An order 3 magic hexagon resembles the shape of a 19-cell honeycomb, arranged in a 3 4 5 4 3 manner. The requirement is to fill the numbers 1-19 in the grids so that each row (15 in total) adds up to 38. Previously invented methods aimed at solving this problem and proving its uniqueness were either not rigorous enough or too intricate. So by analyzing its properties, I wanted to find a combinatorial solution to its construction, prove its uniqueness, and investigate whether its mathematical principles can be used in real-world applications. The difficulty depends on the viewpoint, so the first step was to label each grid in a convenient way. I chose to look at the magic hexagon as a network composed of a center and rings. Then the connections and restrictions of each number set could be found by formula derivation. In a similar fashion, symmetrical properties were also found. The next step was to analyze possible distributions of odd and even numbers. Out of the 9 configurations, only 1 proved to be usable. The final step was construction. With all the properties known, the few impossibilities were easily eliminated, and only one solution remained, thus proving its uniqueness. The procedures used on the order 3 magic hexagon may be extended to those of higher orders, providing more ease in their construction. The unique properties of magic hexagons may be used in some fields of application, such as in password systems, large-scale roof structure, composite material, national security systems and many other fields.

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This paper discusses the problem that making the air flowing into the room maximized by rotating the windows. Two models are built for rotary windows with 2 and 3 sashes respectively. Based on these models and the assumption of wind blowing from different directions with equal chance, the optimal way of opening windows is calculated by using Pascal programs on computer. Finally, the optimal design for window ventilation is found via comparing maximum value of wind quantity in two situations.

Since the traffic congestion become more and more serious in modern society due to the sharp increasing of private cars, how to improve the transportation efficiency and utilize the current road network more effectively has become a crucial issue. In this paper, a new dynamic route guidance algorithm was proposed in order to provide travelers humanized “optimal route” and to alleviate the loss caused by traffic jams. The study built a graph theory model for Beijing’s ring road transportation system, and proposed a evaluation function &σ=V_f/[k×(t+m^(ρ-ρ0))]& to describe the real time complex traffic flow, and realized the route searching by timed recomputation of classic Dijkstra algorithm. Meanwhile, due to the investigation of special features of ring roads, the study improved the priority of ring road nodes during the searching process. Comparing with Dijkstra algorithm, the time-complexity of this new algorithm decreases to 1/(16k^2) (k is the number of ring road in the road network), and extra mileage is less than 5%, which is more effective applying in large scale ring-road networks. The algorithm was realized by C++ language and connected to Google Earth’s map database with easy operation interface. (The operation of the algorithm program was manifested in the appended video)

Japan’s lunar probe satellite “Kaguya”, China’s lunar probe satellite “Chang’ e-1 lunar probe” left the earth on September 14th, 2007 and October 24th, 2007, began the exploration to the moon. The launching of the China’s lunar satellite is the proud to the global Chinese. However, at the same time as we are proud of the event, we must admit that the pictures published which were sent back by Japanese are clearer and more beautiful than Chinese. While we are saying that the Japan has a better technology, maybe we also need to say that the Japanese can hold better chance than Chinese when taking the pictures. The following two pictures were sent back by the satellite. Picture one is sent back by Japan’s satellite, Picture two is sent back by China’s. It can be seen that there is a long way for China if we want to become stronger at science technology. We also hope that we can have some contribution in the prosperity of China now and in the future.