• Communications of Mathematical Education
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• v.15
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• pp.195-200
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• 2003

본 논문은 피타고라스 정리의 다양한 증명 방법을 통하여 피타고라스 정리를 다양한 측면에서 학습할 수 있는 방안을 모색하고자 하였다. 학습자 스스로 증명하는 즐거움을 느낄 수 있도록 피타고라스 정리의 다양한 증명 방법을 체계적으로 제시하였고, 피타고라스 정리의 다양한 증명 방법을 통해 수학적 아름다움을 알 수 있도록 피타고라스 정리의 증명을 활용한 테셀레이션을 제시하였다.

• Communications of Mathematical Education
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• v.13 no.1
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• pp.245-263
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• 2002

인류 문명의 발달과 함께 폭넓게 활용된 수학적 내용 중의 하나가 피타고라스 정리이다. 특히, 이집트, 메소포타미아, 그리고 중국과 같은 고대 문명의 발생지에서 발굴되는 많은 역사적 기록 속에서 피타고라스 정리에 대한 내용을 찾아볼 수 있다. 피타고라스 정리는 중등학교 수학교육에서 매우 중요한 정리로써, 정리 내용 자체뿐만 아니라 다양한 증명 방법과 증명 과정에 내재된 수학적 아이디어는 수학교육적 측면에서 큰 의미를 가지고 있다. 본 연구에서는 중학교 수학 교과 내용과 관련된 피타고라스 정리의 증명 방법들을 소개하고, 각 증명에 내재된 수학적 아이디어를 기술할 것이다.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.221-234
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• 2010

So far, around 370 various verification of Pythagorean Theorem have been introduced and many studies for the analysis of the method of verification are being conducted based on these now. However, we are in short of the research for the study of the generalization for Pythagorean Theorem. Therefore, by abstracting mathematical materials that is, data(lengths of sides, areas, degree of an angle, etc) which is based on Euclid's elements Vol 1 proposition 47, various methods for the generalization for Pythagorean Theorem have been found in this study through scrutinizing the school mathematics and documentations previously studied.

• Journal of the Korean Data and Information Science Society
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• v.27 no.3
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• pp.653-661
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• 2016

In this paper, we provide a suitable optimal exponent in the generalized Pythagorean theorem and propose to use the logistic model & the probit model to estimate the winning rate in Korean professional baseball league. Under a criterion of root-mean-square-error (RMSE), the efficiencies of the proposed models have been compared with those of the Pythagorean theorem. We use the team historic win-loss records of Korean professional baseball league from 1982 to the first half of 2015, and the proposed methods show slight outperformances over the generalized Pythagorean method under the criterion of RMSE.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.887-921
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• 2009

Pythagorean theorem is one of mathematical contents which is widely used during human culture have developed. There are many historial records related to Pythagorean theorem made by Babylonian, Egyptian, and Mesopotamian. The theorem has the important meaning for mathematics education in secondary school education. Along with the importance of the proof itself, diverse proof methods and ideas included in their methods are also important since the methods improve students' ability to think mathematics. Hence, in this paper, we classify and analyze 390 proof methods published in the book "All that Pythagorean theorem" and other materials. Based on the results we derive educational meaning in mathematics with respect to main idea of the proof, the preliminaries of the study, and study skills used for proof.

• 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.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.45-56
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• 2007

The aims of the study were to review the transcriptions of the famous cuneiform tablet 'Plimpton 322' and interpret the meanings of the numbers. Since the tablet was found, many scholars tried to interpretate the relation among numbers. Neugebauer & Sacks, Buck, and Robson's finding are reviewed. This tablet must be the most well known and taken as an important role to complete a proof of the Pytagoras' theorem before the development of Greek Mathematics.

• Communications of Mathematical Education
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• v.13 no.2
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• pp.515-525
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• 2002

중학교 기하영역 중 피타고라스의 정리를 논증적인 증명 대신에 역동적인 방법으로 이해할 수 있도록 GSP(Geometer's Skechpad)를 활용하여 구현했으며, 멀티미디어 환경에 익숙한 중학생들에게 시 ${\cdot}$ 공간을 초월하여 웹 상에서 개별학습, 반복학습을 할 수 있도록 JAVA 언어를 사용하여 웹으로 변환시켰다.

• Journal for History of Mathematics
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• v.31 no.6
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• pp.315-337
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• 2018

Pythagorean thoerem exists in several equivalent forms in the Euclidean plane, that is, the Hilbert plane which in addition satisfies the parallel axiom. In this article, we investigate the truthness and mutual relationships of those propositions in various non-Hilbert planes which satisfy the parallel axiom and all the Hilbert axioms except the SAS axiom.

• Journal of the Korean Data and Information Science Society
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• v.26 no.3
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• pp.653-659
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• 2015

The Pythagorean formula for baseball postulated by James (1982) indicates the winning percentage as a function of runs scored and runs allowed. However sometimes, the Pythagorean formula gives a less accurate estimate of winning percentage. We use the records of team vs team historic win loss records of Korean professional baseball clubs season from 2005 and 2014. Using assumption that the difference between winning percentage and pythagorean expectation are affected by unusual distribution of runs scored and allowed, we suppose that difference depends on mean, standard deviation, and coefficient of variation of runs scored per game and runs allowed per game, respectively. In conclusion, the discrepancy is mainly related to the coefficient of variation and standard deviation for run allowed per game regardless of run scored per game.