gistfile1.rb

# 0 < A < B < 1 を仮定
lower, upper = 0, 1
loop do
  m = Rational(lower.numerator + upper.numerator, lower.denominator + upper.denominator)
  case
  when m < A then lower = m
  when B < m then upper = m
  else p [:found, m]; exit
  end
end