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Journal for History of Mathematics
Journal Basic Information
pISSN :
1226-931X
eISSN :
Journal DOI :
10.14477/jhm
Frequency :
Others
Publisher:
The Korean Society for History of Mathematics
Editor in Chief :
Chang-Il Kim
Volume & Issues
Volume 19, Issue 4 - Nov 2006
Volume 19, Issue 3 - Aug 2006
Volume 19, Issue 2 - May 2006
Volume 19, Issue 1 - Feb 2006
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1
On the Historical investigation of Sums of Power of Consecutive Integer
Kang Dong-Jin ; Kim Dae-Yeoul ; Park Dal-Won ; Seo Jong-Jin ; Rim Seog-Hoo ; Jang Lee-Chae ;
Journal for History of Mathematics, volume 19, issue 1, 2006, Pages 1~16
Abstract
In 1713, J. Bernoulli first discovered the method which one can produce those formulae for the sum
for any natural numbers k ([5],[6]). In this paper, we investigate for the historical background and motivation of the sums of powers of consecutive integers due to J. Bernoulli. Finally, we introduce and discuss for the subjects which are studying related to these areas in the recent.
2
Leonhard Euler, the founder of topology
Kim, Sang-Wook ; Lee, Seung-On ;
Journal for History of Mathematics, volume 19, issue 1, 2006, Pages 17~32
Abstract
Topology began to be studied relatively later than the other branches of mathematics, such as geometry, algebra and analysis. Leonhard Euler is generally considered to be the founder of topology. In this paper we first investigate the beginning of topology and its development and then study Euler's life and his achievements in mathematics.
3
A Characterization of Isomorphism Problem of Combinatorial objects and the Historical Note
Park, Hong-Goo ;
Journal for History of Mathematics, volume 19, issue 1, 2006, Pages 33~42
Abstract
In this paper, we study the theoretical and historical backgrounds with respect to isomorphism problem of combinatorial objects which is one of major problems in the theory of Combinatorics. And also, we introduce a partial result for isomorphism problem of Cayley objects over a finite field.
4
Golden Section Found in Hand Axe
Han, Jeong-Soon ;
Journal for History of Mathematics, volume 19, issue 1, 2006, Pages 43~54
Abstract
The purpose of this paper, followed by 'Nature
Human, and Golden Section I ', is to study aesthetic consciousness, mentality model and body proportion of human, and the golden section applied to architecture and hand axe of stone age. In particular, handaxes of one million years ago have shown that they had critical competency to the basis of art and mathematics in the future. Furthermore, without pen, paper and ruler, the existence of mentality model made fundamental conversion of mathematics possible. Different sizes of handaxes were made by maintaining the equal golden section. This was the first example in relation to the principle mentioned in 'Stoicheia' by Euclid which was published hundred thousands of years later.
5
History of modern mathematics
Park, Choon-Sung ;
Journal for History of Mathematics, volume 19, issue 1, 2006, Pages 55~64
Abstract
The thesis is about the development of mathematics starting from the old Greece and the old Babylonia. The modem mathematics has been developed, based on the set theory in the axiomatic method since the 19th century. The primary impetus of this thesis will be to summary the development of topology.
6
The mathematical proofs of refraction law and its didactical significances
Kang, Heung-Kyu ;
Journal for History of Mathematics, volume 19, issue 1, 2006, Pages 65~78
Abstract
The law of refraction, which is called Snell's law in physics, has a significant meaning in mathematics history. After Snell empirically discovered the refraction law
through countless observations, many mathematicians endeavored to deduce it from the least time principle, and the need to surmount these difficulties was one of the driving forces behind the early development of calculus by Leibniz. Fermat solved it far advance of others by inventing a method that eventually led to the differential calculus. Historically, mathematics has developed in close connection with physics. Physics needs mathematics as an auxiliary discipline, but physics can also belong to the lived-through reality from which mathematics is provided with subject matters and suggestions. The refraction law is a suggestive example of interrelations between mathematical and physical theories. Freudenthal said that a purpose of mathematics education is to learn how to apply mathematics as well as to learn ready-made mathematics. I think that the refraction law could be a relevant content for this purpose. It is pedagogically sound to start in high school with a quasi-empirical approach to refraction. In college, mathematics and physics majors can study diverse mathematical proof including Fermat's original method in the context of discussing the phenomenon of refraction of light. This would be a ideal environment for such pursuit.
7
Derivating the Ratios of Trigonometric Special Angles by Constructing Regular Polygon
Cho, Cheong-Soo ;
Journal for History of Mathematics, volume 19, issue 1, 2006, Pages 79~90
Abstract
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.