过山车的水平坐标随时间变化
几何画板及绘图内容加载中,请稍等……
该范例演示了过山车在运行过程中水平坐标随时间的变化。涉及的核心数学概念包括三角函数和解析几何。通过使用GeoGebra命令如Line, Rotate, OrthogonalLine, Intersect等,可以构造出过山车的运动轨迹。适合高中数学教学或学习使用。
GeoGebra 命令及参数
Line(G1, G2) → qRotate(Zero, α, C) → Zero'OrthogonalLine(Zero', q) → rIntersect(r, q) → ASegment(Zero', A) → sPoint(s) → GPoint(s) → FLine(G, F) → h_1OrthogonalLine(C, s) → f_1Circle(C, 50) → cSegment(C, G1) → aSegment(C, G2) → bAngle(Zero, C, Zero') → βSegment(C, Zero') → dRotate(Zero, 30° + α, C) → Zero'_1Angle(Zero, C, Zero'_1) → γSegment(C, Zero'_1) → eRotate(Zero, 60° + α, C) → Zero'_2Angle(Zero, C, Zero'_2) → δSegment(C, Zero'_2) → fRotate(Zero, 90° + α, C) → Zero'_3Angle(Zero, C, Zero'_3) → εSegment(Zero'_3, C) → gRotate(Zero, 120° + α, C) → Zero'_4Angle(Zero, C, Zero'_4) → ζSegment(Zero'_4, C) → hRotate(Zero, 150° + α, C) → Zero'_5Angle(Zero, C, Zero'_5) → ηSegment(Zero'_5, C) → iRotate(Zero, 180° + α, C) → Zero'_6Angle(Zero, C, Zero'_6) → θSegment(Zero'_6, C) → jRotate(Zero, 210° + α, C) → Zero'_7Angle(Zero, C, Zero'_7) → ιSegment(Zero'_7, C) → kRotate(Zero, 240° + α, C) → Zero'_8Angle(Zero, C, Zero'_8) → κSegment(Zero'_8, C) → lRotate(Zero, 270° + α, C) → Zero'_9Angle(Zero, C, Zero'_9) → λSegment(Zero'_9, C) → mRotate(Zero, 300° + α, C) → Zero'_{10}Angle(Zero, C, Zero'_{10}) → μSegment(Zero'_{10}, C) → nRotate(Zero, 330° + α, C) → Zero'_{11}Angle(Zero, C, Zero'_{11}) → νSegment(Zero'_{11}, C) → pOrthogonalLine(Zero'_1, d) → tIntersect(d, t) → BOrthogonalLine(Zero'_2, d) → b_1Intersect(b_1, d) → DDistance(D, C) → distanceDCIntersect(h_1, f_1) → ESegment(C, E) → g_1
AI 绘图提示语参考
绘制一个摩天轮的水平坐标随时间变化的图形。首先画一条水平线,然后围绕一个中心点旋转,创建一系列垂直线,这些垂直线与水平线相交,形成摩天轮的轮辐。接着,通过旋转和角度测量,构造出摩天轮的轮盘,并在轮盘上标记出不同角度的位置点,最后连接这些点形成摩天轮的轮廓。
以上提示语为根据原始绘图命令整理而来,仅供参考。