Christmas card 7:几何作图与三角函数应用
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所属专题
STEAM like Leonardo
该范例演示了如何利用GeoGebra进行几何作图,并结合三角函数与不等式概念。核心数学概念包括三角形性质、三角函数图像及不等式求解。作图要点涉及使用Segment、Sequence等命令构建图形,并应用Prism、Nierówności等标签。适合高中生或大学低年级学生用于学习几何与三角函数的基础知识,以及理解几何作图在数学中的应用。
GeoGebra 命令及参数
Segment(A, B) → fSegment(A, C) → gSequence(A + (i / n * (B - A)), i, 1, n) → l1, {(-1.924, -4.1882248672916385), (-1.928, -3.6890659481993784), (-1.932, -3.1899070291071183), (-1.936, -2.6907481100148587), (-1.94, -2.191589190922599), (-1.944, -1.6924302718303386), (-1.948, -1.193271352738079), (-1.952, -0.6941124336458193), (-1.956, -0.1949535145535597), (-1.96, 0.30420540453869993), (-1.964, 0.8033643236309596), (-1.968, 1.302523242723221), (-1.972, 1.8016821618154806), (-1.976, 2.30084108090774), (-1.98, 2.8)}Sequence(A + (i / n * (C - A)), i, 1, n) → l2, {(-1.3853333333333333, -4.6833837863838985), (-0.8506666666666667, -4.679383786383898), (-0.31599999999999984, -4.6753837863838985), (0.21866666666666656, -4.671383786383898), (0.753333333333333, -4.6673837863838985), (1.2880000000000003, -4.663383786383898), (1.8226666666666667, -4.6593837863838985), (2.357333333333333, -4.655383786383898), (2.8919999999999995, -4.6513837863838985), (3.426666666666666, -4.647383786383898), (3.9613333333333323, -4.6433837863838985), (4.496, -4.639383786383898), (5.030666666666667, -4.6353837863838985), (5.565333333333333, -4.631383786383898), (6.1, -4.6273837863838985)}Sequence(Segment[Element[l1, i], Element[l2, n - i]], i, 1, n) → l3, {7.50243317899925, 7.0227173678458685, 6.589398065824041, 6.212191765317101, 5.901867349086053, 5.669418127223363, 5.52468258041275, 5.474621936288361, 5.5218117583099255, 5.663821753999343, 5.893801883834325, 6.201973593030554, 6.5773554160736944, 7.009157161029136, NaN}Segment(B, D) → hSegment(D, C) → iSequence(D + (i / n * (B - D)), i, 1, n) → l4, {(5.3933333333333335, 2.8), (4.866666666666666, 2.8), (4.34, 2.8), (3.813333333333333, 2.8), (3.2866666666666666, 2.8), (2.76, 2.8), (2.233333333333333, 2.8), (1.706666666666666, 2.8), (1.1799999999999997, 2.8), (0.6533333333333333, 2.8), (0.12666666666666693, 2.8), (-0.40000000000000036, 2.8), (-0.9266666666666676, 2.8), (-1.453333333333334, 2.8), (-1.9800000000000004, 2.8)}Sequence(D + (i / n * (C - D)), i, 1, n) → l5, {(5.9319999999999995, 2.3048410809077398), (5.944, 1.8096821618154801), (5.9559999999999995, 1.31452324272322), (5.968, 0.8193643236309602), (5.9799999999999995, 0.3242054045387004), (5.992, -0.17095351455355967), (6.004, -0.6661124336458193), (6.016, -1.1612713527380794), (6.028, -1.656430271830339), (6.04, -2.151589190922599), (6.052, -2.646748110014858), (6.064, -3.141907029107119), (6.076, -3.6370659481993792), (6.088, -4.132224867291638), (6.1, -4.6273837863838985)}Sequence(Segment[Element[l1, i], Element[l4, n - i]], i, 1, n) → l6, {7.004056960572518, 6.565869731004808, 6.182718675254993, 5.865399269053174, 5.625063593303911, 5.471864924069088, 5.4132064934789845, 5.452140571378311, 5.586627117889353, 5.810034575959505, 6.112620916480434, 6.483309389392439, 6.911150431282421, 7.386219154905109, NaN}Sequence(Segment[Element[l2, i], Element[l5, n - i]], i, 1, n) → l7, {7.493629779032726, 7.004651139557827, 6.561703358512035, 6.1747005919157, 5.854747380630247, 5.613320714041377, 5.460845634411571, 5.404855567316714, 5.448325928276839, 5.588936409945056, 5.819650163418935, 6.1303025138447405, 6.509458722076431, 6.945909577159736, NaN}Sequence(Segment[Element[l4, i], Element[l5, n - i]], i, 1, n) → l8, {6.966943618867196, 6.549679773285034, 6.186956856367482, 5.888861810094959, 5.665604995065043, 5.526264087761806, 5.477247286834372, 5.520960892856598, 5.655254970877808, 5.873920041734749, 6.167989363935135, 6.527279463636403, 6.9416705384994275, 7.401913995690645, NaN}
AI 绘图提示语参考
画一个包含两个三角形和多个线段的几何图形,其中一个三角形的顶点在x轴上,另一个在y轴上。通过这两个三角形,绘制一系列连接对应顶点的线段,形成复杂的几何结构。注意线段的长度和位置关系,以及整体图形的对称性和层次感。
以上提示语为根据原始绘图命令整理而来,仅供参考。