A gymnast with mass m1 = 43 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 =
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Statement :- We assume the orthagonal sequence in Hilbert space, now
, the Fourier coefficients are given by:
Then Bessel's inequality give us:
Proof :- We assume the following equation is true
So that, is projection of
onto the surface by the first
of the
. For any event,
Now, by Pythagoras theorem:
Now, we can deduce that from the above equation that;
For , we have
Hence, Proved