Contents of the Dragon Boat Festival Mathematics Handwritten Paper:

Zongzi is an indispensable traditional delicacy during the Dragon Boat Festival. Chinese rice dumplings not only have rich and varied fillings, but also come in various shapes, including bamboo tube-shaped, Rectangle, cone, pyramid, triangle, etc., but the most common one is "four-corner zongzi", which is a triangular tetrahedral zongzi. Why are zongzi triangular?

Faced with such a problem, different people will always have different ideas: Mathematical experts will say: Triangles are more stable. Foodies say: You can eat the filling in one bite with triangular rice dumplings! As the saying goes, benevolence sees benevolence, and the wise see wisdom. Everyone has different opinions on this issue. In fact, some people have specially studied the shape of zongzi and gave a reasonable explanation from the perspective of practicality and folklore.

Economic use of materials

The materials used to make rice dumplings vary from place to place, but they are basically the leaves of plants. The leaves are wide and long and tough, but they are leaves after all, and their width is limited. The triangular wrapping method only requires 1 or 2 leaves, while the rectangular shape requires about 3 or 4 leaves. Therefore, wrapping the rice dumplings in a tetrahedral shape can save raw materials without losing the fullness.

The shape is reasonable

The complete leaves can be used on all four sides of the triangular rice dumplings, and no unnecessary bending is required. If the rice dumplings are made into a square, then any side should be consistent with the shape of the rice dumplings. To connect the other sides without letting the rice leak out, you need to fold the leaves and buckle them inward. The leaves are tough along the direction of the plant fibers, but they are easy to break in the vertical direction.

Next, let’s analyze the doorways in zongzi from a geometric perspective.

First of all, unlike the instability of parallelepipeds (for example, the cube frame can swing left and right), the properties of tetrahedrons are very stable. As long as the lengths of the six edges are determined, a unique tetrahedron can be assembled. Therefore, tetrahedral rice dumplings are less likely to deform.

Although the four-cornered rice dumplings are not necessarily regular tetrahedrons, the four faces are usually the same isosceles triangles. If you take apart the surface of this tetrahedron, you can get two equal rhombuses, which means using two A similar slender leaf can just wrap it up and make the best use of it.

Another characteristic of the regular tetrahedron is that it has four threefold rotational symmetry axes and six symmetry planes. Each two opposite sides are perpendicular to each other. This shows that no matter how it is placed in the container, , the rice dumplings all look like they are lying flat on their backs neatly, without giving people the impression of lying on their sides.

The right triangular pyramid also has a center of gravity, which is also the center of its circumscribed sphere and inscribed sphere. It is on the line (height) connecting the vertex and the center of gravity of the base. This height is divided into 3: 1, which is one-quarter of the distance from the ground. Therefore, if you use toothpicks or chopsticks to tie up the rice dumplings and find this point, you can best ensure that the force is even and will not fall or break easily.

A small tetrahedral rice dumpling contains so much geometric knowledge. Friends who like mathematics may wish to observe more and you will find more interesting discoveries.