积极 AI Logo 积极 AI

滚动正方形

滚动正方形
几何画板及绘图内容加载中，请稍等……
2015-08-07 04:39
多边形变换几何作图滑块动画轨迹
所属专题 GCSE Higher Ch8 Transformations & Constructions Rolling Circles and Polygons Rolling Circles and Polygons Rolling Circles and Polygons
这个范例演示了一个正方形在平面上滚动的动态过程。核心数学概念包括几何变换和轨迹。通过使用Polygon, Rotate, CurveCartesian等命令，展示了正方形滚动时各顶点的轨迹。适合初中及以上学生学习几何变换和轨迹概念。

GeoGebra 命令及参数

  1. Polygon((-1, 0), (1, 0), 4) → poly1
  2. Rotate(poly1, If[a < π / 2, (-a), -1.5707963267948966], (1, 0)) → poly1'
  3. Rotate(poly1', If[π / 2 < a < (2 * π / 2), (-(a - π / 2)), -1.5707963267948966], (3, 0)) → poly1''
  4. Rotate(poly1'', If[(2 * π / 2) < a < (3 * π / 2), (-(a - (2 * π / 2))), -1.5707963267948966], (5, 0)) → poly1'''
  5. Rotate(poly1''', If[(3 * π / 2) < a < (4 * π / 2), (-(a - (3 * π / 2))), -1.5707963267948966], (7, 0)) → poly2
  6. Rotate(poly2, If[(4 * π / 2) < a < (5 * π / 2), (-(a - (4 * π / 2))), -1.5707963267948966], (9, 0)) → poly2'
  7. Rotate(poly2', If[(5 * π / 2) < a < (6 * π / 2), (-(a - (5 * π / 2))), -1.5707963267948966], (11, 0)) → poly2''
  8. Rotate((-1, 2), If[a < π / 2, (-a), -1.5707963267948966], (1, 0)) → A'
  9. Rotate(A', If[π / 2 < a < (2 * π / 2), (-(a - π / 2)), -1.5708], (3, 0)) → A''
  10. Rotate(A'', If[(3 * π / 2) < a < (4 * π / 2), (-(a - (3 * π / 2))), -1.5707963267948966], (7, 0)) → A'''
  11. Rotate(A''', If[(4 * π / 2) < a < (5 * π / 2), (-(a - (4 * π / 2))), -1.5707963267948966], (9, 0)) → B
  12. Rotate(B, If[(5 * π / 2) < a < (6 * π / 2), (-(a - (5 * π / 2))), -1.5707963267948966], (11, 0)) → B'
  13. CurveCartesian(1 + (sqrt(8) * cos((3 * π / 4) - t)), (sqrt(8) * sin((3 * π / 4) - t)), t, 0, If[a < π / 2, a, 1.5708]) → b
  14. CurveCartesian(3 + (2 * cos(π / 2 - t)), (2 * sin(π / 2 - t)), t, 0, If[a < π, a - π / 2, 1.5708]) → c
  15. CurveCartesian(7 + (2 * cos((2 * π / 2) - t)), (2 * sin((2 * π / 2) - t)), t, 0, If[a < (4 * π / 2), a - (3 * π / 2), 1.5708]) → e
  16. CurveCartesian(9 + (sqrt(8) * cos((3 * π / 4) - t)), (sqrt(8) * sin((3 * π / 4) - t)), t, 0, If[a < (5 * π / 2), a - (4 * π / 2), 1.5708]) → f
  17. CurveCartesian(11 + (2 * cos(π / 2 - t)), (2 * sin(π / 2 - t)), t, 0, If[a < (3 * π), a - (5 * π / 2), 1.5708]) → g