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Volume of a Parallelopiped by John Rodgers

Volume of a Parallelopiped by John Rodgers
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2017-04-25 21:16
VectorSolid GeometryCalculusGeometric Construction
This example demonstrates the calculation method for the volume of a parallelepiped. It involves core mathematical concepts such as vectors, linear functions, polygons, difference and slope, and indefinite integrals. The construction utilizes GeoGebra commands/objects like Vector, Segment, Angle, OrthogonalLine, Point, Midpoint, and Intersect. Suitable for high school and above students studying solid geometry and calculus.

GeoGebra Commands & Parameters

  1. Vector(O, B) → u
  2. Vector(O, A) → v
  3. Vector(O, C) → w
  4. Segment(A, D) → f
  5. Segment(B, D) → g
  6. Segment(D, E) → h
  7. Segment(C, F) → i
  8. Segment(C, G) → j
  9. Segment(G, E) → k
  10. Segment(B, G) → l
  11. Segment(F, A) → m
  12. Segment(F, E) → n
  13. Angle(B, O, A) → α
  14. Vector(O, O + v ⊗ u) → a
  15. Segment(O, H) → p
  16. OrthogonalLine(C, p, space) → q
  17. Point(q) → I
  18. Vector(O, I) → b
  19. Segment(C, I) → r
  20. Midpoint(O, I) → J
  21. Midpoint(O, H) → K
  22. Segment(O, B) → s
  23. OrthogonalLine(A, s, space) → t
  24. Intersect(s, t) → L
  25. Segment(A, L) → c
  26. Angle(O, L, A) → β
  27. Midpoint(O, A) → M
  28. Midpoint(O, B) → N
  29. Midpoint(O, C) → P