• Communications of Mathematical Education
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• v.30 no.4
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• pp.469-497
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• 2016

In this research, we develop a systematic learning the materials on constructibility of cubic roots. We propose two sets of materials: one is based on concepts of field, vector space, minimal polynomial in abstract algebra, another based on properties of cubic roots in elementary algebra. We assess the validity, applicability, defects and merits of developed materials through prospective teachers, in-service teachers, and professionals. It could be expected that materials be used for advanced secondary students, mathematics majoring college students and mathematics teachers. Furthermore, we may expect the materials be useful for understanding and solving the (un)constructibility problems.

• The Science & Technology
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• no.6 s.433
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• pp.104-105
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• 2005

• Journal of the Korean Society of Propulsion Engineers
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• v.26 no.3
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• pp.22-31
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• 2022

Existing Finocyl grain designs assume configurations and repeat the process of configuration modification and confirmation of the requirements through burn-back analysis. Such a design increases the design fatigue of workers and has a problem of different design completeness depending on capabilities. Therefore, this study devised an optimal design method that applied genetic algorithms to the Burn-back automation analysis program to solve the problem of existing design. For stable search, variable-offset and non-drawable configuration control techniques were developed. The program performance was verified through the searching neutral and double thrust grains.