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the staircase paradox 🪜
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#math #paradox #calculus #stem
answer: No matter how many stairs you draw, it will never actually become the diagonal line. Even though it appears to look like it, it is fundamentally different because if you zoom in far enough, you will still see vertical and horizontal lines instead of a smooth slope. In fact, if you approach this problem with a calculus lens and think about the arc length formula, you realize that in order for the stairs to converge to the diagonal, it must be differentiable. However, the derivatives of the segments are zero and undefined. Therefore, the jagged steps will always be jagged.
come on who knows