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混合颜料比例

混合颜料比例
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2017-03-13 01:59
测试改名0立体几何
①本范例演示混合不同比例的颜料生成不同颜色混合效果的可视化；②涉及核心数学概念包括比例、直方图、不等边三角形、频率分布、圆锥、质心或重心；③作图要点提炼自构造摘要，使用了Segment、Conic、Sequence、Polygon、SelectedIndex、Midpoint、Circle、CircleSector等GeoGebra命令与对象；④适合高中阶段数学教学，用于理解比例、统计与几何作图结合的应用。

GeoGebra 命令及参数

  1. Segment(Can1PtMaster, Can1PtTopL) → Can1segL
  2. Segment(Can1PtBottomR, Can1PtTopR) → Can1segR
  3. Conic(Midpoint[Can1PtTopL, Can1PtTopR] + (0, -0.5), Can1PtTopR + (-0.04, 0), Midpoint[Can1PtTopL, Can1PtTopR] + (canWidth / 3, 0.5), Midpoint[Can1PtTopL, Can1PtTopR] + (((-canWidth)) / 3, 0.5), Can1PtTopL + (0.04, 0)) → can1lidConic
  4. Sequence(i, i, 0, cupsMax) → mix1cupsWhite
  5. Sequence(i, i, 0, cupsMax) → mix1cupsGreen
  6. Polygon(Can1PtMaster + (0, -0.006), Can1PtMaster + (canWidth, -0.006), Can1PtMaster + (canWidth, (canHeight * mix1cupsTotal / ((2 * cupsMax))) - 0.1), Can1PtMaster + (0, (canHeight * mix1cupsTotal / ((2 * cupsMax))) - 0.1)) → can1fillRectGreen, g, a, b, c
  7. Polygon(Can1PtMaster + (0, -0.013), Can1PtMaster + (canWidth, -0.013), Can1PtMaster + (canWidth, (canHeight * mix1cupsTotal / ((2 * cupsMax)))), Can1PtMaster + (0, (canHeight * mix1cupsTotal / ((2 * cupsMax))))) → can1fillRectWhite, d, e, f, q
  8. Polygon((-10, -2.02734), (99.12, -2.02734), (19.12, 97.97266), (-10, 17.97266)) → BackgroundYellow, l, m, n, p
  9. Polygon(Can1PtMaster + (-0.1, 0.048), Can1PtBottomR + (0.1, 0.048), Can1PtTopR, Can1PtTopL) → can1fillRectYellowBack, h, i, j, k
  10. Conic(Midpoint[Can1PtMaster, Can1PtBottomR] + (0, -0.5), Can1PtBottomR, Midpoint[Can1PtMaster, Can1PtBottomR] + (canWidth / 3, 0.5), Midpoint[Can1PtMaster, Can1PtBottomR] + (((-canWidth)) / 3, 0.5), Can1PtMaster) → can1bottomConic
  11. Polygon(A, B, C, D, E, F, G) → can1brushColorGreen, a_1, b_1, c_1, d_1, e_1, f_1, g_1
  12. Polygon(A, B, C, D, E, F, G) → can1brushColorWhite, a_2, b_2, c_2, d_2, e_2, f_2, g_2
  13. Conic(Midpoint[Can1PtMaster, Can1PtBottomR] + (0, -0.45), Can1PtBottomR + (0, 0.1), Midpoint[Can1PtMaster, Can1PtBottomR] + (canWidth / 3, 0.6), Midpoint[Can1PtMaster, Can1PtBottomR] + (((-canWidth)) / 3, 0.6), Can1PtMaster + (0, 0.1)) → can1bottomConicGreen
  14. Conic(Midpoint[Can1PtMaster, Can1PtBottomR] + (0, -0.49), Can1PtBottomR + (0, 0.05), Midpoint[Can1PtMaster, Can1PtBottomR] + (canWidth / 3, 0.6), Midpoint[Can1PtMaster, Can1PtBottomR] + (((-canWidth)) / 3, 0.6), Can1PtMaster + (0, 0.05)) → can1bottomConicWhite
