3D空间轨迹及其他：利用3D打印创作抽象艺术
3D Space Trajectories and beyond: Abstract Art Creation with 3D Printing
AI总结：
本文研究二维与三维圆周复合轨迹，从平面扩展到非平面模型，并将其用于数学艺术和3D打印对象创作及学生活动。
摘要：
我们提出了空间中二维和三维轨迹的简单模型。最初的示例对同向双圆周运动进行建模，属于经典曲线（外摆线等）。随后，我们探索二维和三维中的反向双圆周运动以及三圆周运动，以研究行星外运动的复杂可视化。这些运动首先在平面环境中进行研究。接着，通过不断增加复杂性，我们在非平面环境中对其进行探索，这是更接近真实情况的模型。在探索之后，我们利用这些方法创作二维数学艺术和三维打印物体，提供数学表示的新途径。围绕这一探索还组织了学生活动。
英文摘要：
We present simple models of trajectories in space, both in 2D and in 3D. The first examples, which model bicircular moves in the same direction, are classical curves (epicycloids, etc.). Then, we explore bicircular moves in reverse direction and tricircular moves in 2D and 3D, to explore complex visualisations of extraplanetary movements. These moves are studied in a plane setting. Then, adding increasing complexity, we explore them in a non planar setting (which is a closer model of the real situation). The exploration is followed by using these approaches for creating mathematical art in 2D and 3D printed objects, providing new ways of mathematical representations. Students' activities are organized around this exploration.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
