Estimate Fraction in a Set

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2019-01-01 13:50

This example demonstrates how to estimate fractions within a set through dynamic visualization and interactive operations, intuitively showcasing probability distributions. Core math concepts include fractions, probability, geometric distribution, and coordinate geometry. Construction highlights involve GeoGebra commands like Sequence, Mod, Flatten, Shuffle, and Translate, utilizing objects such as d, n, move, c, r, q, c1, c2, grid, s, mix, part, remix, part2, a, mix', text1, text2, b, e. Suitable for middle school and above, ideal for teaching demonstrations and explorations in probability statistics and coordinate geometry.

GeoGebra Commands & Parameters

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 Drawing Prompt Reference

Generate multiple random points on a coordinate grid and represent them with small circles. Arrange these points into a rectangular grid following specific rules. Shuffle the points in the grid and rearrange them. Finally, represent the shuffled points with circles to visualize the probability distribution.

The prompt above was compiled from the original drawing commands and is for reference only.