- #1
fourier jr
- 765
- 13
Take the unit square & make a zig-zag line like a staircase from one corner to the opposite one. Then the total distance if you add up the vertical parts & & horizontal parts is 2. Even if you make trillions & trillions of 'stairs' the sum of all the vertical parts & horizontal parts is still 2 even though the graph would look more & more like a diagonal line, whose length of course is [tex]\sqrt{2}[/tex]. Someone mentioned this example before & put up a link to the mathworld page on it but I couldn't find it & nothing I searched for seemed to work.