The light intensity c received from H is 1 ℎ 2 The light intensity c received from A and B is 1 2 + 1 2
ℎ ℎ equal to 1 ℎ 2
Therefore, we can transfer a bulb at H to two bulbs at A and B.
5. Now we come to the most important part of the proof.
We firstly construct a circle, which has center 1 with
diameter 2 π
, then we construct a circle with diameter 4 π
which
centered at 2 , which is the opposite end of O of the
diameter.
We can place a bulb at 2 and do a horizontal line through
it which intersects with circle 2 at A and B. Connect OA
and OB. AS AB is diameter, ∠ AOB=90. Therefore, we
can replace the bulb at 2 with bulb at A and B. We can
continually do this step to infinite (double the radius and
replace the bulb)
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