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在网格上创建不同类型的角度

在网格上创建不同类型的角度
几何画板及绘图内容加载中，请稍等……
2023-01-25 06:33
角几何作图
本范例通过在网格上移动第三点来展示不同类型的角度。核心数学概念包括角度识别与绘制（锐角、直角、钝角和直角）。作图要点包括使用GeoGebra命令如RandomUniform、Polygon、Angle等来构造角度。适合小学四年级至五年级学生使用，用于几何作图练习。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.29175957441687134, 0.12397914842976555, 0.28082368892259707, 0.8167611566633118, 0.7369889489795545, 0.6350615464344525, 0.14795868621133645, 0.6013390059755165, 0.8984748280531879, 0.1743192606927562, 0.7122809603666932, 0.8467107274815218, 0.9898554724443788, 0.23011287684276735, 0.6775606859528955, 0.5792345019203615, 0.08534903299211545, 0.5405419436428717, 0.3632793160303772, 0.47554249956316436, 0.41849734145128614, 0.14141667973480704, 0.459911670815373, 0.3949562842525164, 0.6001571903028503, 0.8985209510726911, 0.30041024418098855, 0.5307449788473522, 0.35174575306570305, 0.28222164439108205, 0.354772508330246, 0.777553289524493, 0.36172921678828474, 0.14563381304694756, 0.050773076026189266, 0.508450239017891, 0.8212641776996717, 0.044142798598010555, 0.13108165163272878, 0.9096099393237453, 0.8887578241992986, 0.03411389031684126, 0.265063173670326, 0.37363323770692464, 0.5529086439345049, 0.02208675420406112, 0.802571137018419, 0.6939552630044665, 0.16952157025167006, 0.09265621175882711, 0.11699512376854974, 0.022656790695128673, 0.14906129322959352, 0.6135829472860902, 0.18571359695841017, 0.11230731854593226, 0.10951484280440422, 0.02045658900404131, 0.827927769232214, 0.2792168799104575, 0.1126799192338404, 0.9304508336287735, 0.12261724816368516, 0.6606579211067791, 0.5314771618366095, 0.24536421421574944, 0.22305854936954664, 0.6322427976896947, 0.46130517745375343, 0.7182324728306769, 0.4989863638071775, 0.23370198442946863, 0.4598140252744335, 0.49532681474471707, 0.10305425372988734, 0.0618069432502336, 0.016768010344952903, 0.30632036585088984, 0.9747640788531907, 0.7981164772882511, 0.9389013366296676, 0.4398084304744648, 0.942485431377163, 0.616599046751104, 0.6338392464958948, 0.7892101932159377, 0.9025750007221895, 0.9219935140410465, 0.9122658101512593, 0.7653595145526649, 0.2539313322025758, 0.7840193492237568, 0.09856361655149695, 0.9468079720253819, 0.03658468814682424, 0.9152323085637921, 0.7071332513059155, 0.32701884061073405, 0.31412304243844147, 0.5914454178626483, 0.24452059448603045, 0.5292216846599369, 0.9018930205066357, 0.07319460651664514, 0.19633717467370962, 0.11472698355255272, 0.5059917868721222, 0.034727545392398786, 0.652753783171657, 0.9689666981764928, 0.08207902944646525, 0.4134285686310568, 0.7370799004853473, 0.2714312036898786, 0.26798934444273736, 0.39746700731745777, 0.028611629031787475, 0.7710148281398529, 0.4800140601684482, 0.8527652552743974, 0.43353803868138907, 0.40706115462987214, 0.2795481766859554, 0.4521322954207649, 0.8662409413151704, 0.8986167420553928, 0.6245605465356946, 0.6695930611609611, 0.23780502542139823, 0.8300553553334229, 0.6490482820942213, 0.5715675939412672, 0.3889762146860606, 0.08032741600702517, 0.5032735550444536, 0.6536141250727574, 0.0411623922649936, 0.5856180016472641, 0.06815783740426413, 0.3069485799164093, 0.5013662822988968, 0.801164155262808, 0.2887224776918408, 0.4928881003392948, 0.7851724845852981, 0.3173857848137972, 0.1439149708026047, 0.9757400132734718, 0.4360807005907811, 0.45832712111090224, 