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Unfinished Box Sketch with Volume Graph

Unfinished Box Sketch with Volume Graph
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2016-09-24 22:43
TrigonometrySolid GeometryCalculusGeometric ConstructionGraphing
This example demonstrates an unfinished box sketch along with its volume graph. Core math concepts include volume, indefinite integral, trigonometry, circumcircle, boxplot, and reflection. Construction highlights involve commands/objects like Point, Ray, Intersect, OrthogonalLine, Polygon, Midpoint, Segment, LineBisector, Circle, Mirror, Vector, Translate, Locus from GeoGebra. Suitable for high school and above students to learn solid geometry, calculus, and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(xAxis) → K
  2. Ray(O, K) → r
  3. Point(yAxis) → L
  4. Ray(O, L) → s
  5. Intersect(xAxis, yAxis) → A
  6. Point(r) → B
  7. Ray(A, B) → f
  8. Point(s) → C
  9. Ray(A, C) → g
  10. OrthogonalLine(C, g) → h
  11. OrthogonalLine(B, f) → i
  12. Intersect(h, i) → D
  13. Polygon(B, A, C, D) → thebigrect, b, height, width, d
  14. Midpoint(height) → E
  15. Segment(E, C) → j
  16. LineBisector(b) → p
  17. LineBisector(d) → q
  18. Circle(C, squaresidemax) → c
  19. Intersect(c, height, 1) → F
  20. Intersect(c, width, 1) → G
  21. Segment(C, F) → k
  22. Segment(C, G) → l
  23. Circle(C, side) → e
  24. Intersect(e, k, 1) → H
  25. Intersect(e, width, 1) → I
  26. OrthogonalLine(I, width) → m
  27. OrthogonalLine(H, k) → n
  28. Intersect(m, n) → J
  29. Polygon(C, H, J, I) → poly1, c_1, h_1, j_1, i_1
  30. Mirror(C, p) → C'
  31. Mirror(H, p) → H'
  32. Mirror(J, p) → J'
  33. Mirror(I, p) → I'
  34. Polygon(C', H', J', I') → poly1', c', h', j', i'
  35. Mirror(C', q) → C''
  36. Mirror(H', q) → H''
  37. Mirror(J', q) → J''
  38. Mirror(I', q) → I''
  39. Polygon(C'', H'', J'', I'') → poly1'', c'', h'', j'', i''
  40. Mirror(C'', p) → C'''
  41. Mirror(H'', p) → H'''
  42. Mirror(J'', p) → J'''
  43. Mirror(I'', p) → I'''
  44. Polygon(C''', H''', J''', I''') → poly1''', c''', h''', j''', i'''
  45. Polygon(O, S, T, R) → poly2, o, s_1, t, r_1
  46. Vector(T, U) → u
  47. Translate(S, u) → S'
  48. Translate(O, u) → O'
  49. Translate(R, u) → R'
  50. Polygon(O', O, S, S') → poly3, o', o_1, s_2, s'
  51. Polygon(S, S', U, T) → poly4, s_3, s'_1, u_1, t_1
  52. Polygon(R', R, T, U) → poly5, r', r_2, t_2, u_2
  53. Polygon(R, R', O', O) → poly6, r_3, r'_1, o'_1, o_2
  54. Locus(P, side) → thecurve

AI Drawing Prompt Reference

Draw an unfinished box sketch with its volume graph. Start by setting up coordinate axes, picking points on the x-axis and y-axis, and drawing rays from the origin. Use the origin as a corner, pick points on each ray, and draw perpendiculars to form a large rectangle. Take the midpoint of one side, draw a perpendicular bisector, and use a vertex as center to draw a circle intersecting the rectangle sides, creating a small square. Mirror this square across the two bisectors to get four squares, forming the box net. Finally, plot a volume graph showing how the box volume changes with side length.
The prompt above was compiled from the original drawing commands and is for reference only.