滚动的等边三角形

几何画板及绘图内容加载中，请稍等……

2015-08-06 20:53

测试改名0 变换几何作图

所属专题 Rolling Circles and Polygons Rolling Circles and Polygons Rolling Circles and Polygons

这个范例演示了一个等边三角形在平面上滚动的动态过程。核心数学概念包括等边三角形的性质、旋转和平移变换。通过使用GeoGebra命令如Polygon、Rotate和CurveCartesian，可以构造出三角形的滚动轨迹。适合初中及以上学生学习几何变换和动态几何。

GeoGebra 命令及参数

Polygon((-1, 0), (1, 0), 3) → poly1
Rotate(poly1, If[a < (2 * π / 3), (-a), -2.0944], (1, 0)) → poly1'
Rotate(poly1', If[(2 * π / 3) < a < (4 * π / 3), (-(a - (2 * π / 3))), -2.0943951023931953], (3, 0)) → poly1''
Rotate(poly1'', If[(4 * π / 3) < a < (6 * π / 3), (-(a - (4 * π / 3))), -2.0944], (5, 0)) → poly1'''
Rotate(poly1''', If[(6 * π / 3) < a < (8 * π / 3), (-(a - (6 * π / 3))), -2.0944], (7, 0)) → poly2
Rotate(poly2, If[(8 * π / 3) < a < (10 * π / 3), (-(a - (8 * π / 3))), -2.0944], (9, 0)) → poly2'
Rotate(poly2', If[(10 * π / 3) < a < (12 * π / 3), (-(a - (10 * π / 3))), -2.0944], (11, 0)) → poly2''
Rotate(A, If[a < (2 * π / 3), (-a), -2.0944], (1, 0)) → A'
Rotate(A', If[(4 * π / 3) < a < (6 * π / 3), (-(a - (4 * π / 3))), -2.0944], (5, 0)) → A''
Rotate(A'', If[(6 * π / 3) < a < (8 * π / 3), (-(a - (6 * π / 3))), -2.0944], (7, 0)) → A'''
Rotate(A''', If[(10 * π / 3) < a < (12 * π / 3), (-(a - (10 * π / 3))), -2.0944], (11, 0)) → B
CurveCartesian(1 + (2 * cos((2 * π / 3) - t)), (2 * sin((2 * π / 3) - t)), t, 0, If[a < (2 * π / 3), a, 2.0944]) → b
CurveCartesian(5 + (2 * cos(π - t)), (2 * sin(π - t)), t, 0, If[a < (2 * π), a - (4 * π / 3), 2.0943951023931953]) → c
CurveCartesian(7 + (2 * cos((2 * π / 3) - t)), (2 * sin((2 * π / 3) - t)), t, 0, If[a < (8 * π / 3), a - (2 * π), 2.0944]) → e
CurveCartesian(11 + (2 * cos(π - t)), (2 * sin(π - t)), t, 0, If[a < (4 * π), a - (10 * π / 3), 2.0944]) → f

AI 绘图提示语参考

绘制一个等边三角形沿着平面滚动的动态过程。首先画一个等边三角形，然后围绕不同的点旋转它，每次旋转的角度和旋转中心都不同，直到三角形完全滚动一圈。最后，绘制三角形滚动轨迹的曲线。

以上提示语为根据原始绘图命令整理而来，仅供参考。