The formula for the “Moving Stick Problem”

In this math lesson, we derive the elegant formula for the classic "Moving Stick Problem" (also known as the pipe or ladder problem). We explore the maximum length a stick can be to successfully turn a corner in a hallway with widths A and B, assuming it's held horizontally. What’s fascinating is that while we're looking for the longest possible stick, the math actually requires us to find the minimum of a specific length function. We'll use trigonometry, derivatives, and some algebraic simplification to arrive at a "super version" of the Pythagorean theorem.

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