Discovered by a French watchmaker Achille Brocot (1817–1878) http://en.wikipedia.org/wiki/Achille_Brocot
Mediant = $latex \frac {a+c}{b+d}$
$latex \frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d} $
a= 132/456 = 0.07
b= 258/338 = 0.76
find c between a, b ?
$Latex c = \frac {132+258} {456+338}
= \frac{390}{794} =0.49$
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