Free kicks play an important role in a modern soccer match. A skillful soccer player usually uses the opportunity of a free kick to score a goal. There are mainly two ways to give a free kick, falling ball and banana ball. The last thesis analyzes the path of falling soccer in two-dimensional plane. This thesis mainly focuses on using geometrical ways to generate a graph in three-dimensional coordinate system to analyze the path of banana ball and find out the most suitable distance to give a free kick.

Nowadays, China has become the country with the largest aging population. The increasing proportion of the elders inspires the development of related industries. Falling is extremely dangerous for the elders. Thus, it is of vital importance to detect it and send an SOS signal immediately when an elder falls. Existing methods in fall detection include vision based, wearable sensor-based, ambinent device-based techniques. However, there are drawbacks in these existing methods. The video detection cannot guarantee the privacy of the elderly. Monitoring the changing of the environment requires high cost and its accuracy may be degraded by similar phenomena like strenuous exercise or a heavy object dropping down. The wearable sensors need to be worn all the time which is uncomfortable. In this paper, widely deployed Wi-Fi system is used for detecting a fall. It has little influence on the daily life of the elderly and can make up the drawbacks of the methods above. Because human movements would affect wifi signal propagation, we could detect human behaviors, like falling, through wifi. We firstly extract Channel State Information(CSI) from the original wifi signals collected. After performing noise and dimensionality reduction via Principal Component Analysis (PCA), the characteristic data of the Wi-Fi signal is obtained. Then, the detection model is trained using Recurrent Neural Networks (RNN) based on the PyTorch deep learning. Finally, fall detection is achieved automatically based on the trained model. For further improvement of its function, a strategy based on Random State Reset (RSR) and RNN is brought up in this paper, called RSR-RNN. Related experiments have been conducted to verify the feasibility of the method developed in this paper. Six types of fall scenarios are designed according to the data collected under different situations. The results of the experiments show that the RNN model can detect a fall effectively at an accuracy of 84.67%. The average accuracy of detection is further increased to 85.83% using RSR-RNN, which indicates that this strategy is effective. Keywords:

In view of such problems as lacking interaction between figures and text and difficulty in simultaneous positioning of explanation with figures in chinese geometry exercise solution, a Win32 C++ voice lecturing tool integrated with HTML5 dynamic geometry software is designed to realize free control of lecturing progress, random skipping through double-click, simultaneous interaction and highlighting of figure and text, and automatic synchronized reading. On the basis of JavaScript regular expression, the semantic comprehension of geometry exercise text is realized and the production rule set of automatic plotting is designed. During voice synthesising line by line, the mathematic language undergoes normalization processing and figure highlighting information extraction. The study can shed some light on the GeoGebra integrated development and semantic comprehension-based automatic plotting application, and it can be applied to innovative geometry teaching and knowledge base structuring fields.

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The traditional kaleidoscope uses the prism as a basic unit. Through the reflections of the mirrors on the inner surfaces of a prism, we can see many symmetric axles and patterns. However, traditional kaleidoscope only presents two-dimensional images. The three-dimensional kaleidoscope we designed uses the pyramid as a basic unit. We can see three-dimensional images via mirror faces on the inner surfaces of the pyramid. Our examination shows that not all pyramids are able to show three-dimensional images but only pyramids with specific angles do. The kaleidoscope we designed differs from the traditional kaleidoscope in the following ways: ①Our three-dimensional kaleidoscope not only shows three-dimensional space, but also shows it through two-dimensional planes. ②Our three-dimensional kaleidoscope is based on three kinds of pyramid: three-sided pyramid (tetrahedron), four-sided pyramid (square pyramid) and five-sided pyramid (pentagonal pyramid). Each kind of pyramid has its own charm in showing its reflected images. ③Each kind of pyramid is separated from its entire geometry. However, it can present the whole view of the geometry after mirrored. Our exploration shows that two dimensional and three dimensional worlds can change into one another under specific conditions. Perhaps before long we can discover more dimensions and explain the relationships between each kind of dimension. This treatise mainly involves the principles of Euclidean Geometry and Projective Geometry.