 Problem #57  Posted Tuesday, September 14, 1999
 Close to the Line (back
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 The picture at the right shows a line of
slope /2 (square root of 2), through
the origin, that passes "close" to the point (2,3).
This means that the slope
3/2 is close to /2. We
define "m/n is really
close to /2" to
mean that its distance from /2 is less than 1/n^2. (In our example,
3/2  /2 := 1.5001.414 := 0.086 < 1/4, so 3/2 is "really
close.") What are
all fractions m/n, with 0<m+n<75, that are really close
to /2? (m and n have
to be integers.) The winner is the
first entry with the largest difference of (correct fractions)
 (incorrect fractions).

 click here
 for picture
