The Historical development of the Theory of Human Proportion

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  • ヨーロッパにおける人体比例論の系譜
  • ヨーロッパにおける人体比例論の系譜--数学的知の展開からの一試論
  • ヨーロッパ ニ オケル ジンタイ ヒレイロン ノ ケイフ スウガクテキ チ ノ テンカイ カラノ イチ シロン
  • From a viewpoint of mathematical thought in Europe
  • 数学的知の展開からの一試論

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Abstract

Mathematics can be viewed as a discipline that enjoys absolute "universality". However, whether mathematics possessed this same "universality" at its beginnings is doubtful. Abstraction and universality have gradually been incorporated at each step of mathematical development over time. The question thus becomes, "Why has universality been incorporated in a step by step manner throughout the history of mathematics?" Human activities, which have formed the basis of mathematics, must be examined to answer this question. One part of these human activities is mathematics itself, especially mathematical thought, from the standpoint of its theoretical development, as well as its philosophical and practical aspects. At the same time, mathematics and mathematical thought has played a vital role in other human activities, such as the arts precisely because of its "universality." The "Theory of Human Proportion" has a close relation to mathematics in the same manner as described above. This theory, which is a part of traditional European art theory, strives to establish the "canon" (rule) of the beauty of the ideal human body. The underlying principle is that "ideal beauty must be universal, " and many theoreticians of the arts have applied mathematical methods in order to crystallize ideal beauty. In this article, we shall trace the history of the "Theory of Human Proportion" from ancient Greece to the Renaissance from the viewpoint of the development of mathematical thought. Four mathematical methods shall be examined, specifically, the "fractional method" of ancient Greece, the "modulus method" in the Byzantine and Arabic style of the Middle Ages, the "geometrical construction method" in the European gothic style of the Middle Ages and the "quasi-decimal method" of the Renaissance. Mathematics shall be examined herein as an aspect of human activity with which relationships have been established with other aspects of human activities against the backdrop of the aforementioned four methods and their development. We endeavor to demonstrate that mathematics, through these relationships, is one of the most vibrant of areas of culture at large. Moreover, the illumination of the cultural and social aspects of mathematics should significantly contribute to our overall understanding of mathematics.

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