  15. Polygon(Mix1visualsMasterPt + (0, tapeDiagramHeight + 0.1), Mix1visualsMasterPt + (If[SelectedElement[mix1cupsGreen] ≥ SelectedElement[mix1cupsWhite], tapeDiagRectModelWidth, (SelectedElement[mix1cupsGreen] * tapeDiagRectModelWidth / SelectedElement[mix1cupsWhite])], tapeDiagramHeight + 0.1), Mix1visualsMasterPt + (If[SelectedElement[mix1cupsGreen] ≥ SelectedElement[mix1cupsWhite], tapeDiagRectModelWidth, (SelectedElement[mix1cupsGreen] * tapeDiagRectModelWidth / SelectedElement[mix1cupsWhite])], (2 * tapeDiagramHeight)), Mix1visualsMasterPt + (0, (2 * tapeDiagramHeight))) → mix1tapeDiagGreenPoly, mix1tapeDiagGreenPolySeg_1, mix1tapeDiagGreenPolySeg_2, mix1tapeDiagGreenPolySeg_3, mix1tapeDiagGreenPolySeg
  16. Polygon(Mix1visualsMasterPt + (0, 0), Mix1visualsMasterPt + (If[SelectedElement[mix1cupsWhite] ≥ SelectedElement[mix1cupsGreen], tapeDiagRectModelWidth, (SelectedElement[mix1cupsWhite] * tapeDiagRectModelWidth / SelectedElement[mix1cupsGreen])], 0), Mix1visualsMasterPt + (If[SelectedElement[mix1cupsWhite] ≥ SelectedElement[mix1cupsGreen], tapeDiagRectModelWidth, (SelectedElement[mix1cupsWhite] * tapeDiagRectModelWidth / SelectedElement[mix1cupsGreen])], tapeDiagramHeight - 0.1), Mix1visualsMasterPt + (0, tapeDiagramHeight - 0.1)) → mix1tapeDiagWhitePoly, mix1tapeDiagWhitePolySeg_1, mix1tapeDiagWhitePolySeg_2, mix1tapeDiagWhitePolySeg_3, mix1tapeDiagWhitePolySeg
  17. Polygon(Mix1visualsMasterPt + (0, rectModelVerticalOffset), Mix1visualsMasterPt + (tapeDiagRectModelWidth, rectModelVerticalOffset), Mix1visualsMasterPt + (tapeDiagRectModelWidth, 3 + rectModelVerticalOffset), Mix1visualsMasterPt + (0, 3 + rectModelVerticalOffset)) → mix1rectAreaOutline, mix1rectAreaOutlineSeg_3, mix1rectAreaOutlineSeg, mix1rectAreaOutlineSeg_1, mix1rectAreaOutlineSeg_2
  18. SelectedIndex(mix1visualType) → mix1visualTypeSelected
  19. Polygon(Mix1visualsMasterPt + (0, rectModelVerticalOffset), Mix1visualsMasterPt + ((SelectedElement[mix1cupsGreen] * tapeDiagRectModelWidth / mix1cupsTotal), rectModelVerticalOffset), Mix1visualsMasterPt + ((SelectedElement[mix1cupsGreen] * tapeDiagRectModelWidth / mix1cupsTotal), 3 + rectModelVerticalOffset), Mix1visualsMasterPt + (0, 3 + rectModelVerticalOffset)) → mix1rectAreaGreenPoly, r, s, t, h_1
  20. Midpoint(Mix1visualsMasterPt, Mix1visualsMasterPt + (tapeDiagRectModelWidth, 3.8)) → Mix1circleModelCenter
  21. Circle(Mix1circleModelCenter, circleModelRadius) → mix1circleModelOutline
  22. Circle(Mix1circleModelCenter, circleModelRadius) → mix1circleModelGreenSector
  23. Sequence(Segment[Mix1circleModelCenter, Rotate[Mix1circleModelSectorRefPt, (i * (2 * π / mix1cupsTotal)), Mix1circleModelCenter]], i, 0, mix1cupsTotal - 1, 1) → mix1circleModelDividers
  24. CircleSector(Mix1circleModelCenter, Mix1circleModelSectorRefPt, Rotate[Mix1circleModelSectorRefPt, ((1.99999999999999 * π) * SelectedElement[mix1cupsWhite] / mix1cupsTotal), Mix1circleModelCenter]) → mix1circleModelWhiteSector
