卡瓦列里原理演示

GeoGebra 命令及参数

1. Polygon(A, B, C) → poly1, c, a_1, b
2. Prism(poly1, 3.245704115496874) → d, D, edgeCF, edgeDE, edgeEF, edgeDF, E, F, faceABED, faceBCFE, faceACFD, faceDEF, edgeAD, edgeBE
3. Height(d) → h
4. If(t < 0.5, 0, (2 * (t - 0.5))) → t2
5. If(t < 0.5, (2 * t), 1) → t1
6. Polygon(C', A', B') → poly2, b', c', a'
7. CurveCartesian(f(u) + x1, y1, u, u, 0, h) → e
8. CurveCartesian(f(u) + x2, y2, u, u, 0, h) → g
9. CurveCartesian(f(u) + x3, y3, u, u, 0, h) → i
10. Surface((u * (f(v) + x1)) + ((1 - u) * (f(v) + x2)), (u * y1) + ((1 - u) * y2), v, u, 0, 1, v, 0, h) → j
11. Surface((u * (f(v) + x1)) + ((1 - u) * (f(v) + x3)), (u * y1) + ((1 - u) * y3), v, u, 0, 1, v, 0, h) → a
12. Surface((u * (f(v) + x2)) + ((1 - u) * (f(v) + x3)), (u * y2) + ((1 - u) * y3), v, u, 0, 1, v, 0, h) → k
13. Segment(G, G + (0, 0, h)) → l
14. Point(l) → H
15. Polygon(I, J, K) → poly3, k_1, i_1, j_1
16. Polygon(L, M, N) → poly4, n, l_1, m
17. Polygon(O, P, Q) → poly5, q, o, p
18. Polygon((-7, -7, h'), (7, -7, h'), (7, 7, h'), (-7, 7, h')) → poly6, r, s, b_1, c_1
19. Segment(A, B) → d_1
20. Segment(B, C) → e_1
21. Segment(C, A) → f_1
22. Sequence(Prism[Polygon[(f((i * δ)) + x1, y1, (i * δ)), (f((i * δ)) + x2, y2, (i * δ)), (f((i * δ)) + x3, y3, (i * δ))], δ], i, 0, w - 1) → list2
23. Sequence(Prism[Polygon[(f((i * δ)) + x1, y1, (i * δ)), (f((i * δ)) + x2, y2, (i * δ)), (f((i * δ)) + x3, y3, (i * δ))], δ], i, 0, w - 1) → list2'
24. Sequence(Prism[Polygon[A + (0, 0, (i * δ)), B + (0, 0, (i * δ)), C + (0, 0, (i * δ))], δ], i, 0, w - 1) → list1
25. Sequence(Prism[Polygon[A + (0, 0, (i * δ)), B + (0, 0, (i * δ)), C + (0, 0, (i * δ))], δ], i, 0, w - 1) → list1'