• Journal for History of Mathematics
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• v.22 no.3
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• pp.131-152
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• 2009

The Eudoxean theory of Proportion is correlated with 'Dedekind cut' with which Dedekind defined the real number system in modern usage. Dedekind established a firm foundation for the real number system by retracing some of Eudoxus' steps of over two thousand years earlier. Thus it should be quite worthy that we separate Greek inheritance from the definition of Dedekind, However, there is a fundamental difference between Eudoxean theory of proportion and Dedekind cut. Basically, it seems impossible for Greeks to distinguish between the distinction between number and magnitude. In this paper, we will consider how the Eudoxean theory of proportion was related to Dedekind cut introduced to prove the Dedekind's real number completion and how it influenced Dedekind cut by looking at the relation between Eudoxos's explication of the notion of ratio and Dedekind's well-known construction of the real numbers.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.939-947
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• 2010

The Golden ratio which was started to be use by Eudoxos, Greek mathematician, is being used as a tool to explain beauty in various fields like architecture, art, society, nature and so on. In addition, people not only use the golden ratio, also use obesity to consider a standard of beauty. This study's subjects are students of H university. We researched their Golden ratios of their whole body, upper body and lower body. Also, to research their obesity levels, we used Obesity degree, Waist-hip ratio and Percent body fat. According to different features of the subjects, we study differences between the golden ratio and obesity and how the golden ratio of body affects obesity.