PHASES OF THE MOON FOR 2026
  Times given in UTC (UTC+0)

  🌑 New Moon         🌓 First Quarter    🌕 Full Moon        🌗 Last Quarter
  Date   Time         Date   Time         Date   Time         Date   Time
  ────────────────    ────────────────    ────────────────    ────────────────
                                          Jan 03  10:04       Jan 10  15:49
  Jan 18  19:53       Jan 26  04:48       Feb 01  22:10       Feb 09  12:44
  Feb 17  12:02       Feb 24  12:28       Mar 03  11:39       Mar 11  09:39
  Mar 19  01:24       Mar 25  19:18       Apr 02  02:13       Apr 10  04:52
  Apr 17  11:52       Apr 24  02:32       May 01  17:24       May 09  21:11
  May 16  20:02       May 23  11:12       May 31  08:46       Jun 08  10:01
  Jun 15  02:55       Jun 21  21:56       Jun 29  23:57       Jul 07  19:30
  Jul 14  09:44       Jul 21  11:06       Jul 29  14:36       Aug 06  02:22
  Aug 12  17:37       Aug 20  02:47       Aug 28  04:19       Sep 04  07:52
  Sep 11  03:28       Sep 18  20:44       Sep 26  16:50       Oct 03  13:26
  Oct 10  15:51       Oct 18  16:13       Oct 26  04:12       Nov 01  20:29
  Nov 09  07:03       Nov 17  11:49       Nov 24  14:54       Dec 01  06:09
  Dec 09  00:53       Dec 17  05:43       Dec 24  01:29       Dec 30  19:00

  50 phases total:  🌑 New Moon ×12   🌓 First Quarter ×12   🌕 Full Moon ×13   🌗 Last Quarter ×13

Have you ever wondered how far can you see to the horizon from an elevated position ? Using simple trigonometry the distance to the horizon along the Earth’s surface can be easily determined. Two cases are considered: (i) light travels in a straight line and (ii) light travels along a curved path as a result of atmospheric refraction. In both cases it will be assumed that the Earth is a sphere resulting in a circular cross section when examining the problem in two dimensions.

\(\pi\) is a mathematical constant defined as the ratio of the circumference of a circle to its diameter. There are many other definitions including the ratio of the area of a circle to the square of its radius. It is a constant that also appears in many formulae used in mathematics, physics and engineering.

\(\pi\) is an irrational number. It cannot be expressed as a ratio of two whole numbers $a/b$. Throughout history ingenious ways have been devised to calculate this constant with increasing accuracy. In this article I’ll describe three methods to determine a decimal representation of \(\pi\) (3.14159…):

• The Monte Carlo method where we use a statistical approach to estimate the area of a circle
• The Leibniz formula for \(\pi\) consisting of the evaluation of a simple series
• Machin’s formula for \(\pi\). A more advanced method using a trigonometric relationship