  25. Sequence(Segment[Mix1visualsMasterPt + (0 + i, 0), Mix1visualsMasterPt + (0 + i, tapeDiagramHeight - 0.1)], i, 0, If[SelectedElement[mix1cupsWhite] ≥ SelectedElement[mix1cupsGreen], tapeDiagRectModelWidth, (SelectedElement[mix1cupsWhite] * tapeDiagRectModelWidth / SelectedElement[mix1cupsGreen])], If[SelectedElement[mix1cupsWhite] ≥ SelectedElement[mix1cupsGreen], tapeDiagRectModelWidth / SelectedElement[mix1cupsWhite], tapeDiagRectModelWidth / SelectedElement[mix1cupsGreen]]) → mix1tapeDiagramWhiteDividers
  26. Sequence(Segment[Mix1visualsMasterPt + (0 + i, tapeDiagramHeight + 0.1), Mix1visualsMasterPt + (0 + i, (2 * tapeDiagramHeight))], i, 0, If[SelectedElement[mix1cupsGreen] ≥ SelectedElement[mix1cupsWhite], tapeDiagRectModelWidth, (SelectedElement[mix1cupsGreen] * tapeDiagRectModelWidth / SelectedElement[mix1cupsWhite])], If[SelectedElement[mix1cupsGreen] ≥ SelectedElement[mix1cupsWhite], tapeDiagRectModelWidth / SelectedElement[mix1cupsGreen], tapeDiagRectModelWidth / SelectedElement[mix1cupsWhite]]) → mix1tapeDiagramGreenDividers
  27. Sequence(Polygon[Mix1cupsGreenImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i, i - cupsMax / 2]), If[i < cupsMax / 2, 0, (-cupImagesHeight) - 0.1]), Mix1cupsGreenImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i + 0.5, i - cupsMax / 2 + 0.5]), If[i < cupsMax / 2, 0, (-cupImagesHeight) - 0.1]), Mix1cupsGreenImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i + 0.59, i - cupsMax / 2 + 0.59]), If[i < cupsMax / 2, cupImagesHeight, -0.1]), Mix1cupsGreenImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i - 0.09, i - cupsMax / 2 - 0.09]), If[i < cupsMax / 2, cupImagesHeight, -0.1])], i, 0, SelectedElement[mix1cupsGreen] - 1, 1) → mix1cupImagesGreen
  28. Sequence(Polygon[Mix1cupsWhiteImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i, i - cupsMax / 2]), If[i < cupsMax / 2, 0, (-cupImagesHeight) - 0.1]), Mix1cupsWhiteImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i + 0.5, i - cupsMax / 2 + 0.5]), If[i < cupsMax / 2, 0, (-cupImagesHeight) - 0.1]), Mix1cupsWhiteImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i + 0.59, i - cupsMax / 2 + 0.59]), If[i < cupsMax / 2, cupImagesHeight, -0.1]), Mix1cupsWhiteImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i - 0.09, i - cupsMax / 2 - 0.09]), If[i < cupsMax / 2, cupImagesHeight, -0.1])], i, 0, SelectedElement[mix1cupsWhite] - 1, 1) → mix1cupImagesWhiteFill
  29. Sequence(Polygon[Mix1cupsWhiteImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i, i - cupsMax / 2]), If[i < cupsMax / 2, 0, (-cupImagesHeight) - 0.1]), Mix1cupsWhiteImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i + 0.5, i - cupsMax / 2 + 0.5]), If[i < cupsMax / 2, 0, (-cupImagesHeight) - 0.1]), Mix1cupsWhiteImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i + 0.59, i - cupsMax / 2 + 0.59]), If[i < cupsMax / 2, cupImagesHeight, -0.1]), Mix1cupsWhiteImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i - 0.09, i - cupsMax / 2 - 0.09]), If[i < cupsMax / 2, cupImagesHeight, -0.1])], i, 0, SelectedElement[mix1cupsWhite] - 1, 1) → mix1cupImagesWhiteOutline
