Posts tagged 'geometric-mean'

F.10 Circles and Geometric Mean

In a semicircle on diameter AB = m + n, the perpendicular altitude h = CH from a point C on the circumference to AB is the geometric mean sqrt(m*n) of the segments AH = m and HB = n, while the radius OC = (m + n)/2 is their arithmetic mean.

F.27 Harmonic Mean

If C and D are harmonic conjugates with respect to segment AB (so |AC|/|CB| = |AD|/|BD|), then the length |CD| is the harmonic mean of |BD| and |AD|: |CD| = 2 |BD| |AD| / (|BD| + |AD|) = r (gamma + 1/gamma).