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"content": "Continuing with Christmastime is Christmas Math Time, consider the classic English Christmas carol ”The Twelve Days of Christmas”.\n\nThe \"Twelve Days of Christmas” has all kinds of interesting mathematical features. For example, it is an example of a cumulative song, in which the lyrics detail a series of increasingly numerous gifts given to the speaker by their ”true love” on each of the twelve days of Christmas (the twelve days that make up the Christmas season, starting with Christmas Day) [1]. This cumulative property leads to a bunch of interesting questions including ”How many gifts are given each day?” and ”What is the total number of gifts given during the 12 Days of Christmas?”.\n\nThe first few verses of the carol are:\n\n- On the first day of Christmas my true love sent to me: A partridge in a pear tree.\n- On the second day of Christmas my true love sent to me: Two turtle doves, and a partridge in a pear tree.\n- On the third day of Christmas my true love sent to me: Three French hens, two turtle doves, and a partridge in a pear tree.\n...\n\nThe key property is that on day n you receive n gifts *plus* the sum of the gifts received on the previous days. So how many gifts do you receive on day n, and what is the total number of gifts received by day n?\n\nIt turns out that the number of gifts received on day n on is T_{n}, the nth triangular number, and the total number gifts received by day n is T_{e_{n}}, the nth tetrahedral number. See the figure below (or left) for the details.\n\n#12daysofchristmas #christmastimeischristmasmathtime #triangularnumbers #tetrahedralnumbers #mathematics #merrychristmas \n\n(1/2)\n\nhttps://media.mathstodon.xyz/media_attachments/files/113/638/423/649/179/602/original/b2333973efe4a1d8.jpg\nhttps://media.mathstodon.xyz/media_attachments/files/113/638/423/652/521/061/original/3bb0d5195c4fcf8f.jpg\nhttps://media.mathstodon.xyz/media_attachments/files/113/638/423/659/583/074/original/ca7a492846e2ef80.jpg\nhttps://media.mathstodon.xyz/media_attachments/files/113/638/423/660/199/280/original/e6f1dcebc4c7c8dd.jpg",
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