积极 AI Logo 积极 AI

使用量角器绘制角度

使用量角器绘制角度
几何画板及绘图内容加载中，请稍等……
2022-12-21 01:30
角几何作图滑块动画
本范例演示如何使用量角器绘制指定大小的角度。核心数学概念包括角度测量与圆周度数（360度）。作图要点涉及使用GeoGebra命令如RandomUniform、Polygon、Angle等构建动态角度图形。适合小学高年级学生或数学课堂练习，用于理解角度的基本概念和作图技巧。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.8137602474657514, 0.3062438103764016, 0.6097102239064658, 0.06286411336398408, 0.2988247754887157, 0.3979910338126235, 0.10430735447183934, 0.22455033143884204, 0.8157351166778034, 0.8574047699951022, 0.6085637154155399, 0.9109049314721442, 0.26441995462471524, 0.5632592226993015, 0.1641216362149642, 0.4401293735704895, 0.11072879987039164, 0.928268329278164, 0.7441964283312047, 0.6789444513016941, 0.44118411757316145, 0.6812690993114908, 0.8256946371135659, 0.7856319890161692, 0.17196618147330567, 0.3303699866569479, 0.21253405057437724, 0.10600388249598819, 0.16979689348411547, 0.2861822613785002, 0.360560746387816, 0.7355138985765768, 0.7127687323656955, 0.559243301815275, 0.3434330234841677, 0.018060937197297688, 0.3242340127570959, 0.6229176360143929, 0.19750416697003143, 0.5365543503327381, 0.952625047711478, 0.002427951648928313, 0.9820853840188972, 0.37202093122125685, 0.7845196790988612, 0.5422196502190998, 0.8195079122393081, 0.1369292899848916, 0.7573966104676414, 0.21760405229983737, 0.7171271165299068, 0.3044918310663479, 0.7323446309618534, 0.24255213863309294, 0.6508242912498573, 0.2589754818586227, 0.43549439173176424, 0.31362642500601123, 0.04666093599162182, 0.7825118885411194, 0.18013554963008388, 0.410341240318355, 0.6141277029154869, 0.9015437373840272, 0.19936275840777976, 0.27473183810173224, 0.880904502020125, 0.8108782134368809, 0.4016621240018666, 0.39759052527427907, 0.4552108583436939, 0.725339898362658, 0.5491060706979806, 0.655693131567394, 0.9776747421532369, 0.17822462360950372, 0.18976736295150717, 0.31339225893189515, 0.9001852739100294, 0.032151827717003444, 0.1325943145070234, 0.18319330809602055, 0.9644197189127663, 0.1914975433343327, 0.9543074284389776, 0.27335780192458387, 0.21764685184713856, 0.39636109191762775, 0.753883483189296, 0.9661931208960345, 0.2680083871985672, 0.03597795737447448, 0.2608866171300605, 0.19849080996821036, 0.735767781871102, 0.19463749189374815, 0.7392867218020394, 0.5755658396593714, 0.10098959539823986, 0.505498228506839, 0.18847368255916733, 0.8325266958415479, 0.5217753962176087, 0.377215119246303, 0.6879322064582051, 0.0007720831959965035, 0.22053121521557287, 0.3650018670830243, 0.701485118221244, 0.9542615241029143, 0.12877914522591474, 0.4216481314496633, 0.3411436170438701, 0.30884886485664, 0.18375008237875945, 0.5550950972497956, 0.9494219255483315, 0.858894206218004, 0.11240643648424072, 0.2974450187500107, 0.20247919802241368, 0.6784856581079791, 0.23064400941129534, 0.015738315782320638, 0.9646449339515825, 0.649905011837268, 0.9072084087855885, 0.7574794605575633, 0.007765258214203629, 0.8294612226979688, 0.14333664851556782, 0.8137259119751014, 0.436375469799075, 0.9404940794959553, 0.07029656830950089, 0.45957633013450344, 0.2519603034280163, 0.2252147142548106, 0.6178460453157782, 0.9061032305187183, 0.39650680293788537, 0.941103362911431, 0.9571712328854733, 0.5491714985813986, 0.3571852914052726, 0.5338242055430454, 0.05208809669862052, 0.6391686073538666, 0.040312422647207004, 0.04704524621032214, 0.6122025421038207, 0.8514433847097609, 0.1837564021073334, 0.2601664151350334, 