What value of x gives an orange square of half the area?pic.twitter.com/ToPy12ZnUT
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What value of x gives an orange square of half the area?pic.twitter.com/ToPy12ZnUT
This frustrates me. Of course I see that the solution is x = 2 - sqrt(3), but my methods are clearly not God's. My argument of the moment is that the ratio of the hypotenuse of the large triangle to the side of the orange square is (1 - x)/(1 + x^2). Which is true, but opaque.
The thing is, 2 - sqrt(3) so imperatively cries out to be the difference between the side and the altitude of an equilateral triangle of side 2. It's so obviously not a random answer. So there should be a picture that reveals it as such -- especially since 15 degrees arises here.
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