0.2535497411290035, 0.10546720029864086, 0.15958419879564087, 0.3966843438941388, 0.5574178534541786, 0.300709762967467, 0.37643822645663966, 0.819411852559987, 0.5168839785114794, 0.00042788236073745486, 0.3915445655911259, 0.8510543957881244, 0.6454902256864773, 0.04855408142497964, 0.03279936760409595, 0.8585435407649729, 0.5022247158384929, 0.9506034905793722, 0.34810785942704775, 0.9612266165811734, 0.47918953685824667, 0.3441888694806333, 0.15856519710321504, 0.6633627882225864, 0.21441579053462312, 0.5368226671481743, 0.8515347295124007, 0.6032255613122159, 0.7005250291513155, 0.12426138263790786, 0.3890248333644126, 0.7932924409479495, 0.7408248269803608, 0.21095809613750194, 0.8743734234724253, 0.7097819688073551, 0.6262527009041239, 0.6709372167299589, 0.8937933856277245, 0.5270152478049485, 0.6393456400694676, 0.14259050052871586, 0.1488152522829246, 0.47273315596355764, 0.3151146198709464, 0.5045173852398305, 0.7310830243593471, 0.6645921491076847, 0.9633410906536767, 0.9415922714608314}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. If(countQuestion ≟ 0, 1, 1 + floor((currentRandomSeeds(2) * 3))) → orientationType
  4. Element({(4, 0), (0, 4), (3, 3)}, orientationType) → FixedB
  5. Element({(-4, 0), (0, -4), (-3, -3)}, orientationType) → FixedA
  6. UnitVector(FixedB - FixedA) → uAB
  7. UnitOrthogonalVector(uAB) → perpAB
  8. Polygon({FixedA + (0.3 * perpAB), FixedA - (0.3 * perpAB), FixedB - (0.3 * perpAB), FixedB + (0.3 * perpAB)}) → straightRegion
  9. Midpoint(FixedA, FixedB) → Anchor
  10. Distance(Anchor, FixedB) → circRadius
  11. Circle(Anchor, circRadius - 0.3) → circInner
  12. Remove(Sequence[A, A, 5, 355, 5], {180}) → rightDegrees
  13. RemoveUndefined(Flatten[Sequence[Sequence[If[Distance[(i, j), Anchor] > circRadius + 0.5, (i, j)], i, minX + 1, minX + boxWidth - 1, 0.2], j, minY + 1, minY + boxHeight - 1, 0.2]]) → acutePoints
  14. Point(acutePoints) → PAcute
  15. Point(Zip[Rotate[FixedA, K°, Anchor], K, rightDegrees]) → PRight
  16. Point(Sequence[FixedA + (K * UnitVector[FixedB - FixedA]), K, 1, Distance[FixedB, FixedA] - 1]) → PStraight
  17. RemoveUndefined(Flatten[Sequence[Sequence[If[IsInRegion[(i, j), circInner] ∧ (¬IsInRegion[(i, j), straightRegion]), (i, j)], i, -5, 5, 0.2], j, -5, 5, 0.2]]) → obtusePoints
  18. Point(obtusePoints) → PObtuse
  19. Polygon({(minX + 1, minY + 1), (minX + boxWidth - 1, minY + 1), (minX + boxWidth - 1, minY + boxHeight - 1), (minX + 1, minY + boxHeight - 1)}) → moveBox
  20. PointIn(moveBox) → PMove
  21. Circle(Anchor, Distance[Anchor, FixedB]) → circRight
  22. Element({isAcute, isObtuse, isRight, isStraight}, caseNum) → correct
  23. Corner(5) → layoutAppSize
  24. Element({"an acute", "an obtuse", "a right", "a straight"}, caseNum) → angleWord
  25. Element({PAcute, PObtuse, PRight, PStraight}, caseNum) → PSoln
  26. PolyLine({FixedA, PSoln, FixedB}) → solnSegments
  27. Angle(FixedA, PSoln, FixedB) → solnAngle
  28. circlePixels(PMove, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingCircle
  29. Semicircle(PStraight + uAB, PStraight - uAB) → straightDisplay

AI 绘图提示语参考

创建一个网格上的角度，固定点A和B位于坐标轴上，A在x轴正方向，B在y轴正方向。通过移动点P，画出不同类型的角：锐角、直角、钝角和直线角。首先画出固定点A和B，然后画出一个直角区域，接着画出一个以A和B为直径端点的圆，从中选取锐角点PAcute。接着画出一个以B为中心的圆，从中选取直角点PRight。再画出一个以A和B为端点的线段，从中选取钝角点PObtuse。最后，画出一个移动框，用于移动角度点P，确保P在直角区域内但不在直角线段上。
以上提示语为根据原始绘图命令整理而来，仅供参考。