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@vfrmedia @jens @sophieschmieg

Try this out on the next grapefruit you see:

Draw a circle around the equator of your grapefruit.

Draw a line from the equator to the north pole of your grapefruit.

Make a right angle at the north pole, then draw that line down to the equator. You will have a triangle covering 1/8 of the grapefruit.

Every angle of the filled-in triangle is a right angle.

Every right angle has 90 degrees, so that triangle has 270 degrees inside of it.

(This works because it's on a sphere, not on a plane.)