In 1930s, Japanese mathematicians raised the question of how many convex polygons can be spelled out by a jigsaw puzzle. Finally, it was solved by two scholars of Zhejiang University. Their paper "A Theorem on Tangram" was published in the 49th volume of American Mathematical Monthly (1942), signed by Fu Traing Wan and Chuan Chih Xiong. I dare not translate the name casually. )

The method adopted is: the puzzle is regarded as a "basic triangle" composed of 16 identical isosceles small right-angled triangles, and the right side of this triangle is called a rational edge and the hypotenuse is called an unreasonable edge. Then, the number of convex polygons that may be formed by these 16 basic triangles is obtained through four lemmas, and the convex polygons that cannot be formed by the puzzle are eliminated. Finally, their final theorem was proved: through jigsaw puzzles.

I can't get the map. ...

In addition, eight of these figures are symmetrical and five are asymmetrical. If mirror images of asymmetric convex polygons are included, the total number is 18.

Non-convex 7, 8 sides ...