||Extreme Lengths for Chords of an Ellipse
||Wei-Chi YANG, Vladimir SHELOMOVSKII and Skip THOMPSON
The problem originated in a Chinese university entrance practice problem. We extend the original circle case to more challenging ones for ellipses. It is evident that technological tools provide us crucial intuitions before attempting for more rigorous analytical solutions. We use GinMA  and ClassPad Manager  for simulating where the possible solutions maybe in 2D. Next, we introduce two analytical methods: applying the Lagrange multiplier method that involves two parameters, and applying the trigonometry method using one parameter. Finally, with the help of Maple  as a computational engine, we verify our results using the mentioned two methods do indeed coincide with each other and are consistent with our geometry conjectures. The content is accessible to those who have completed the calculus courses.