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From 3D to 2D: Parabola as Projection of a Circle

From 3D to 2D: Parabola as Projection of a Circle
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2019-09-13 18:22
CircleSolid GeometryGeometric Construction
This example demonstrates how a parabola can be generated as the projection of a circle. Key mathematical concepts include circles, geometric transformations, and projections. Using GeoGebra commands such as Polygon, Midpoint, and Circle, a 3D cube is constructed, and its projection results in a parabola. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4, xOyPlane) → poli1, f, g, h, i, C, D
  2. Midpoint(B, C) → J
  3. Cube(poli1, true) → a, E, spigoloAE, spigoloDH, spigoloEH, spigoloEF, spigoloBF, spigoloFG, spigoloCG, spigoloGH, F, G, H, facciaADHE, facciaABFE, facciaBCGF, facciaCDHG, facciaEFGH
  4. Midpoint(G, C) → M
  5. Midpoint(F, G) → I
  6. Midpoint(E, H) → L
  7. Midpoint(I, J) → K
  8. Circle(J, M, I) → c
  9. Point(c) → P
  10. Line(L, P) → j
  11. Intersect(j, z = 0) → P'