Friday, December 16, 2005

The gifts add up...

You know how the carol goes. It starts with:

On the first day of Christmas,
my true love sent to me
A partridge in a pear tree.

And finishes:

On the twelfth day of Christmas,
my true love sent to me
Twelve drummers drumming,
Eleven pipers piping,
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree!


So, have you ever wondered just how much this "true love" actually gave?
The popular Christmas carol starts innocuously enough. On day one, the character in the song gets a single present (a partridge in a pear tree). But on day two, the beneficiary receives a new present (a pair of turtle doves) plus another partridge in a pear tree. Day three brings a second helping of day two's gifts, plus more new items (three French hens). By the twelfth day, the narrator is an undeniable pack rat - and maybe in violation of local zoning - after receiving 12 drummers drumming, and new copies of all the previous day's gifts.

Here is the tally:
12 partridges in pear trees
22 turtle doves
30 French hens
36 calling birds
40 gold rings
42 geese-a-laying
42 swans-a swimming
40 maids-a-milking
36 ladies dancing
30 lords-a-leaping
22 pipers piping
and
12 drummers drumming

WOW! thats a lot of birds and a lot of noise! 364 gifts in all!

When searching for interesting mathematical explanations for the numerical progression of gifts (12,22,30,36,40,42,42,40,36,30,22,12), I came across this gem. The real price of the 12 days of Christmas. Apparently, this Christmas carol is a source of mathematical study with numerous sites dedicated to the analysis of the daily totals.

The most common comes with Pascal's Triangle- an endless source of school maths projects (See here).

I was going to finish by saying "trust mathematicians to make a Christmas carol geeky" but I guess I have done it too!

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