Tangram

'seven boards of skill') is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes.

Alternatively the tans can be used to create original minimalist designs that are either appreciated for their inherent aesthetic merits or as the basis for challenging others to replicate its outline.

It is one of the most widely recognized dissection puzzles in the world and has been used for various purposes including amusement, art, and education.

[6] In either case, the first known use of the word is believed to be found in the 1848 book Geometrical Puzzle for the Young by mathematician and future Harvard University president Thomas Hill.

In particular, the modular banquet tables of the Song dynasty bear an uncanny resemblance to the playing pieces of the tangram and there were books dedicated to arranging them together to form pleasing patterns.

[10] The prominent third-century mathematician Liu Hui made use of construction proofs in his works and some bear a striking resemblance to the subsequently developed banquet tables which in turn seem to anticipate the tangram.

[11] The early years of attempting to date the Tangram were confused by the popular but fraudulently written history by famed puzzle maker Samuel Loyd in his 1908 The Eighth Book Of Tan.

This work contains many whimsical features that aroused both interest and suspicion amongst contemporary scholars who attempted to verify the account.

"[6] Along with its many strange details The Eighth Book of Tan's date of creation for the puzzle of 4000 years in antiquity had to be regarded as entirely baseless and false.

The earliest extant tangram was given to the Philadelphia shipping magnate and congressman Francis Waln in 1802 but it was not until over a decade later that Western audiences, at large, would be exposed to the puzzle.

[13] Soon, tangram sets were being exported in great number from China, made of various materials, from glass, to wood, to tortoise shell.

Like most modern sets, this wooden tangram is stored in the square configuration.
A caricature published in France in 1818, when the tangram craze was at its peak. The caption reads: " 'Take care of yourself, you're not made of steel. The fire has almost gone out and it is winter.' 'It kept me busy all night. Excuse me, I will explain it to you. You play this game, which is said to hail from China. And I tell you that what Paris needs right now is to welcome that which comes from far away.' "
Explanation of the two-monks paradox:
In figure 1, side lengths are labelled assuming the square has unit sides.
In figure 2, overlaying the bodies shows that footless body is larger by the foot's area. The change in area is often unnoticed as √2 is close to 1.5.
The 13 convex shapes matched with tangram set