Okay, math heavier.  This is going to suck, doing in plain text, but
here goes.

The arbitrary field strength from a magnet dipole is

H~ = (m/4*pi*(R' )^3)(Rhat*2cosX + Xhat*sinX)

where H~ is the magnetic field strength vector at the sensor,
m is the magnetic moment of the dipole, R' is the magnitude
of the distance from the dipole, Rhat is the unit radius vector
and Xhat is the unit vector of deflection from the axis of the
magnetic field.  This is in spherical coordinates; the Yhat
vector plays no role since it represents rotation about the
magnetic field axis.  Classically, X should be theta and Y
should be phi, but including those in a plain text e-mail is
just asking for trouble.

Anyway, in this case, we have a magnet and sensor, between
which the distance isn't changing, we can write off the first
portion of the RHS, (m/4*pi*(R' )^3), as a constant k.  That
leaves

H~ = k(Rhat*2cosX + Xhat*sinX)

The single sensor in this case gives us only magnitude, not
direction.  So we're really interested in |H~|.  Nothing in the
magnitude operation is going to alter or remove those two
sinusoidal functions, so the resulting measurement will
clearly be sinusoidal.

The current position along a sinusoid can be fixed if we
know magnitude and slope, so the sensor must be both
reading the current value and comparing it to prior values
to establish the current position.

It has to have some help from the user to figure out which
direction it's turning, though, because without that info,
the sensor won't know if it's gone, say, 10 degrees 
clockwise versus 350 degrees anti-clockwise.

I hope this is clear enough.  It's been a while since I did
too much of this sort of thing.

Mike H.
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