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Explore Triangle Formation with Side Lengths

Explore Triangle Formation with Side Lengths
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2022-12-23 23:10
TriangleInequalityGeometric ConstructionSlider Animation
This example explores whether three given side lengths can form a triangle. Key mathematical concepts include the conditions for triangle formation. It utilizes GeoGebra commands such as RandomUniform, Take, Element, and more, suitable for middle school students.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create a visual demonstration exploring whether three random side lengths can form a triangle. Start with one side and draw two random length segments, then attempt to locate the possible position of the third side. Use animations to show angle changes and check the triangle inequality. The final image should depict a dynamic construction process of a triangle, highlighting key inequalities.
The prompt above was compiled from the original drawing commands and is for reference only.