<?php

  /*  The mean tropical year is the number of days it takes the earth to orbit the sun.
   *  It is a constant of nature, whose accepted value in 1582, the date the Gregorian
   *  Calendar was promulgated, was  365 days, 5 hours, 49 minutes,and 16 seconds, or
   *  365.242546296 days (see the Wikipedia article for Mean Tropical Year).
   *
   *  The purpose of this program is to calculate fractions of whole numbers which are
   *  close to the decimal part of the MTY. For purposes of comparison, the Gregorian
   *  calendar uses the approximation 97 / 400 (97 leap years every 400 years).
   */

  // Number to approximate (decimal part of the MTY).
  $mtyDecimal = 0.242546296;

  // Largest denominator to test.
  $limit = 400;

  // Largest error to report out.
  $largestError = 0.001;

  print("den num   error\r\n");
  print("------------------\r\n");

  // Run thru denominators ($denom), calculating numerator ($numer),
  //  then find the closest integer to $numer.
  for ($denom = 4; $denom <= $limit; $denom++)
  {
    $numer = $mtyDecimal * $denom;
    $low = floor($numer);
    $hi  = ceil($numer);

    // Take the one closest to $numer.
    $intNumer = (($numer - $low) < ($hi - $numer)) ? $low : $hi;
    $error = $intNumer / $denom - $mtyDecimal;
    // gcd > 1 means there is common factor, so has appeared earlier in list.
    //  Also, limit output to denominators with small error.
    if ((gcd($denom, $intNumer) == 1) and (abs($error) < $largestError))
      printf("%3d %3d  %+1.6f\r\n", $denom, $intNumer, $error);
  }

  // http://stackoverflow.com/questions/13828011/look-for-the-gcd-greatest-common-divisor-of-more-than-2-integers
  function gcd($a, $b)
  {
    return $b ? gcd($b, $a % $b) : $a;
  }

?>