[00:01] video and based on a couple comments I realized that I could have been clearer about what makes this puzzle tricky the question starts by supposing that you have a disc with radius one and you cover it with a whole bunch of strips
[00:13] when I say strip here I mean a region that's Bound by two parallel lines and the quantity that you'll care about is the width of that strip the distance between those lines the question is supposing that your strips completely
[00:26] cover the disc what is the smallest possible value for the sum of all of those widths for example if you just used a bunch of parallel strips then the sum of all of the widths would be the diameter of the circle which is two Now
[00:41] spoiler alert it turns out that two is the smallest that you can get and a don't see the point this is obvious parallel strips should be optimal CU otherwise you would have some kind of overlap and overlap is clearly wasteful
[00:55] that would be true if we were trying to minimize the total area that these strips have in that case overlap is necessarily a waste of area but that's not the challenge the tricky part here is that the width of a strip is not
[01:08] proportional to the area it's perfectly possible to have a very fat strip near the edge of the circle with a bigger width but a smaller area than a thinner strip near the center of the circle so for all you know there might be a clever
[01:20] covering that has a little overlap here and there which trades off an inefficient use of area for a more efficient use of the total width the challenge is to find find a rigorous way to prove that this is not possible that
[01:33] cannot be lower than the diameter of the circle it's really not an obvious fact and if you appreciate this it makes the solution that we cover in the main video all the more beautiful