Assuming all lenses are radially symmetric, the area projected on the lens of visible / in focus light is a circle. Why aren't sensors square (or even circular) to take advantage of more image space for the same size lens? I feel like with the current fad of square pictures camera manufacturers should take advantage of that to cut costs / improve quality.
Even if the lens is circular, it is able to render a scene of any shape. Theoretically, if you have an infinite scene, a lens is still able to render it on an infinite film. Therefore, the shape of the lens is not a factor to determine the shape of a sensor.
@leoadberg Cutting circular silicon dies would waste a lot of space, compared to rectangular ones.