Christmas Day – The Mathematics of Gift Giving

The ‘Twelve Days of Christmas’ song: total gifts received = Σ_{n=1}^{12} n(13–n) = Σ n(13–n) = 13Σ n – Σ n² = 13×78 – 650 = 1014 – 650 = 364. One gift for every day except one. The number 360 is the number of degrees in a circle – a full turn. On Christmas, we celebrate completion and return. The number 360 appears in the Babylonian base‑60 system (6×60). 360 days is an approximation of the solar year. Mathematics gives us the circle of the year – and on this day, we complete it.