• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.1-6
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• 1997

We will construct the generalized law of cosines in a tetrahedron, in a natural way, which gives three dimensional Pythagoras' theorem and enables us to calculate the volume of an arbitrary tetrahedron.

• Journal for History of Mathematics
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• v.28 no.3
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• pp.151-164
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• 2015

The purpose of this paper is to develop a teaching and learning material integrated two subjects Pythagorean theorem and Fibonacci numbers. Traditionally the former subject belongs to geometry area and the latter is in algebra area. In this work we integrate these two issues and make a discovery method to generate infinitely many Pythagorean numbers by means of Fibonacci numbers. We have used this article as a teaching and learning material for a science high school and found that it is very appropriate for those students in advanced geometry and number theory courses.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.43-54
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• 2005

The aims of the study were to analyze the contents of elementary mathematics curriculum in order to help students to have ideas about the history of mathematics and to apply the ideas to develop their knowledge of mathematicians or mathematical history into the lesson ideas for preservice elementary teachers and elementary students. As a result, many ideas of mathematical connection into the history of mathematics are reviewed, and posters about Pythagoras and Pascal are designed to help students to reinvent the idea of triangular numbers and square numbers.

• School Mathematics
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• v.9 no.4
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• pp.523-533
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• 2007

This article focused the meaning of Pythagoras' and Euclid's proof about the Pythagorean theorem in a historical and mathematical perspective. Pythagoras' proof using similarity is based on the arithmetic assumption about commensurability. However, Euclid proved the Pythagorean theorem again only using the concept of dissection-rearrangement that is purely geometric so that it does not need commensurability. Pythagoras' and Euclid's different approaches to geometry have to do with Birkhoff's axiom system and Hilbert's axiom system in the school geometry Birkhoff proposed the new axioms for plane geometry accepting real number that is strictly defined. Thus Birkhoff's metrical approach can be defined as a Pythagorean approach that developed geometry based on number. On the other hand, Hilbert succeeded Euclid who had pursued pure geometry that did not depend on number. The difference between the proof using similarity and dissection-rearrangement is related to the unsolved problem in the geometry curriculum that is conflict of Euclid's conventional synthetical approach and modern mathematical approach to geometry.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.923-937
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• 2010

Explain concretely how to apply some integer ratios in making Eastern and Western notes, and show numerically that the chromatic scale coming from the upholding Pythagoras method in Western and the Sambunsonikbub in Eastern are perfectly equal even if they are far from geographically.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.221-232
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• 2007

In school mathematics, activities to make particular convex polygons by attaching edgewise some pieces of tangram are introduced. This paper focus on deepening these activities. In this paper, by using Pick's Theorem and 和 草's method, all the convex polygons by attaching edgewise seven pieces of tangram, Sei Shonagon(淸少納言)'s tangram, and Pythagoras puzzle are found out respectively. By using Pick's Theorem to the square seven-piece puzzles satisfying conditions of the length of edge, it is showed that the number of convex polygons by attaching edgewise seven pieces of them can not exceed 20. And same result is obtained by generalizing 和 草's method. The number of convex polygons by attaching edgewise seven pieces of tangram, Sei Shonagon's tangram, and Pythagoras puzzle are 13, 16, and 12 respectively.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.1-14
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• 2005

This study analyzed the differences in the contents as well as in the methods of development and presentation of learning contents in Korean and German mathematics textbooks for middle school students. For the research we investigated only the area of geometry, and in particular this study performed in-depth analysis concerning 4 subjects; namely congruences of triangles, special points in a triangle, similarity of figures and the theorem of Pythagoras.

• Research in Mathematical Education
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• v.17 no.4
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• pp.279-290
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• 2013

Presently, there has been growing interests in using mathematics' history in teaching mathematics [Katz, V. & Tzanakis, C. (Eds.) (2011). Recent Developments on Introducing a Historical Dimension in Mathematics Education. Washington, DC: Mathematical Association of America]. Thus, this article introduces some work of scholars from ancient East Indian culture like Bhaskara (AD 1114-1185) and Arabic culture such as Ibn Qurrah (AD 9th c) that are related to Pythagoras Theorem. In addition, some Babylonian creative works related to Pythagorean triples found in a tablet known as 'Plimpton 322', and an application of the Pythagorean Theorem found in another tablet named 'Yale Tablet' are presented. Applications of computer animation of dissection Motion Operations concept in 2D and 3D using dynamic software like Geometer's-Sketchpad and Cabri-II-and-3D. Nowadays, creative minds are attracted by the recent stampede in the advances of technological applications in visual literacy; consequently, innovative environments that would help young students, gifted or not, acquiring meaningful conceptual understanding would immerge.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.181-195
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• 1999

This research is produced as a applet of learning materials, and is made with the internet languages HTML, Java, and NamoWebeditor. It contains "Greatest Common Divisor and Least Common Multiple", "Parallel translation of function of second order", "Pythagoras Theorem", which is the current middle school mathmatics textbook for third graders. The keynote of this research is that the students can study individually through logging into the internet on their own computers; the program is made using graphics and animation on order to develop the learners′ interest in mathematics. I hope that this research can supplement our currently insufficient internet educational data.

• Journal for History of Mathematics
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• v.34 no.6
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• pp.205-223
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• 2021

It has been argued that as for the origin of the Pythagorean theorem, the theorem had already been discovered and proved before Pythagoras, and the historical records of ancient mathematics have confirmed various uses of this theorem. The purpose of this study is to examine the relevance of its name caused by Eurocentrism and the weakness of its use in Korean school mathematics and to seek improvements from a critical point of view. To this end, the Pythagorean theorem was reviewed from the perspectives of the history of mathematics and mathematics education. In addition, its name in relation to objective mathematical contents regardless of any specific civilization and its use as a starting point for teaching the theorem in school mathematics were suggested.