用棱柱近似计算棱锥体积

GeoGebra 命令及参数

1. Line(A, (1, 0, 0)) → a
2. Line(A, (0, 1, 0)) → b
3. Line(A, (0, 0, 1)) → c
4. Point(a) → B
5. Point(b) → C
6. Polygon(A, B, D, C) → base, a_1, b_1, d, c_1
7. Midpoint(A, D) → M
8. Line(M, c) → e
9. Point(e) → E
10. Pyramid(base, E) → pyr, faceABE, faceBDE, faceCDE, faceACE, edgeAE, edgeBE, edgeDE, edgeCE
11. Distance(M, E) → height
12. Distance(A, B) → width
13. Distance(A, C) → length
14. Sequence((length / numSplits * n), n, numSplits, 1, -1) → prismLengths
15. Sequence((width / numSplits * n), n, numSplits, 1, -1) → prismWidths
16. Sequence((prismHeight * n), n, 0, numSplits - 1) → prismHeights
17. Sequence(M + Vector[(((-prismWidths(n))) / 2, ((-prismLengths(n))) / 2, prismHeights(n))], n, 1, numSplits) → PyramidCorners
18. Sequence(Polygon[PyramidCorners(n), PyramidCorners(n) + Vector[(prismWidths(n), 0, 0)], PyramidCorners(n) + Vector[(prismWidths(n), prismLengths(n), 0)], PyramidCorners(n) + Vector[(0, prismLengths(n), 0)]], n, 1, numSplits) → prismBases
19. Sequence(Prism[prismBases(n), prismHeight], n, 1, numSplits) → OuterPrisms
20. Prism(base, height) → BigPrism, F, edgeAF, edgeBG, edgeDH, edgeCI, edgeFG, edgeGH, edgeHI, edgeFI, G, H, I, faceABGF, faceBDHG, faceCDHI, faceACIF, faceFGHI
21. Sum(OuterPrisms) → outerSum
22. Sequence(Prism[prismBases(n), (-prismHeight)], n, 2, numSplits) → InnerPrisms
23. Sum(InnerPrisms) → InnerVolume
24. Mean({InnerVolume, outerSum}) → prismAverage