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探究三边能否构成三角形

探究三边能否构成三角形
几何画板及绘图内容加载中，请稍等……
2022-12-23 23:10
测试改名0不等式几何作图滑块动画
本范例通过给定不同长度的三边，探究能否构成三角形。涉及的核心数学概念包括三角形的构成条件。使用了GeoGebra中的RandomUniform、Take、Element等命令，适合初中生学习。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.35877086344219866, 0.42790884712963645, 0.06908008442597964, 0.7571732211122267, 0.5245070453669225, 0.6659834054215008, 0.9735562641620056, 0.47967133168876597, 0.05304567243315124, 0.7221778552082508, 0.383672675102665, 0.29044424886217457, 0.9415098275939133, 0.08325142156460057, 0.7176389869297178, 0.6651532937765215, 0.3222528798637968, 0.3179498694456159, 0.3162565887313476, 0.9260349344820641, 0.6579115940305166, 0.32151576361489165, 0.41570032738607304, 0.33366513149502736, 0.21626233322078584, 0.2958022293997048, 0.7739694853135074, 0.7567219358047438, 0.22106685643188104, 0.20126210168570746, 0.9750015393744521, 0.24331835177604255, 0.8768807650597965, 0.7897304614613516, 0.03732352033871227, 0.4049666424838418, 0.8472727596140849, 0.9767527727309674, 0.33168392134133673, 0.3639138125301503, 0.37706459767679207, 0.5692322773584227, 0.6943642937930006, 0.24645300290120864, 0.45005144244896295, 0.8483790993977652, 0.07981253359588088, 0.718867873805423, 0.05419950883845191, 0.6793403765685267, 0.4078711695005922, 0.4589080033759256, 0.9865420936605661, 0.7974741700221882, 0.36719208153394084, 0.3441204142639083, 0.01990775237197498, 0.2470021762537071, 0.9374349447689879, 0.728978020099304, 0.47321360955457104, 0.570734219977972, 0.27854031229820464, 0.7255481270223234, 0.3863439655637949, 0.5297050828395301, 0.7857486474654523, 0.6574347842335724, 0.6896090152865377, 0.518897304105178, 0.38410533818887105, 0.523906291309138, 0.24644077433861877, 0.8597456575103329, 0.44594766915325684, 0.17048415847044837, 0.45633237239846075, 0.49182761433467065, 0.4193124777069888, 0.32382304619864144, 0.5530647880229107, 0.08504107583687495, 0.9643349892874569, 0.4824512810854264, 0.060989031810447146, 0.10965382981651126, 0.1585267546301373, 0.7508688244207137, 0.45954406600591047, 0.5248816247401197, 0.5403273671752103, 0.4626155929551924, 0.08329065572407138, 0.02711002331776743, 0.903517007430226, 0.3182250536437202, 0.6915280537864247, 0.8165220395453359, 0.07295878040172402, 0.3364688536334343, 0.8880352554100327, 0.09572745956533217, 0.30470734374897873, 0.6019752036655122, 0.047640724042964815, 0.90601094803155, 0.10077650698197356, 0.1491700676365741, 0.39217371996918854, 0.4760258756839239, 0.2108020618906005, 0.8515417042000422, 0.08388811936948697, 0.11415602507652513, 0.5394662995890033, 0.466470360650014, 0.8296735329801519, 0.11935252777233696, 0.9598700027055126, 0.02929215837009695, 0.614281083946835, 0.14602399940902275, 0.019042351538017272, 0.16588135062661358, 0.8353907169341137, 0.1565174536226945, 0.32247401863624053, 0.7608383397132767, 0.5876340341166224, 0.4098734479918889, 0.7799378906628622, 0.278360591941445, 0.8966608720197987, 0.17787358230128808, 0.7049318699748545, 0.02505143469210218, 0.3380009460596218, 0.9789191728722086, 0.5848326982261696, 0.31828739416407725, 0.9688201352530459, 0.3869898086723899, 0.748294124461926, 0.17031670134415983, 0.46370931465642423, 0.0668261919110386, 0.8705529538113453, 0.5170024682191661, 0.9783674059587824, 0.0875658627376408, 0.17612517112238257, 0.8310514855080278, 0.7574530330741177, 0.8553323816394328, 0.22188000575674313, 0.8526848268898694, 0.33497824316362385, 0.0407368779662324, 0.4616734481695312, 0.8760094185853813, 0.8774052643279641, 0.18989751598635354, 0.906603298430486, 0.8868394440673905, 0.7410817440264904, 0.6374167761554022, 0.9625163541541276, 0.16739487842043532, 0.7368119961992048, 0.21677758422761018, 0.028654019025900902, 0.7051690775729441, 0.0052112440538857165, 0.9478282328510403, 0.3182663626260252, 0.06731051512890365, 0.8170275499119978, 0.1324228916371247, 0.46365495333864665, 0.5381036050578774, 0.4528397425431169, 0.9878681712182046, 0.284423787357055, 0.8855617685600597, 0.8764527265745353, 0.7035979189324658, 0.758722751777838, 0.8437605064665559, 0.3359108423675769, 0.879456983579756, 0.5129624012214563, 0.65034167342109, 0.7253364708553844, 0.01412190868866036, 0.6458584269956089, 0.9236097614309297, 0.2497767197615753, 0.7295198015465562, 0.7577338647316681, 0.8208191780202188}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Element({-3, -2.5, -2, -1.5, -1, 0, 1, 2}, 1 + floor((currentRandomSeeds(4) * 8))) → randomSide3Start
