It was on this date in history that the B 29, Enola Gay, dropped an Atomic Bomb on Hiroshima, Japan killing over 90,000 people instantly. I first visited the site in Hiroshima after living in Northern Japan for several years. I still get an empty feeling when I think of it… “Ain’t gonna study war no more.”

The Japanese custom holds that we come from the water, and so to guide the dead back home, back to the sea, they float candles down the river. In Hiroshima, the Toro Nagashi, or lantern floating festival, is on this day to commemorate the dead from that blast.

Tanabata is also a Japanese festival, the festival of seven nights (or perhaps the seventh night), and is often celebrated on July 7^th, but the festival as I knew it always took place this month (this year I think the date is August 19^th ) in Sendai, Japan. The festival date in Sendai is drawn from the seventh day of the seventh month in the old Japanese calendar which had a mixed lunar and solar base.

The festival celebrates the rejoining of the two separated lovers Altair (Hikoboshi) and Vega (Orihime), who spend the year separated by the Milky Way. Orihime is the “Weaving Princess” who wove beautiful fabric for her father, the Sky King (not to be confused with the old flying cowboy serials of my youth), and Hikoboshi is the “cow herd”. By some process, the lonely princess and the lowly cowherd met and fell deeply in love, so in love, in fact, that they could not concentrate on their work. Orihime could not focus on her weaving, and Hikoboshi let his cows wander across the skies. The Sky King was so upset, that he separated them by a river of stars. Orihime cried to her father so long that he promised that if they did their jobs well all year, they could meet on the seventh day of the seventh month, but when they tried to meet, they found they could not cross the river because there was no bridge. An arrangement was made with the magpies to gather and spread their wings to form a bridge for the lovers to meet, but if it rains, the magpies will not be able to come, so go to the temple and pray for the sky to be clear at night.

I first heard of the festival in conjunction with a geometric puzzle called tangram (see picture at top). Tangram is a name of a Chinese puzzle of seven pieces that became popular in England around the middle of the 19th century. It seems to have been brought back to England by Sailors returning from Hong Kong. The origin of the name is not definite. One theory is that it comes from the Cantonese word for chin. A second is that it is related to a mispronunciation of a Chinese term that the sailors used for the ladies of the evening from whom they learned the game. [Concubines on the floating brothels of Canton, Hong Kong, and many other ports belonged to an ethnic group called the Tanka whose ancestors came from the interior of the country to become fishermen and pearl divers. They were considered as non-chinese by the govenments of China until 1731. They were unique among Chinese women in refusing to have their feet bound. ] A third suggestion is that it is from the archaic Chinese root for the number seven, which still persists in the Tanabata Festival.

Whatever the origin of the name, the use of the seven shapes as a game in China were supposed to date back to the origin of the Chou dynasty over one thousand years before the common era. The Chinese name is Ch'i ch'iao t'u which translates, so I am told, as "ingenious plan of seven". It appears however, that the game and the name are both much more modern than believed. From the MathPuzzle.com website, I found that " The Tangram was invented between 1796 and 1802 in China by Yang-cho-chu-shih. He published the book Ch'i ch'iao t'u (Pictures using seven clever pieces). The first European publication of Tangrams was in 1817. The word Tangram itself was coined by Dr. Thomas Hill in 1848 for his book Geometrical Puzzles for the Young. He became the president of Harvard in 1862, and also invented the game Halma which is the original Chinese Checker game.

Tangrams received a boost in popularity when mathematician Charles Dodgeson, writing as Lewis Carroll, used them to create illustrations of the Characters in the "Alice" books. In the Penguin Books translation of Tangram by Joost Elffers he states that English Puzzle writer H. E. Dudney purchased a copy of a play-book called “The Fashionable Chinese Puzzle” from Dodgeson's estate. This book seems to be the most common source of the assertion that Napoleon was an avid Tangram player,

I have recently been writing about the incredible genius of Archmedes, so I should point out that Archimedes created a similar game with the disection of a square into 14 pieces. See one at this page from the MAA which also includes a nice history about the puzzle and the discovery of an Archimedian Palimpset recently. The object of the puzzle is to put the pieces back together to form a square. A more difficult question, unknown for over 2000 years, is how many unique ways are there of putting the pieces together to form a square. Bill Cutler used a computer program to show that there are 536 unique ways to assemble the pieces not counting similar rotations and reflections. All 536 solutions are visible in the article mentioned above.

The puzzle goes under the names of Stomachion or Loculus. Stomachion is from the Greek word for stomach. Loculus seems to be a word related to the division of a tomb area into small chambers for different bodies and is related to the diminutive of locus for a point or place, thus "a little place". (I don't yet get the connection between the puzzle and stomach, so anyone who knows might drop me a note)

If the History of the tangram puzzle is of interest to you, I just saw on Amazon that you can buy a copy of the book, “The Tangram Book”. by Jerry Slocum for $2.00.

And if you just want to play, you can download a game (FREE) from my notes on tangram, some of which is included above.