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TaxiCab Parabola

TaxiCab Parabola
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2017-03-14 08:53
VectorCoordinate GeometryOptimizationGeometric Construction
This example demonstrates the formation of a parabola under the Manhattan distance metric, also known as the TaxiCab distance. Key mathematical concepts include TaxiCab geometry, vectors, polygon construction, and coordinate geometry. The construction utilizes GeoGebra commands such as Line, TaxicabCirclewithCenterthroughPoint, TaxicabDistance, Point, TaxicabCirclewithCenterandRadius, Intersect, and Locus. It is suitable for high school students and above to explore non-Euclidean geometric transformations and locus problems.

GeoGebra Commands & Parameters

  1. Line(B, C) → l
  2. TaxicabCirclewithCenterthroughPoint(A, D) → E, F, G, H, c, d, e, f
  3. TaxicabDistance(A, D) → h
  4. Point(l) → I
  5. TaxicabCirclewithCenterandRadius(I, h) → j, k, l_1, m_1, J, K, L, M
  6. Line(L, l) → m
  7. Intersect(m, c) → N
  8. Intersect(m, e) → O
  9. Intersect(m, f) → P
  10. Intersect(m, d) → Q
  11. TaxicabCirclewithCenterandRadius(A_2, t) → a_1, b_1, c_1, d_1, S, T, U, V
  12. Line(W, Z) → l_2
  13. Point(l_2) → A_1
  14. TaxicabCirclewithCenterandRadius(A_1, t) → f_1, g_1, h_1, i_1, B_1, C_1, D_1, E_1
  15. Line(D_1, l_2) → m_2
  16. Intersect(m_2, d_1) → F_1
  17. Intersect(m_2, a_1) → G_1
  18. Intersect(m_2, c_1) → H_1
  19. Intersect(m_2, b_1) → I_1
  20. Locus(G_1, t) → loc1
  21. Locus(H_1, t) → loc2
  22. Locus(F_1, t) → loc3
  23. Locus(I_1, t) → loc4

AI Drawing Prompt Reference

Draw a parabola under the taxi geometry. Start by drawing a line and a point, then draw a taxi distance circle centered at the point. Next, take a point on the line and draw another circle centered at that point with the previously calculated taxi distance. Then, draw a line through the center of the new circle and find its intersections with the previous two circles. Finally, construct the locus of the parabola using these intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.