions made of Taxicab Geometry One Main Difference Dt=|x1-x2|+|y1-y2|**Differences**Dt=|x1-x2|+|y1-y2| De= Crows Fly Vs. Urban Geography Dt=|3-1|+|1-4|=5**Redistricting Problem**Say you have three schools, K,N, and M. Using the Taxicab Distance, where should the school districts be drawn to keep all the districts the same size in area?**Geometric Figures**Circles The set of all points equidistant from a point p with radius r**Geometric Figures**Parabolas set of all points that are the same distance from a fixed line and a fixed point not on the line**Geometric Figures**Parabolas set of all points that are the same distance from a fixed line and a fixed point not on the line**Bisectors**• In Taxicab In Euclidean**Now back to the problem**What should be done first? What figures should be used?**Further Application**Ellipses The set of all points where the sum of the distances from any point on the curve to the two fixed points remain a constant**Applications for Teaching**• Easier way to measure distance • Applicable to the Urban Setting • Uses technology in the Classroom**Book Used**• Eugene F. Krause Taxicab Geometry: An Adventure in Non-Euclidean Geometry