Introduction to the project (Provided by the school):

TWGHs Kwok Yat Wai College

Title of Project: Tangram

Members:  K. K. CHAN

                 K. Y. CHAN

                 S. L. FOK

                 L. K. SO

                 Y. M. WONG

                 C. F. YIU

At the beginning of our project, we searched for the history of the tangram, which included where it came from and why it was named. Then, we analyzed the basic structure of a tangram. We discovered that each component of a tangram was a combination of congruent, right-angled isosceles triangles. We called each of these right-angled isosceles triangles the “basic triangle”. A lot of geometric figures could be formed by combining basic triangles. For example, two basic triangles could form a large triangle, a square or a parallelogram. We then used different combinations of these geometric figures to create thirty different sets of tangram. Also, we tried to use at most three different colours to distinguish the boundary of those seven components of each tangram set. By making use of these thirty different sets of tangram, we built up some interesting and meaningful figures such as a tree, a bird and a house. Also, we used these figures to tell some short stories. Finally, we analyzed the properties of the reflectional symmetry and rotational symmetry of the seven components of a tangram. Also, we discovered that for any two similar triangles the square of the ratio of the lengths of their corresponding sides was equal to the ratio of their areas.