A ladder is leaning against a tree. On the center rung is a pussycat. She must be a very determined pussycat, because she remains on that rung as we draw the foot of the ladder away from the tree until the ladder is lying flat on the ground. What path does the pussycat describe as she undergoes this indignity?
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Perhaps surprisingly, she describes a quarter circle whose center is at the foot of the tree. As we draw out the ladder, essentially we’re creating a series of right triangles with the same hypotenuse (the ladder). The midpoint of the hypotenuse (the pussycat) will always maintain the same distance from all three vertices, including the right angle.
Another way to see this is to remove the pussycat and visualize two ladders joined by a hinge at their midpoints. These make a scissoring motion as the first ladder descends, the second ladder drawing a simple circular arc whose center is at the base of the tree.
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