  4. Point(Circle[PointStart, randomSide1]) → inputPoint
  5. Angle(Vector[PointStart, inputPoint]) → angle1A
  6. Circle(PointSide1, randomSide2) → circleRight
  7. Circle(PointStart, randomSide1) → circleLeft
  8. ClosestPoint(thirdPointPossibilities, inputPoint) → PointInputClosest
  9. If(canBeTriangle, Angle[inputPoint, PointStart, PointInputClosest], 0.1°) → angle1AnimationRange
  10. Angle(Vector[PointSide1, PointInputClosest]) → angle2B
  11. Point(Circle[PointSide1, randomSide2]) → PointSide2
  12. Angle(PointSide2, PointSide1, PointInputClosest) → angle2Acute
  13. If(canBeTriangle, angle2Acute, 2°) → angle2AnimationRange
  14. Angle(Vector[PointSide1, PointSide2]) → angle2A
  15. Rotate(PointSide2, (If[boolAngle2Clockwise, -1, 1] * easeIn2a(angleSlider)), PointSide1) → PointAnimation2
  16. If(anTime < 1, anTime, 1) → anTime_1
  17. Rotate(PointSide2, easeIn2(anTime_1), PointSide1) → PointAnimation2NTa
  18. If(anTime < 1 ∨ isLine, 0, anTime - 1) → anTime_2
  19. Rotate(inputPoint, (-easeIn1(anTime_1)), PointStart) → PointAnimation1NTa
  20. Angle(Vector[PointStart, PointInputClosest]) → angle1B
  21. Rotate(inputPoint, (-easeIn1a(angleSlider)), PointStart) → PointAnimation1b
  22. Rotate(inputPoint, easeIn1a(angleSlider), PointStart) → PointAnimation1a
  23. If(boolAngle1Clockwise, PointAnimation1b, PointAnimation1a) → PointAnimation1
  24. Distance(PointSide2, inputPoint) → connectDistance
  25. Sequence(Corner[textSide2, n], n, 1, 4) → corners2
  26. Sequence(Corner[textSide1, n], n, 1, 4) → corners1
  27. Segment(PointStart, If[anTime ≟ 0, PointAnimation1, anTime_2 ≟ 0, PointAnimation1NTa, PointAnimation1NTb]) → segmentSide3
  28. Sequence(Corner[textSide3, n], n, 1, 4) → corners3
  29. Polygon(Zip[PixelsToPoint[(xMin, yMin), (xMax, yMax), (800, 500), A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, 500 - pixelsBottom), (800, 500) - (pixelsRight, pixelsBottom), (800 - pixelsRight, pixelsTop)}]) → borderBox
  30. Segment(PointStart, PointSide1) → segmentSide1
  31. Segment(PointSide1, If[anTime ≟ 0, PointAnimation2, anTime_2 ≟ 0, PointAnimation2NTa, PointAnimation2NTb]) → segmentSide2
  32. Point(Circle[PointStart, randomSide1]) → PointSide3Start
  33. Segment(PointStart, PointSide3Start) → segmentSide3Start
  34. Polygon({PointStart, PointSide1, PointTriangle}) → connectingTriangle
  35. Intersect(segmentSide2, segmentSide3) → PointInt
  36. Sequence({abs(x(textCorners(n, 1)) - x(textCorners(n, 3))), abs(y(textCorners(n, 1)) - y(textCorners(n, 3)))}, n, 1, Length[textCorners]) → widthsHeights
  37. Angle(PointStart, PointSide1, PointAnimation2) → angleSide2
  38. Angle(segmentSide1, segmentSide3) → angleSide3
  39. If(segmentSide1 + segmentSide2 < segmentSide3, "<", segmentSide1 + segmentSide2 > segmentSide3, ">", "=") → textInequality1
  40. If(segmentSide3 + segmentSide1 < segmentSide2, "<", segmentSide3 + segmentSide1 > segmentSide2, ">", "=") → textInequality2
  41. If(segmentSide3 + segmentSide2 < segmentSide1, "<", segmentSide3 + segmentSide2 > segmentSide1, ">", "=") → textInequality3
  42. ClosestPoint(thirdPointPossibilities, PointSide2) → PointSide2Closest
  43. Polygon({PointStart, PointSide1, PointAnimation2}) → incorrectTriangle

AI 绘图提示语参考

绘制一个探索三角形形成的演示图。首先生成三组随机长度，并展示它们能否构成三角形。接着，以其中一组为起始边，绘制两条随机长度的线段，并尝试找到第三条边的可能位置。通过动画展示角度的变化，判断是否满足三角形不等式。最终呈现一个动态的三角形构造过程，并标注关键不等式。
以上提示语为根据原始绘图命令整理而来，仅供参考。