• Journal for History of Mathematics
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• v.16 no.2
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• pp.23-34
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• 2003

In this paper, we consider relationship between the mathematics and the fine arts. The former is one of the advanced sciences, the latter is one of the arts. But there is correlation between the mathematics and the arts. Here, we concern with the ancient greek mathematics, Euclidean geometry and the ancient greek arts. The ancient greek arts is classified with Geometric Style, Archaic Style, Classical Style and Hellenistic Style. The Geometric Style, Classical Style and Hellenistic Style are very effected by Euclidean geometry. Because the greek artists as keep the geometric proportion as the Euclidean's 5th postulates. The artist's cannon in just golden ratio 1:(1＋$\sqrt{5}$)/2.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.45-61
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• 2011

The starting point of education is the ancient Greek philosophy. In this paper, we research the Hellenism culture: two famous poleis such as Sparta and Athens. Moreover, we investigate prominent philosopher Plato and Aristotle. In particular, we notice early childhood and female education through Hellenism culture. Finally, we study culture, politics and educations of the ancient Roman in order to compare those of our society.

• Journal for History of Mathematics
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• v.13 no.1
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• pp.113-124
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• 2000

In this paper, I will investigate the cultural factors that determine the direction of development of early mathematics. And I will survey the philosophical background of Greek logical mathematics. Then, I will survey the distinctive features of Korean.Chinese ancient mathematics which hindered the development of mathematics.

• Journal for History of Mathematics
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• v.17 no.1
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• pp.119-125
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• 2004

Truth, goodness, and beauty are originated from the Greek philosophy and these concepts are unified by Kant. This article shows that these three concepts correspond to three conditions of axiomatics, that is, consistency, completeness, and independence, respectively.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.57-65
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• 2011

The conceptions of definition and proof radically change in the transition from secondary to tertiary mathematics. Specifically this paper analyses the historical development of the axiomatic method from Greek to modern mathematics. To understand Greek and modern axiomatic method, it is important to know the different characteristics of the primitive terms, constant and variable. Especially this matter of primitive terms explains the change of conceptions of definition, proof and mathematics. This historical analysis is useful for introducing the meaning of formal definition and proof.

• Journal for History of Mathematics
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• v.16 no.4
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• pp.59-68
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• 2003

Mathematics and arts are reflection of the spirit of the ages, since they have human inner parallel vision. Therefore, in ancient Greek ages, the artists' cannon was actually geometric ratio, golden section. However, in middle ages, the Euclidean Geometry was disappeared according to the Monastic Mathematics, then the art was divided two categories, one was holy Christian arts and the other was secular arts. In this research, we take notice of Renaissance Painting and Perspective Geometry, since Perspective Geometry was influenced by Renaissance notorious painter, Massccio, Leonardo and Raphael, etc. They drew and painted works by mathematical principles, at last, reformed the paradigm of arts. If we can say Euclidean Geometry is tactile geometry, the Perspective Geometry can be called by visual geometry.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.229-237
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• 1999

In this paper I examined the tangents to curves through the history of mathematics, expecially that of the Greek geometry and seventeenth century. The purpose of this examination is to show that the mathematical concept of curves is changed by the problems. And I analyzed the text books from the junior to high school. I found that the tangents which aretaught in junior school correspond to those of Greece, and the tangents in high school those of seventeenth century.

• Journal for History of Mathematics
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• v.1 no.1
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• pp.14-32
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• 1984

The concepts of zero, minus, infinite, ideal point, etc. are not real existence, but are pure mathematical objects. These entities become mathematical objects through the process of a philosophical filtering. In this paper, the writer explores the relation between natural conditions of different cultures and philosophies, with its reference to fundamental philosophies and traditional mathematical patterns in major cultural zones. The main items treated in this paper are as follows: 1. Greek ontology and Euclidean geometry. 2. Chinese agnosticism and the concept of minus in the equations. 3. Transcendence in Hebrews and the concept of infinite in modern analysis. 4. The empty and zero in India.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.261-267
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• 2010

Both history of mathematics and education of mathematics is old subject. The question arises wether can these two important subjects can help each other or not. Unfortunately this idea made mathematics society into two groups; one has idea that history of mathematics can help education of mathematics and other group has idea that not only history of mathematics can not help education of mathematics but also it makes some confusion. In this article the author is going to do some comparison and take some conclusion that history of mathematics can make education of mathematics so active and interesting.

• Journal for History of Mathematics
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• v.33 no.2
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• pp.115-132
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• 2020

Social awareness of mathematics and academic attitudes toward the value of mathematics education has kept changing according to the intellectual, political and religious contexts. In this article, we examine how mathematics was defined and recognized in liberal arts education of the Roman Empire and early medieval Western Europe. This study analyzes how mathematics was described in encyclopedic works written in the Roman era after the mid-second century BC and in the Western European monasteries and cathedral schools after the fifth century. Ancient Greek mathematics took a clear place in liberal arts education through encyclopedia writings and prepared a mathematics curriculum for medieval universities. I hope this study will contribute to understanding the origin and context of the mathematics curriculum of medieval universities.