Why is the diagonal in a unit square √2? Shouldn’t it add up to 2 since it has to go up 1 unit and right 1 unit? If I made infinitely small vectors zig-zaging like stairs towards the opposite vertex wouldn’t the distance covered add up to 2?

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Why is the diagonal in a unit square √2? Shouldn’t it add up to 2 since it has to go up 1 unit and right 1 unit? If I made infinitely small vectors zig-zaging like stairs towards the opposite vertex wouldn’t the distance covered add up to 2?

In: Mathematics

The thing about infinitely small components is if you consider the wrong distance, the result changes drastically. Even if you create small zigzag lines of length dx and dy, each time, you’re not travelling along the two lines, but along their diagonal. So counting the two lengths is incorrect.

If you don’t believe, just put a ruler, it’ll be about 1.41

The way a ladder is taller standing straight up, then when at a 45 degree incline. To reach the same height as say 10′ ladder going straight up, a ladder at a 45 degree slope would have to be roughly 1.4x as long to reach 10 feet in height.