Addendum to the Preliminary Geometry Analysis
of the Rockville Crop Formation
by Dr. Jean-Noel Aubrun
Probability analysis
The probability of crop circles diameters being within a certain range of a diatonic ratio is evaluated here. Assuming a given range dr and a total of N possible diatonic ratios from Rmin to Rmax , the probability to randomly pick up a number matching any of the N diatonic ratios within a value of dr is given by:
P(1) = ( N dr ) / (Rmax - Rmin ) (1)
In the Rockville formation, the smallest circle was chosen arbitrarily to represent Fo, if we assume, very conservatively, that the error in the measurement of the circles was 10 inches, this corresponds to a range of dr = 0.11 in the ratios of all the circles to the baseline Fo. With N = 27 and (Rmax - Rmin ) = 16.67, Eq. 1 gives:
P(1) = 0.18 ~ 1 / 6
The probability to find 9 circles diameters matching diatonic ratios within dr is then
P(9) = P(1)9 = 2.1 10-7 ~ 1 / 4.5 millions.
Figure 1 shows the distribution of the diatonic ratios and of the circle diameter measurements.
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