  30. Sequence(Polygon[Mix1cupsGreenImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i, i - cupsMax / 2]), If[i < cupsMax / 2, 0, (-cupImagesHeight) - 0.1]), Mix1cupsGreenImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i + 0.5, i - cupsMax / 2 + 0.5]), If[i < cupsMax / 2, 0, (-cupImagesHeight) - 0.1]), Mix1cupsGreenImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i + 0.59, i - cupsMax / 2 + 0.59]), If[i < cupsMax / 2, cupImagesHeight, -0.1]), Mix1cupsGreenImagesMasterPt + ((cupImagesSpacing * If[i < cupsMax / 2, i - 0.09, i - cupsMax / 2 - 0.09]), If[i < cupsMax / 2, cupImagesHeight, -0.1])], i, 0, SelectedElement[mix1cupsGreen] - 1, 1) → mix1cupImagesGreenOutline
  31. Sequence(Segment[Mix1visualsMasterPt + (i, rectModelVerticalOffset), Mix1visualsMasterPt + (i, 3 + rectModelVerticalOffset)], i, 0, tapeDiagRectModelWidth, tapeDiagRectModelWidth / mix1cupsTotal) → mix1rectAreaDividers
  32. Conic(Can1PtMaster + (0, -0.1) + (canWidth / 2, (canHeight * mix1cupsTotal / ((2 * cupsMax))) - 0.5), Can1PtMaster + (0, -0.1) + (canWidth - 0.02, (canHeight * mix1cupsTotal / ((2 * cupsMax)))), Can1PtMaster + (0, -0.1) + ((5 / 6 * canWidth), (canHeight * mix1cupsTotal / ((2 * cupsMax))) + 0.5), Can1PtMaster + (0, -0.1) + (canWidth / 6, (canHeight * mix1cupsTotal / ((2 * cupsMax))) + 0.5), Can1PtMaster + (0, -0.1) + (0.02, (canHeight * mix1cupsTotal / ((2 * cupsMax))))) → can1fillTopConicGreen
  33. Conic(Can1PtMaster + (0, -0.1) + (canWidth / 2, (canHeight * mix1cupsTotal / ((2 * cupsMax))) - 0.5), Can1PtMaster + (0, -0.1) + (canWidth - 0.02, (canHeight * mix1cupsTotal / ((2 * cupsMax)))), Can1PtMaster + (0, -0.1) + ((5 / 6 * canWidth), (canHeight * mix1cupsTotal / ((2 * cupsMax))) + 0.5), Can1PtMaster + (0, -0.1) + (canWidth / 6, (canHeight * mix1cupsTotal / ((2 * cupsMax))) + 0.5), Can1PtMaster + (0, -0.1) + (0.02, (canHeight * mix1cupsTotal / ((2 * cupsMax))))) → can1fillTopConicWhite
  34. Conic(Can1PtMaster + (0, -0.1) + (canWidth / 2, (canHeight * mix1cupsTotal / ((2 * cupsMax))) - 0.5), Can1PtMaster + (0, -0.1) + (canWidth - 0.02, (canHeight * mix1cupsTotal / ((2 * cupsMax)))), Can1PtMaster + (0, -0.1) + ((5 / 6 * canWidth), (canHeight * mix1cupsTotal / ((2 * cupsMax))) + 0.5), Can1PtMaster + (0, -0.1) + (canWidth / 6, (canHeight * mix1cupsTotal / ((2 * cupsMax))) + 0.5), Can1PtMaster + (0, -0.1) + (0.02, (canHeight * mix1cupsTotal / ((2 * cupsMax))))) → can1fillTopConicWhiteOutline