• Journal for History of Mathematics
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• v.21 no.2
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• pp.119-134
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• 2008

In this paper we study a book 'Method of Ruler and Compass' written in Russia three hundreds years ago. In this book many construction problems related with plane figures and solid figures are solved. In this study we analyze construction method of some regular polygon(square, regular pentagon, regular octagon, regular decagon) suggested in 'Method of Ruler and Compass', give mathematical proofs of these construction.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.79-90
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• 2006

The purpose of this paper is to derive the ratios of trigonometric special angles from Euclid's by constructing regular pentagon and decagon. The intention of this paper is started from recognizing that teaching of the special angles in secondary math classroom excessively depends on algebraic approaches rather geometric approaches which are the origin of the trigonometric ratios. In this paper the method of constructing regular pentagon and decagon is reviewed and the geometric relationship between this construction and trigonometric special angles is derived. Through such geometric approach the meaning of trigonometric special angles is analyzed from a geometric perspective and pedagogical ideas of teaching these trigonometric ratios is suggested using history of mathematics.

• Ocean Systems Engineering
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• v.6 no.2
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• pp.203-216
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• 2016

Over recent years the offshore wind turbines are becoming more feasible solution to the energy problem, which is crucial for Egypt. In this article a three floating support structure, tension leg platform types (TLP), for 5-MW wind turbine have been considered. The dynamic behavior of a triangular, square, and pentagon TLP configurations under multi-directional regular and random waves have been investigated. The environmental loads have been considered according to the Egyptian Metrological Authority records in northern Red sea zone. The dynamic analysis were carried out using ANSYS-AQWA a finite element analysis software, FAST a wind turbine dynamic software, and MATLAB software. Investigation results give a better understanding of dynamical behavior and stability of the floating wind turbines. Results include time history, Power Spectrum densities (PSD's), and plan stability for all configurations.