How to write columns header to a csv file with Ruby?

I would recommend to use the CSV-library instead:

require 'csv'

CSV.open('test.csv','w', 
    :write_headers=> true,
    :headers => ["numerator","denominator","calculation"] #< column header
  ) do|hdr|
  1.upto(12){|numerator|
    1.upto(12){ |denominator|
      data_out = [numerator, denominator, numerator/denominator.to_f]
      hdr << data_out
    }
  }
end

If you can’t use the w option and you really need the a+ (e.g., the data isn’t available all at once), then you could try the following trick:

require 'csv'

column_header = ["numerator","denominator","calculation"]
1.upto(12){|numerator|
  1.upto(12){ |denominator|
    CSV.open('test.csv','a+', 
        :write_headers=> true,
        :headers => column_header
      ) do|hdr|
          column_header = nil #No header after first insertion
          data_out = [numerator, denominator, numerator/denominator.to_f]
          hdr << data_out
        end
  }
}