Sliding Ladder, Ellipse

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The Falling Ladder The falling ladder is a timeless classic in school mathematics. Depending on the location of the person, the sliding trajectory is either an ellipse or a circle (a circle being a special case of an ellipse, of course). Three pencil holes are drilled into the ladder (1/4, 1/2, 3/4) for tracing part of the curves. Two designs are offered. The circular sliders can be printed together with the rails. After some physical experimentation, one should attempt to prove a solution. Here are some fundamental principles: (1) the ladder has a fixed length; (2) right triangles are intriguing (the Pythagorean Theorem); and (3) there are numerous similar triangles in the background. Enjoy the challenge! References https://demonstrations.wolfram.com/PhysicsOfASlidingLadder/ http://physics.princeton.edu/~mcdonald/examples/ladder.pdf