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Horizon-Split Ambient Occlusion - How to derive the formula?

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There's this paper about horizon based ambient occlusion [1] which you may or may not know. It essentially states that ambient occlusion (which afaik is proportional to an area on the surface of a hemisphere) may be approximated by a sum of sin² functions. Here's how it is shown in the GDC08 slides on this topic courtesy of Miguel Sainz:


It is shown in [1] that the H is basically the sine of the elevation angle of the blue arrows in the right depiction. Another way to think of this as the height of those linear section from the ground. So it's essentially the squared height of the sections which is summed up. Anybody got an idea how this relates to the area of the hemisphere or to the general ambient occlusion formulation. Basically I'm wondering what this formula is expressing and where it is coming from. Thanks.

edit: The above picture is taken from a pdf containing the slides. However there's also a ppt version which seems to add another bit of information:
It's almost the same, but maybe it helps someone understand it just the little bit better.

[1] [url=""]http://artis.inrialp...a5-dimitrov.pdf[/url]

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