0.691325569096488, 0.8202093268154741, 0.9526371543408872, 0.3777615666791719, 0.14372525204447423, 0.7788153074876507, 0.9435559972088063, 0.4095307348409308, 0.6997737650583599, 0.1466197177252994, 0.5676568959914017, 0.046736167730034285, 0.9112080502612911, 0.4872265212612964, 0.8325777413908454, 0.6904613442793492, 0.4545738116243559, 0.02454987531813154, 0.49779324375625444, 0.8485847723072109, 0.5894584548947781, 0.04207079128561589, 0.746981964981508, 0.6621004818035886, 0.1258442526649966, 0.3067335438312079, 0.17486843910331007, 0.8373451445289917, 0.4523240409268853, 0.5422005151598844, 0.05449692336593456, 0.6788066085331007, 0.5040223391374213, 0.416643417983654, 0.9440870618136158, 0.9274916027053689, 0.8158512566047948, 0.5078954025990042, 0.2605022466195847, 0.7023208076198433, 0.4732054265048332, 0.7736224055516332, 0.458930100312238, 0.4466965933629691, 0.4383623738933385, 0.8861935347347519}
  2. Polygon({(-4.5, -3.7), (4.5, -3.7), (4.5, 3.7), (-4.5, 3.7)}) → graphicArea
  3. Sequence(((2 * cos(ii)), (2 * sin(ii))), ii, 0°, 360°, 1°) → PointsRayMovable
  4. Point(PointsRayMovable) → EndPointRay2
  5. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  6. Sequence(((2 * cos(ii)), (2 * sin(ii))), ii, 5°, 360°, 2°) → PointsRayFixed
  7. Element(PointsRayFixed, randomNum2) → EndPointRay1
  8. IntersectPath(Ray[Center, EndPointRay1], graphicArea) → Ray1
  9. If(Defined[Slope[Ray1]], y ≥ (Slope[Ray1] * x), x ≥ 0) → reg1
  10. Min(Angle[Vector[EndPointRay1], Vector[(1, 0)]], Angle[Vector[(1, 0)], Vector[EndPointRay1]]) → rotAngleRightProt
  11. Sequence(10, 175, 1) → angles
  12. Element(angles, randomNum1) → randomAngle
  13. Dilate(EndPointRay1, r / 2) → IniCorrectArc
  14. Rotate(IniCorrectArc, (randomAngle° * If[RotateRight, 1, -1])) → EndCorrectArc
  15. Circle(ProtractorCenter_{1}, r) → ProtractorCircle_{1}
  16. Point(ProtractorCircle_{1}) → ProtractorLeft_{1}
  17. DynamicCoordinates(ProtractorLeft_{1}, x(ProtractorLeft_{1}), y(ProtractorLeft_{1})) → ProtractorLeftDyn_{1}
  18. Point(ProtractorCircle_{1}) → ProtractorRight_{1}
  19. DynamicCoordinates(ProtractorRight_{1}, x(ProtractorRight_{1}), y(ProtractorRight_{1})) → ProtractorRightDyn_{1}
  20. Arc(ProtractorCircle_{1}, ProtractorRightDyn_{1}, ProtractorLeftDyn_{1}) → c
  21. Intersect(c, LineBisector[ProtractorRightDyn_{1}, ProtractorLeftDyn_{1}]) → D, E
  22. If(x(D) ≥ 0 ∧ y(D) ≥ 0, If[standardSol, 1, 3], x(D) < 0 ∧ y(D) ≥ 0, If[standardSol, 2, 4], x(D) < 0 ∧ y(D) < 0, If[standardSol, 3, 1], If[standardSol, 4, 2]) → quadrantProtractorCenter
  23. Dilate(Dilate[EndPointRay1, r / 2], 1.02) → IniIncorrectArc
  24. Angle(Vector[EndPointRay1], Vector[EndPointRay2]) → angleToShow
  25. Textfield(input1) → InputBox1
  26. Corner(5) → layoutAppSize
  27. sectorPixels(A, B, C, haloPixels + 40, Corner[1], Corner[3], Corner[5]) → pulsingObject
  28. sectorPixels(A, B, C, 40, Corner[1], Corner[3], Corner[5]) → displayAngle
  29. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  30. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  31. IntersectPath(Ray[Center, EndPointRay2], graphicArea) → Ray2
  32. Translate((0, 0), v) → LabelPosAngleToShow
  33. If(quadrantProtractorCenter ≟ 4, If[altSol, 4, 2], quadrantProtractorCenter ≟ 2, If[altSol, 2, 4], quadrantProtractorCenter ≟ 3, If[altSol, 3, 1], If[altSol, 1, 3]) → quadrantLegend
  34. Element(LegendPositions, quadrantLegend) → Legend2
