• East Asian mathematical journal
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• v.30 no.4
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• pp.405-438
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• 2014

This study analyzed and discussed instruction methods of polyhedrons in elementary mathematics textbook by using the didactic transposition theory. By further segmenting instruction methods, we analyzed the period and order of teaching of polyhedrons, its definitions and presentation methods, and how instruction methods has changed so far. In elementary mathematics textbooks from the 1st to the 2007 revised curriculum, we choose the part where polyhedrons are introduced as the search-target, and analyzed instruction methods in these textbooks by using phenomenological description. The instruction period and order of polyhedrons were systemized when the system of Euclid geometry was introduced, considering the psychological condition of students, and the instruction period and order had been refined according to the curriculum. And methods of definition took into consideration both the academic systems and psychological situations. Also, the subject of learning has changed from textbook and teachers to students. Polyhedrons were connected to real life and students could build up their knowledge by themselves. Constructions were aimed at the understanding of meaning of contents, rather than at itself. Through these analyses, we have some suggestions on the teaching of polyhedrons in the elementary mathematics.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.47 no.1
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• pp.1-14
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• 2010

With the rapid growth of 3D content industry fields, 3D content-based hashing (or hash function) has been required to apply to authentication, trust and retrieval of 3D content. A content hash can be a random variable for compact representation of content. But 3D content-based hashing has been not researched yet, compared with 2D content-based hashing such as image and video. This paper develops a robust 3D content-based hashing based on key-dependent 3D surface feature. The proposed hashing uses the block surface coefficient using shape coordinate of 3D SSD and curvedness for 3D surface feature and generates a binary hash by a permutation key and a random key. Experimental results verified that the proposed hashing has the robustness against geometry and topology attacks and has the uniqueness of hash in each model and key.