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Let we have a horizontal line segment of 1-unit length and at the left edge point of the line segment we have a perpendicular line segment of 1-unit length, i.e., both the line segments are perpendicular to each other. If we make a “staircase” of equal steps from the top of the perpendicular line segment to the right edge point of the horizontal line segment, we find the length of staircase is always 2 units, no matter how small steps we make (see also the photo attached).

But as soon as the staircase becomes a straight line, its length becomes $\sqrt{2}$ (the hypotenuse of the right-angled triangle with adjacent and perpendicular of 1 unit each). I'm confused between the staircase of a large number of steps (steps being too small as if the staircase were a straight line) having length of 2 units and the a straight line there with length of $\sqrt{2}$.

amWhy
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Muhammad Imran
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    https://math.stackexchange.com/a/12907/766324 – ARROW Jul 31 '20 at 06:14
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    and you should type the question , it is not convenient for all users to see the question in the Image , in case you need help with math jax : https://math.meta.stackexchange.com/q/5020/766324 – ARROW Jul 31 '20 at 06:16
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    I discard such questiosn as they are too bothersome to read because of the hsnd writing and the glare. – William Elliot Jul 31 '20 at 07:35

1 Answers1

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It's the difference between Taxicab geometry and Euclidean geometry - different metrics give different values to distances, like 'as the crow flies' (a straight line) or 'by road'.

JMP
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