  35. Translate(Legend1, (0, -0.5)) → Legend3
  36. Translate(Legend2, (0, -0.5)) → Legend4
  37. Segment(Legend2, Legend1) → segmentLegendCorrect
  38. Segment(Legend4, Legend3) → segmentLegendIncorrect
  39. Text("\textsf{ Correct solution\\}", Legend1, true, true, If[2 ≤ quadrantLegend ≤ 3, -1, 1], 0) → legendCorrect
  40. Text("\textsf{ Your solution\\}", Legend3, true, true, If[2 ≤ quadrantLegend ≤ 3, -1, 1], 0) → legendIncorrect
  41. Sector(x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), IniCorrectArc, EndCorrectArc) → CorrectArc1
  42. Sector(x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), EndCorrectArc, IniCorrectArc) → CorrectArc2
  43. Dilate(Dilate[EndPointRay2, r / 2], 1.02) → EndIncorrectArc
  44. Arc(x^(2) + y^(2) = Distance[Center, IniIncorrectArc]^(2), IniIncorrectArc, EndIncorrectArc) → IncorrectArc1
  45. Arc(x^(2) + y^(2) = Distance[Center, IniIncorrectArc]^(2), EndIncorrectArc, IniIncorrectArc) → IncorrectArc2
  46. Segment(Center, EndIncorrectArc) → segmentCorrect
  47. Text((input1 * "°"), (x(Dilate[EndIncorrectArc, 1.1]), Max[y(Dilate[EndIncorrectArc, 1.1]), -3.55]), true, true, 0, 0) → labelPointIncorrect
  48. Rotate(IniCorrectArc, ((anim * randomAngle°) * If[RotateRight, 1, -1])) → IniCorrectArc'
  49. Arc(x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), IniCorrectArc, IniCorrectArc') → arcAnim1
  50. Arc(x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), IniCorrectArc', IniCorrectArc) → arcAnim2
  51. circlePixels(ProtractorLeftDyn_{1}, 5 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObjectLeft
  52. circlePixels(ProtractorRightDyn_{1}, 5 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObjectRight
  53. circlePixels(ProtractorCenter_{1}, 5 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObjectCenter
  54. Text("\alpha", LabelPosAngleToShow, true, true, 0, 0) → labelAngleToShow
  55. Mirror(IniIncorrectArc, Line[(0, 0), EndPointRay1]) → IniIncorrectArc'
  56. Mirror(EndIncorrectArc, Line[(0, 0), EndPointRay1]) → EndIncorrectArc'
  57. Mirror(EndIncorrectArc, Line[(0, 0), EndPointRay1]) → EndIncorrectArc'_{1}
  58. Mirror(IniIncorrectArc, Line[(0, 0), EndPointRay1]) → IniIncorrectArc'_{1}
  59. Mirror(IniCorrectArc, Line[(0, 0), EndPointRay1]) → IniCorrectArc'_{1}
  60. Mirror(EndCorrectArc, Line[(0, 0), EndPointRay1]) → EndCorrectArc'
  61. Mirror(EndCorrectArc, Line[(0, 0), EndPointRay1]) → EndCorrectArc'_{1}
  62. Mirror(IniCorrectArc, Line[(0, 0), EndPointRay1]) → IniCorrectArc'_{2}
  63. Min(Angle[Vector[EndPointRay1], Vector[(-1, 0)]], Angle[Vector[(-1, 0)], Vector[EndPointRay1]]) → rotAngleLeftProt
  64. Rotate(pic1, 180°) → pic1'
  65. Segment(Center, IniCorrectArc') → segAnim
  66. Sector(Mirror[x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), Line[(0, 0), EndPointRay1]], IniCorrectArc'_{1}, EndCorrectArc') → CorrectArc1'
  67. Sector(Mirror[x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), Line[(0, 0), EndPointRay1]], EndCorrectArc'_{1}, IniCorrectArc'_{2}) → CorrectArc2'
  68. circlePixels(EndPointRay2, 9 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObjectAngle

AI 绘图提示语参考

在坐标平面中画一个带量角器外观的动态角度示意：先给定圆心Center与一条半径为r的圆，并在圆上取两条可变射线的端点，形成一条圆弧刻度区。用从圆弧两端到圆心的平分线确定量角器刻度所在象限位置，生成量角器圆弧c及其中心位置标记。再用同一圆心画出两条射线对应的角度，并以圆心为顶点标注当前角度大小（带输入框让角度值可变）。同时呈现“正确解弧”和“你的解弧”两段圆弧：正确解弧由输入角绕中心旋转得到，另一路由另一端射线产生；用两段细线与文本分别标出正确与错误。
以上提示语为根据原始绘图命令整理而来，仅供参考。