Yesterday I thought of a math problem, and it seems very simple, as I assume the solution is, and I want to know the answer more than I want to figure it out myself.(adsbygoogle = window.adsbygoogle || []).push({});

Ok imagine point A and point B. The shortest path from A to B is a straight line. Lets now go from A to B in two orthogonal lines. I like to think of a right triangle as the two different paths, (hypotenuse is the shortest path and the legs form the longer path.) Now, if you take yet another path but in 4 lines, and then in 8 lines, 16 lines, and on and on, you will eventually be matching the shortest path, or the hypotenuse, however the problem is, the total distance travelled in each successive path is still the same, how does it all of a sudden get to the shortest? In other words the limit as the number of component paths you take, n (n being even and and in the pattern, 2,4,8,16... required geometrically) goes to infinity of the total distance travelled, the path seems to go to the hypotenuse, yet mathematically remains the sum of the two legs, making it seem like (if each leg is 1 unit) 2 = sqrt(2) which of course is wrong.

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# Limit of orthogonal lines to straight line help?

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