1. On the twelfth day of Christmas my true love sent to me: 12 drummers drumming, 11 pipers piping,10 lords a leaping, 9 ladies dancing, 8 maids a milking, 7 swans a swimming, 6 geese a laying, 5 gold rings, 4 calling birds, 3 French hens, 2 turtle doves and a partridge in a pear tree.

2. Day NumberNumber of PresentsRunning Total 1 2 3 4 5 6 7 8 9 10 11 12

3. Day NumberNumber of PresentsRunning Total 111 234 3610 4 20 51535 62156 72884 836120 945165 1055220 1166286 1278364

6. The numbers of new gifts given on the consecutive days

7. The combined gifts given on the consecutive days

8. The cumulative total number of gifts given

9. Pascal’s triangle is called after the French mathematician, and physicist Blaise Pascal (1623 – 1662)

10. Although Pascal’s Triangle is named after the seventeenth century mathematician, Blaise Pascal, several other mathematicians knew about the triangle hundreds of years before his birth in 1623. The triangle appears to have been discovered independently by both the Persians and the Chinese during the eleventh century.

11. The title of this diagram is “The Old Method Chart of the Seven Multiplying Squares“. It is from the front of Chu Shi-Chieh's book "Ssu Yuan Yü Chien" (Precious Mirror of the Four Elements), written in 1303. In the book it says that the triangle was known about more than two centuries before that.

12. It is thought that the Persian mathematician and poet Ghiyāth ad-Dīn Abul-Fat'h Umar ibn Ibrāhīm Khayyām Neyshābūri knew about this special triangle. He is better known as Omar Khayyam (1048 – 1122)

13. China Persia now Iran France