Sliding Ladder, Ellipse

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The sliding ladder is a classic problem in school mathematics that has been puzzling students for years. The falling trajectory of the person on the ladder can be either an ellipse or a circle, depending on their location. A circle is actually a special case of an ellipse, which makes it even more fascinating. To tackle this problem, three pencil holes are made along the length of the ladder at 1/4, 1/2, and 3/4 marks for tracing parts of these curves. The circular sliders can be printed together with the rails to create a model. However, one must attempt to prove it after some physical modeling. Here are some basic concepts that come into play when dealing with the sliding ladder problem: (1) the length of the ladder remains constant; (2) right triangles are crucial and can be analyzed using the Pythagorean Theorem; and (3) there are numerous similar triangles present in the background. These elements can be used to develop a proof for this intriguing problem. Two designs are provided to help visualize the sliding ladder problem. One design consists of circular sliders that can be printed along with the rails, allowing students to create a physical model. The other design is likely to be more complex and might require some experimentation before arriving at a solution. References: 1. https://demonstrations.wolfram.com/PhysicsOfASlidingLadder/ 2. http://physics.princeton.edu/~mcdonald/examples/ladder.pdf