π = 2? — A Visual Paradox of Semicircle Sequences

① This example demonstrates a seemingly absurd conclusion: a sequence of semicircles forming a zigzag path has a total length that remains constant (equal to 2) as the number of semicircles increases, challenging the idea that π equals 2. ② Core mathematical concepts include limits, arc length, and the nature of π, highlighting the misconception that a jagged curve approximating a straight line must have length approaching that line's length. ③ Construction details: using GeoGebra commands Semicircle, Sequence, and Segment; objects include parameter n (number of semicircles), list1, length calculation a, text1/text2, and point A; a slider controls n to visualize the constant length. ④ Suitable for high school to undergraduate mathematics, this example is ideal for discussing rigorous definitions of limits, the true meaning of curve length, and the pitfalls of geometric intuition, serving as a springboard for paradox-based inquiry or critical thinking exercises.