集合中分数的估计

几何画板及绘图内容加载中，请稍等……

2019-01-01 13:50

①本范例演示了如何在集合中估计分数，通过动态演示和交互操作直观展示概率分布；②涉及的核心数学概念包括分数、概率、几何分布和坐标几何；③作图要点提炼自 GeoGebra 命令：使用 Sequence 创建序列，Mod 进行模运算，Flatten 和 Shuffle 进行数组处理，Translate 进行平移变换，涉及对象如 d, n, move, c, r, q, c1, c2, grid, s, mix, part, remix, part2, a, mix', text1, text2, b, e；④适合初中及以上学段，用于概率统计和解析几何的教学演示与探索。

GeoGebra 命令及参数

Sequence(RandomPointIn[(0 * k), 10, (0 * k), 1], k, 1, d) → move, {(1.4635851498786423, 0.011928271083743835), (8.37990030842024, 0.46131720687058886), (4.977117227862018, 0.713686411412778), (5.555035769131406, 0.8846976659715752), (4.585136885245239, 0.30189919688054545), (8.203220801485486, 0.480488811152639), (3.3748616986688127, 0.904360572889298), (2.663669672978507, 0.955483057545491), (8.71399433316061, 0.7418840054485261), (4.05384379692456, 0.7629923865943025), (8.63043223545717, 0.3208158863614753), (9.609914746545268, 0.3364079723629453), (5.404500245350561, 0.7633054367066124), (8.63428388093347, 0.10309422313210437), (0.787771920196525, 0.6229870441180456), (4.7142197027874655, 0.751273734446459), (9.762539295496346, 0.7837315244371649), (8.375676191227676, 0.47255880413123474), (2.255994865031404, 0.28912254871331267), (0.8363537511326979, 0.15278668344115753), (4.723188260177733, 0.20031425673917103), (2.022066543847252, 0.7338138944861441), (6.0128182081298185, 0.8299266184736429), (8.510477319158339, 0.21892651242528005), (4.429926644503549, 0.9496345719884937), (9.566263289874716, 0.04452224176231956), (5.409552803332725, 0.8191072385212087), (1.931775435504699, 0.7907209542662579), (1.715411552225824, 0.13395357854646284), (6.5372523176757955, 0.45355931668453664), (0.5776604267141661, 0.24033052867833327), (2.7946535505060046, 0.7514266451590095), (4.68381344757627, 0.21387003546971695), (8.639173039994803, 0.18839726433493964), (6.436869676942455, 0.6505812866914072), (6.982495571021752, 0.8471163814132888), (7.394714522458622, 0.2673840718695486), (1.7418591657006854, 0.13389528212778845), (7.304857647493992, 0.6599299526435363), (9.108985227055536, 0.9486723895104774), (9.648571531641991, 0.815367122569016), (2.2229400093528238, 0.002496119087066706), (3.108491335749405, 0.22770552516934095), (9.9109887585046, 0.25518610861871804), (0.8737387001126906, 0.7134381918165272), (2.6615053933246458, 0.6958288528891445), (2.1966336318494264, 0.27507513727706734), (1.4930010827084605, 0.9387640310809768)}
Mod(d, c) → q
Sequence(Sequence[(i, j), j, 0, c - 1], i, 0, r - 1) → c1, {{(0, 0), (0, 1), (0, 2), (0, 3)}, {(1, 0), (1, 1), (1, 2), (1, 3)}, {(2, 0), (2, 1), (2, 2), (2, 3)}, {(3, 0), (3, 1), (3, 2), (3, 3)}, {(4, 0), (4, 1), (4, 2), (4, 3)}, {(5, 0), (5, 1), (5, 2), (5, 3)}, {(6, 0), (6, 1), (6, 2), (6, 3)}, {(7, 0), (7, 1), (7, 2), (7, 3)}, {(8, 0), (8, 1), (8, 2), (8, 3)}, {(9, 0), (9, 1), (9, 2), (9, 3)}, {(10, 0), (10, 1), (10, 2), (10, 3)}, {(11, 0), (11, 1), (11, 2), (11, 3)}}
Sequence((r, j), j, 0, q - 1) → c2
Flatten(Join[{c1, c2}]) → grid
Sequence(Circle[Element[grid, k] + (s * Element[move, k]), 0.2], k, 1, d) → mix
Sequence(Element[mix, k], k, 1, n) → part
