Page "Olbers' paradox" Paragraph 5

To show this, we divide the universe into a series of concentric shells, 1 light year thick ( say ).

Thus, a certain number of stars will be in the shell 1, 000, 000, 000 to 1, 000, 000, 001 light years away, say.

If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell between 2, 000, 000, 000 to 2, 000, 000, 001 light years away.

However, the second shell is twice as far away, so each star in it would appear four times dimmer than the first shell.

Thus the total light received from the second shell is the same as the total light received from the first shell.