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I've came across with very cool problem.

Consider some land with rectangle shape $H$ by $L$ ( height, length ) Length is also given, just forgot to show it on a picture.


Now we are in left top corner and want to travel to right bottom corner. We can move on grass with time $T_1$ per unit, but in the water with time $T_2$ per unit. Now we want to minimize the time we need to spend by traveling.

I started to try to do this task and I found out that function which represents this... walk(?) is unimodal.

But I'm not so sure.

How can we construct function and search for minimum of it?

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This problem is equivalent to refraction of light in geometrical optics, so see Fermat's principle of least time and Snell's law. –  Henning Makholm Oct 24 '11 at 22:50
What do you mean by "the function which represents this"? Presumably, your walk is going to be three line segments, which gives you two variables: where you cross into the water, and where you leave it. So, you are looking for a function of those two variables, is that right? –  Gerry Myerson Oct 25 '11 at 0:22
yes, you are right –  Chris Oct 25 '11 at 8:39
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