用立方体堆叠组成棱柱：体积探索活动

GeoGebra 命令及参数

1. RandomUniform(0, 0.99, 200) → allRandoms, {0.08023138224494726, 0.9438455218086685, 0.1653973417035798, 0.2841900551969421, 0.16048343936616483, 0.3981410347904107, 0.02242700089334765, 0.39794661186928415, 0.9447765018726383, 0.45445037842473895, 0.5374780137398084, 0.24063369354404926, 0.42919581310757465, 0.14836504377652915, 0.34859782499192604, 0.8318572712286445, 0.35043908185631223, 0.25839731404196487, 0.935445348082948, 0.7816436981250213, 0.7309790434870537, 0.539902480265941, 0.31252465232034915, 0.13397871484175405, 0.06114385491671414, 0.05460997754733278, 0.7104220165388052, 0.8192469289597105, 0.8609771316555704, 0.4036429156568177, 0.37347021449868334, 0.8749110731546956, 0.0010978077230705708, 0.5044346266107246, 0.06283964536577213, 0.3692683620249161, 0.5440740411162699, 0.7579175321724735, 0.5055702830654887, 0.5970569556703279, 0.18605841798556333, 0.08176418579004208, 0.8225089423097579, 0.4380581898217002, 0.5026010575906049, 0.03830180723379218, 0.21150558401690422, 0.5306513378866774, 0.5726654543465726, 0.43200159740609423, 0.4065480073488705, 0.2815253413930917, 0.020915870619392585, 0.08115983680050103, 0.7187783944811484, 0.8404375244118856, 0.50032819263043, 0.04154303994836873, 0.49153619426679357, 0.11503241107736219, 0.7250959477818062, 0.8063608669103616, 0.32871037174709883, 0.5052944965561281, 0.637660304007496, 0.8169597631942978, 0.7037604808016569, 0.770206369379815, 0.8034882007695199, 0.4020969245883253, 0.8657793487256172, 0.3806197614648498, 0.6929548365900589, 0.9405591516835137, 0.34892183988261344, 0.9522197280770559, 0.7713570790106058, 0.24223182968780338, 0.8524120664985478, 0.3207726496660692, 0.2556911550839083, 0.0865039648837258, 0.760168562324849, 0.9185972631680894, 0.5503735400209612, 0.15411072224656966, 0.7818497887940516, 0.2963828493188978, 0.48356619362840575, 0.7591698862448504, 0.10082375058047006, 0.8581024293327506, 0.551186685502351, 0.5922604828084171, 0.5692045435310573, 0.8388286150868722, 0.6370422626287194, 0.6529207941707377, 0.42567423633506074, 0.3157585621357409, 0.8848206082538157, 0.8009099663869175, 0.19832263385242566, 0.37168947680361664, 0.5409034475418314, 0.8799816879511099, 0.5221882521884781, 0.3075593630644437, 0.006138511830296889, 0.11576033163343309, 0.9695729351312897, 0.10647827678639624, 0.4998129215568042, 0.7105888070763231, 0.7705284979954672, 0.11592341696327166, 0.28011621282681765, 0.8929349390913388, 0.051177026054281004, 0.6974567930073217, 0.3423632175069936, 0.20709660406280198, 0.968728662336072, 0.8044473918502922, 0.4891673016282403, 0.9105383698672008, 0.9841983383427373, 0.8378402121661767, 0.505611788330766, 0.7012213083657775, 0.03689964875945649, 0.01801270755925883, 0.09726210838331048, 0.9557544737892807, 0.6688076608825214, 0.3071945844813605, 0.3995940120595305, 0.2411009406611979, 0.8218334418778436, 0.5018000945344739, 0.7340827426669365, 0.09791309427308303, 0.7269419984216737, 0.3273323398410428, 0.42880574199132504, 0.1923510503807313, 0.7008713276468963, 0.5702672349057253, 0.5099562577004417, 0.8954549437759067, 0.3039740099654091, 0.27151044707158817, 0.4351476539177407, 0.8147962644400452, 0.4114039382165361, 0.34464351623875966, 0.7798082444741103, 0.5022247122485265, 0.8795094179596437, 0.9092357870161872, 0.44432363120784235, 0.5140572224633524, 0.4198701528597427, 0.4049972302339527, 0.67187895827429, 0.31602162430334774, 0.44492919295629735, 0.8564824760783206, 0.9351852257107005, 0.8446723889823481, 0.9216220229442591, 0.44042934265761385, 0.484444319839745, 0.7298375496353887, 0.1927940449969807, 0.8686260280942094, 0.0990145606734682, 0.7789347383487906, 0.03052311388241317, 0.7784489676245668, 0.6512836207347554, 0.2637120815694483, 0.5807283878359765, 0.17089875926551348, 0.6532377357648356, 0.6331227364541785, 0.8046471886135135, 0.022085019191956663, 0.05413669559992002, 0.7826345186200967, 0.5099005917598695, 0.9486712281274586, 0.4115609307510818, 0.6503054748503543, 0.3819445886736512, 0.09078864968161554, 0.6778921474576899, 0.953421979535975, 0.7357172295781941, 0.7373644324548688}
2. Take(allRandoms, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
3. Flatten(Sequence[Sequence[Sequence[(w, l, h), l, 1, 5], w, 1, 5], h, 1, 5]) → domainPoints
4. Corner(5) → Dims
5. CornerThreeD(-1, 11) → CurrentViewDirection
6. First(startH, height) → hts
7. First(startL, length) → lens
8. Flatten(Sequence[Sequence[lens(n) + hts(t), n, 1, Length[lens]], t, 1, Length[hts]]) → startRows
9. Flatten(Sequence[Sequence[startRows(n) + k, k, 0, width - 1], n, 1, Length[startRows]]) → pointInds
10. Polygon((0, 0, 1), (length, 0, 1), (length, width, 1), (0, width, 1)) → baseQuad, edgeBase9, edgeBase10, edgeBase11, edgeBase12
11. Prism(baseQuad, height) → basePrism, BasePrismH1, edgeBase1, edgeBase2, edgeBase3, edgeBase4, edgeBase5, edgeBase7, edgeBase8, edgeBase6, BasePrismH2, BasePrismH3, BasePrismH4, baseFace1, baseFace3, baseFace4, baseFace2, baseFaceTop
12. Zip(domainPoints(p), p, pointInds) → startPositions
13. Sequence(Zip[Polygon[{n + (-1, -1, k), n + (0, -1, k), n + (0, 0, k), n + (-1, 0, k)}], n, First[startPositions, countBlocks]], k, 0, 1) → blockTopBottom
14. Sequence(Zip[Polygon[{n + (-1, k, 0), n + (0, k, 0), n + (0, k, 1), n + (-1, k, 1)}], n, First[startPositions, countBlocks]], k, -1, 0) → blockFrontBack
15. Sequence(Zip[Polygon[{n + (k, -1, 0), n + (k, 0, 0), n + (k, 0, 1), n + (k, -1, 1)}], n, First[startPositions, countBlocks]], k, -1, 0) → blockLeftRight
16. Zip(Prism[Polygon[{n + (-1, -1, 0), n + (0, -1, 0), n, n + (-1, 0, 0)}], 1], n, First[startPositions, countBlocks]) → blockOutline
17. Zip(Prism[Polygon[{n + (-1, -1, 0), n + (0, -1, 0), n, n + (-1, 0, 0)}], 1], n, startPositions) → blockOutlineStart