MathPlotAI Logo MathPlotAI

GeoGebra Geometric Construction and Parametric Curves Example

GeoGebra Geometric Construction and Parametric Curves Example
Loading the math board and drawing, please wait…
2022-12-05 01:36
VectorCoordinate GeometrySolid GeometryParametric EquationGeometric Construction
This example demonstrates geometric construction and parametric curve creation using GeoGebra. Key mathematical concepts include vectors, ellipses, rotation, parametric equations, and solid geometry. Construction involves commands like If, Point, Polygon, Prism, Net, Arc, Rotate, Conic, Vector, and objects such as b, t, l, e, P1, P2, P3, P4, P5, A, B, D, C, E, F, c1, f, g, h, i, a, G, H, I, J, caraCDHG, caraDEIH, caraEFJI, caraCFJG, caraGHIJ, aristaCG, aristaDH, aristaEI, aristaFJ, aristaGH, aristaHI, aristaIJ, aristaGJ, c, K. Suitable for high school students or college students learning geometric construction and parametric curve drawing.

GeoGebra Commands & Parameters

  1. If(b < 1, 0, b > 2, 1, b - 1) → t
  2. Point(e) → P1
  3. Point(e) → P2
  4. Point(e) → P3
  5. Point(e) → P4
  6. Point(e) → P5
  7. Point(e) → A
  8. Point(e) → B
  9. Polygon(F, E, D, C) → c1, f, g, h, i
  10. Prism(c1, 7) → a, G, aristaCG, aristaDH, aristaEI, aristaFJ, aristaGH, aristaHI, aristaIJ, aristaGJ, H, I, J, caraCDHG, caraDEIH, caraEFJI, caraCFJG, caraGHIJ
  11. Net(a, b) → c, K, T, U, V, W, Z, caraKLMN, caraKLPO, caraLMRQ, caraMNTS, caraKNUV, L, caraOPWZ, aristaKL, aristaLM, aristaMN, aristaKN, aristaKO, aristaOP, aristaLP, aristaLQ, aristaQR, M, aristaMR, aristaMS, aristaST, aristaNT, aristaNU, aristaUV, aristaKV, aristaPW, aristaWZ, aristaOZ, N, O, P, Q, R, S
  12. Arc(e, (0, -9), (0, 3)) → r
  13. Arc(e, (0, -9), (0, 3)) → r'
  14. Rotate(P1, α, l) → R1
  15. Rotate(P2, α, l) → R2
  16. Rotate(P3, α, l) → R3
  17. Rotate(P4, α, l) → R4
  18. Rotate(P5, α, l) → R5
  19. Conic(R1, R2, R3, R4, R5) → k
  20. Rotate((0, 3), α, l) → A1
  21. Rotate((0, -9), α, l) → B1
  22. Arc(k, A1, B1) → q
  23. Arc(k, A1, B1) → q'
  24. If(b < -1.5 ∨ b > 0, 0, b > -0.5, 1, b + 1.5) → s
  25. If(b < -1.5, 0, b > -0.5, 1, b + 1.5) → ss
  26. Vector((-0.57, 1, -0.43)) → v1
  27. Vector((0, 0, -1)) → v2
  28. If(b > 3, v2, Vector[v1 + ((v2 - v1) * (b - 2))]) → v
  29. If(b < -1.5, abs((2 * b) + 3), 0) → co

AI Drawing Prompt Reference

In the same coordinate system, start from a variable point e and construct several points defined by e, then use them to form the base polygonal face and build a prism by extruding that face along a fixed direction and height. Create an unfolding net from the prism for visual reference. Using the same point e, draw a vertical circular arc segment with endpoints at specified vertical offsets, and rotate the generated points around a common axis by a parameter angle. Use the rotated points to define a conic section, then select an arc on this conic between the two rotated reference points obtained from the earlier offsets. Display together the prism and its net, along with the conic arc curve.
The prompt above was compiled from the original drawing commands and is for reference only.