The Pythagorean theorem only holds on a flat surface, not on the inside of a sphere. For small angles, it won't make much difference, but these angles are big

The Pythagorean theorem only holds on a flat surface, not on the inside of a sphere. For small angles, it won't make much difference, but these angles are big enough to matter. Using this solid angle calculator to compute the solid angle covered by a rectangle [1], I get that a 43° x 29° rectangle subtends 0.335 steradian (sr), while a 30° x 17.5° rectangle subtends 0.151 sr, making for a 2.2x increase in solid angle. However, the numbers 43° and 29° apparently come from applying Pythagoras to the 52° diagonal field-of-view (fov). That's also incorrect, and I haven't done the math to correct it. (As an extreme case, for example, a 180° diagonal fov gives 180° horizontal and 180° vertical fov, so Pythagoras clearly breaks down.) [1] http://tpm.amc.anl.gov/NJZTools/XEDSSolidAngle.html http://tpm.amc.anl.gov/NJZTools/XEDSSolidAngle.html