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I see this post and I am stunned. I think this is fallacious but I can't figure where is the fallacy?

If you know the fallacy. Please post a answer.

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marked as duplicate by apnorton, pjs36, user147263, SchrodingersCat, Eric Wofsey Nov 12 '15 at 7:52

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The measurement of the jaggy lines is not the sum of the distances between points. It's the measurement of jagged triangular jags. Or in other words measuring the sum of the x and y offsets. As the curve converges into a line segment the calculation we are making is still not measuring the distance between points. It's always measuring the x and y offsets. When the jags are infinitesimal so that they become co-linear we have not defined our procedure to be anything resembling measuring the distance. Our procedure does not change into something else just because we are now on a line. Our procedure remains measuring the x and y offsets. It was never measuring the distance between points.

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