质数与合数分类：用面积模型解释

GeoGebra 命令及参数

1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.25061870229798106, 0.7639633298111306, 0.5759326798502272, 0.07116121199711072, 0.05524626029503052, 0.54514788959775, 0.08114980591899756, 0.09711418160937234, 0.08458374435798507, 0.43715969773023733, 0.2641862150429725, 0.6486511144422494, 0.53636510127195, 0.8746945410542996, 0.9339611809377307, 0.7660321290713261, 0.16943556843599977, 0.6689837976121323, 0.5819980617906336, 0.11081777144278337, 0.08252403908338714, 0.0645473625299634, 0.31212512483621446, 0.32685118831804993, 0.835060326815393, 0.1551907008952659, 0.22562298402556413, 0.1366733226929351, 0.8466237511392755, 0.2925585291117241, 0.8801195181204912, 0.4541396644966763, 0.5437092031342309, 0.7560170822172259, 0.858725586024662, 0.6693100637576647, 0.04428428741775896, 0.7252827710090928, 0.6487863255777716, 0.8491733849229004, 0.7520851225806592, 0.9070497331504237, 0.7671915706313939, 0.17744639439390394, 0.9037610857680662, 0.7738895928320011, 0.5514435327901718, 0.5085515678923294, 0.9728281428055162, 0.48790611289251734, 0.8926246763670787, 0.29493117019873605, 0.9549274311013454, 0.9730240976232134, 0.3080386373836512, 0.3330953659216228, 0.699110591269102, 0.6783751019374447, 0.61761553709616, 0.16222970566922904, 0.6797850751249817, 0.48101498182318864, 0.16917943894781315, 0.9398024366131953, 0.3535530036749163, 0.399166630014062, 0.5233682690337501, 0.6914152852847948, 0.5544631584839599, 0.3473278137167213, 0.639377993267464, 0.6771309865381832, 0.600171553027478, 0.09191844020723362, 0.8777709033668971, 0.6136891282777126, 0.3001668938021745, 0.16066236069331125, 0.44634385098140955, 0.0813867077161227, 0.5955680313431114, 0.08060850565079597, 0.6994954176453377, 0.07595261207016857, 0.5480366309321103, 0.6885922180160133, 0.2006623651725586, 0.4494859857013675, 0.9530734497306246, 0.8040215598612613, 0.5112132850591693, 0.08045497295821602, 0.4403786080082283, 0.617145334780996, 0.6276941068679921, 0.2908691012737586, 0.6110558689302085, 0.5764179989390671, 0.26251270044331393, 0.169040060362689, 0.7782278547149054, 0.49622356436928766, 0.3410312983463396, 0.5988363990594632, 0.8041038727029921, 0.6410540371425001, 0.9806032324764897, 0.9610155476293443, 0.7927045587403418, 0.5142601965006058, 0.3543471188292484, 0.4290812704727637, 0.8732960084926661, 0.7987008356076402, 0.14439384700839375, 0.5811679617920957, 0.625124693750647, 0.7530132515152324, 0.005973991608310845, 0.16069310870658635, 0.5992677183927351, 0.8208118766514166, 0.7250302943932783, 0.0019470016662887822, 0.06832585842785371, 0.9408935751306519, 0.8980466260474085, 0.3624040167778762, 0.22928638725987482, 0.3344863255593481, 0.6234778721482982, 0.8913427353441967, 0.20916923554719444, 0.9307258314701337, 0.05954582762286968, 0.27435213868868985, 0.5070454925534953, 0.013877128593747365, 0.7632352533957474, 0.5954788145363233, 0.009678613261313624, 0.40534089415651314, 0.3200789895868173, 0.16313575613678005, 0.3113887704089031, 0.2301924078682643, 0.05376566532232459, 0.02244548123256056, 0.9017775619686206, 0.5218981242003192, 0.7887332572878809, 0.17543098395616838, 0.6476754194045379, 0.4899382453538913, 0.1377309679691297, 0.8413954377421138, 0.048085377010089775, 0.5533359090822304, 0.869837212349977, 0.4429468157895144, 0.22299727865890018, 0.2685516010641751, 0.5126149987223515, 0.3384264662273669, 0.6887330649735841, 0.6528490476479768, 0.014967134128002525, 0.50899090637839, 0.7539587140507303, 0.11407164208662904, 0.5048216221772267, 0.4382736991408761, 0.9216601239954294, 0.3347910970530575, 0.40803361925647436, 0.35441953955419914, 0.8032305106257182, 0.16299792508902222, 0.07183394663420284, 0.12833558157823813, 0.7213530639149479, 0.3329005982987541, 0.22778460933388486, 0.5982450871790287, 0.7485883353335836, 0.38798401138660743, 0.5655202870453071, 0.16905628681060017, 0.9184866895864489, 0.8942490531863384, 0.02956082146497501, 0.6856745777688921, 0.15564701652628612, 0.2145146842841958, 0.8971728119683426, 0.7121887661549767, 0.7804289825632611, 0.704809635615633, 0.48563929978032755, 0.06385276118547273}
2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
3. Corner(5) → layoutAppSize
4. Remove(Sequence[k, k, 2, 100], primeList) → compositeList
5. Element(compositeList, 1 + floor((currentRandomSeeds(2) * Length[compositeList]))) → numComposite
6. Element(primeList, 1 + floor((currentRandomSeeds(2) * Length[primeList]))) → numPrime
7. Element({1, numPrime, numPrime, numPrime, numComposite, numComposite, numComposite}, numberIndex) → number
8. KeepIf(number / A ≟ round(number / A), A, Sequence[number]) → allFactorsList
9. Element(allFactorsList, animate) → currentWidth
10. makeBox(boxStart, currentWidth / scaleFactor, currentHeight / scaleFactor) → currentBox
11. Text((("" * currentHeight) * ""), boxStart + (currentWidth / scaleFactor, ((-currentHeight)) / ((2 * scaleFactor))), true, true, 1, 0) → side1Label
12. Text((("" * currentWidth) * ""), boxStart + (currentWidth / ((2 * scaleFactor)), 0), true, true, 0, 1) → side2Label
13. If(numIsComposite, "composite", If[numIsPrime, "prime", "not prime or composite"]) → typeText
14. If(numIsNeither, noSliderText, sliderText) → explanationText
15. If(numIsComposite, textComposite, If[numIsPrime, textPrime, textNeither]) → textDefinition
16. Sequence(Segment[boxStart - ((0, currentHeight / scaleFactor) * k), boxStart + (currentWidth / scaleFactor, 0) - ((0, currentHeight / scaleFactor) * k)], k, 0, 1) → widthSegs
17. Sequence(Segment[boxStart + ((currentWidth / scaleFactor, 0) * k), boxStart - (0, currentHeight / scaleFactor) + ((currentWidth / scaleFactor, 0) * k)], k, 0, 1) → heightSegs
18. If(Defined[allFactorsList], Length[allFactorsList], 3) → lengthAnimate