Shuffle(mix) → remix, {(x - 10.71399433316061)² + (y - 0.7418840054485261)² = 0.04000000000000001, (x - 12.222940009352824)² + (y - 1.0024961190870667)² = 0.04000000000000001, (x - 7.7142197027874655)² + (y - 3.751273734446459)² = 0.04000000000000001, (x - 13.537252317675796)² + (y - 1.4535593166845366)² = 0.04000000000000001, (x - 7.022066543847252)² + (y - 1.733813894486144)² = 0.04000000000000001, (x - 16.39471452245862)² + (y - 0.2673840718695486)² = 0.04000000000000001, (x - 16.304857647493993)² + (y - 2.6599299526435365)² = 0.04000000000000001, (x - 13.762539295496346)² + (y - 0.7837315244371649)² = 0.04000000000000001, (x - 3.787771920196525)² + (y - 2.6229870441180454)² = 0.04000000000000001, (x - 4.836353751132698)² + (y - 3.1527866834411578)² = 0.04000000000000001, (x - 7.931775435504699)² + (y - 3.790720954266258)² = 0.04000000000000001, (x - 5.585136885245239)² + (y - 0.30189919688054545)² = 0.04000000000000001, (x - 9.794653550506006)² + (y - 3.7514266451590093)² = 0.04000000000000001, (x - 11.609914746545268)² + (y - 3.336407972362945)² = 0.04000000000000001, (x - 11.409552803332726)² + (y - 2.819107238521209)² = 0.04000000000000001, (x - 10.741859165700685)² + (y - 1.1338952821277886)² = 0.04000000000000001, (x - 13.196633631849426)² + (y - 2.2750751372770672)² = 0.04000000000000001, (x - 6.05384379692456)² + (y - 1.7629923865943025)² = 0.04000000000000001, (x - 19.64857153164199)² + (y - 0.815367122569016)² = 0.04000000000000001, (x - 11.012818208129818)² + (y - 2.829926618473643)² = 0.04000000000000001, (x - 9.203220801485486)² + (y - 1.480488811152639)² = 0.04000000000000001, (x - 7.577660426714166)² + (y - 2.2403305286783333)² = 0.04000000000000001, (x - 12.68381344757627)² + (y - 0.21387003546971695)² = 0.04000000000000001, (x - 8.715411552225824)² + (y - 0.13395357854646284)² = 0.04000000000000001, (x - 13.510477319158339)² + (y - 3.21892651242528)² = 0.04000000000000001, (x - 1.4635851498786423)² + (y - 0.011928271083743835)² = 0.04000000000000001, (x - 11.87373870011269)² + (y - 0.7134381918165272)² = 0.04000000000000001, (x - 3.663669672978507)² + (y - 3.955483057545491)² = 0.04000000000000001, (x - 10.42992664450355)² + (y - 0.9496345719884937)² = 0.04000000000000001, (x - 13.661505393324646)² + (y - 1.6958288528891445)² = 0.04000000000000001, (x - 13.108491335749406)² + (y - 2.227705525169341)² = 0.04000000000000001, (x - 12.49300108270846)² + (y - 3.938764031080977)² = 0.04000000000000001, (x - 10.63043223545717)² + (y - 2.3208158863614754)² = 0.04000000000000001, (x - 15.566263289874716)² + (y - 1.0445222417623197)² = 0.04000000000000001, (x - 8.404500245350562)² + (y - 0.7633054367066124)² = 0.04000000000000001, (x - 16.6391730399948)² + (y - 1.1883972643349396)² = 0.04000000000000001, (x - 4.977117227862018)² + (y - 2.713686411412778)² = 0.04000000000000001, (x - 8.37990030842024)² + (y - 1.4613172068705889)² = 0.04000000000000001, (x - 4.374861698668813)² + (y - 2.9043605728892983)² = 0.04000000000000001, (x - 9.723188260177732)² + (y - 0.20031425673917103)² = 0.04000000000000001, (x - 11.63428388093347)² + (y - 1.1030942231321044)² = 0.04000000000000001, (x - 18.108985227055534)² + (y - 3.9486723895104774)² = 0.04000000000000001, (x - 12.375676191227676)² + (y - 1.4725588041312347)² = 0.04000000000000001, (x - 14.982495571021751)² + (y - 3.8471163814132887)² = 0.04000000000000001, (x - 6.255994865031404)² + (y - 2.289122548713313)² = 0.04000000000000001, (x - 5.555035769131406)² + (y - 3.8846976659715753)² = 0.04000000000000001, (x - 14.436869676942454)² + (y - 2.6505812866914074)² = 0.04000000000000001, (x - 19.9109887585046)² + (y - 3.255186108618718)² = 0.04000000000000001}
Sequence(Element[remix, k], k, 1, n) → part2
Translate(mix, (0, 0)) → mix'

AI 绘图提示语参考

在一个坐标网格中，随机生成多个点，并用小圆圈表示这些点。将这些点按照一定规则排列成多个行列，形成一个矩形阵列。对矩形阵列中的点进行随机打乱，并重新排列。最后，将这些打乱后的点用圆圈表示，展示出概率分布的视觉效果。

以上提示语为根据原始绘图命令整理而来，仅供参考。