• Title/Summary/Keyword: Pythagorean theorem

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The Study of the Generalization for Pythagorean Theorem (피타고라스 정리의 일반화에 관한 고찰)

  • Yoon, Dae-Won;Kim, Dong-Keun
    • 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.

Pythagorean Theorem I: In non-Hilbert Geometry (피타고라스의 정리 I: 비-힐베르트 기하에서)

  • Jo, Kyeonghee;Yang, Seong-Deog
    • 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.

Analysis of various proofs of Pythagorean theorem (피타고라스 정리의 다양한 증명 방법과 수학교육학적 아이디어 분석)

  • Kim, Young-Rock;Noh, Hee-Sung;Son, Eun-Hae
    • 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.

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유클리드 제 5 공준의 기원에 관한 가설

  • 도종훈
    • Journal for History of Mathematics
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    • v.16 no.3
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    • pp.45-56
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    • 2003
  • In this paper, we investigate the origin of Euclid's fifth postulate. For this we analyze the Euclid's proof of the Pythagorean theorem, so form a hypothesis "The Euclid's fifth postulate originated from the Pythagorean theorem." And we test our hypothesis by some historical evidences.evidences.

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GSP를 활용한 중학교 수학 교과 연구 -피타고라스 정리를 중심으로-

  • 계영희
    • Journal for History of Mathematics
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    • v.13 no.2
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    • pp.121-132
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    • 2000
  • In this paper, we demonstrate the Pythagorean Theorem by using the computer geometric software, Geometer's Skechpad(GSP) in stead of Eucliean logical proof. Also, we show that two applications of Pythagorean Theorem. The one is constructed by the fact that $ka^2+kb^2=kc^2$, where k is a constant, the other is made by the fractal.

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From Visualization to Computer Animation Approaches in Mathematics Learning: the Legacy throughout History of Human Endeavours for Better Understanding

  • Rahim, Medhat H.
    • 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.

Comparative Study on Teaching of Pythagorean Theorem in South and North Korea (피타고라스 정리의 지도에 대한 남북한 비교)

  • 박문환
    • School Mathematics
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    • v.4 no.2
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    • pp.223-236
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    • 2002
  • Researchers have started to conduct comparative studies of mathematics education in South and North Korea. Most of these studies have a tendency to compare with the curriculum of South and North Korea in the macroscopic standpoint. But microscopic comparative studies on each topic of school mathematics have not been attempted yet. Microscopic studies as well as macroscopic studies are required to prepare for unification the curriculum of South and North Korea. This paper attempts to compare the contents related pythagorean theorem which is dealt with in secondary school mathematics textbook of South and North Korea. Through this study, meaningful differences between textbooks are founded and some implications are obtained. Specially, 'cutting off and rearranging' method needs to be taken into consideration for active learning. Also the construction of the figure using the pythagorean theorem needs to be dealt with in order to develop the logical thinking.

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Proof of the Pythagorean Theorem from the Viewpoint of the Mathematical History (수학사적 관점에서 본 피타고라스 정리의 증명)

  • Choi, Young-Gi;Lee, Ji-Hyun
    • 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.

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The estimation of winning rate in Korean professional baseball league (한국 프로야구의 승률 추정)

  • Kim, Soon-Kwi;Lee, Young-Hoon
    • 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.

CHARACTERIZATION OF MINKOWSKI PYTHAGOREAN-HODOGRAPH CURVES

  • Lee, Sun-Hong;Kim, Gwang-Il
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.521-528
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    • 2007
  • We present a new proof of the characterization theorem for Minkowski Pythagorean-hodograph curves in the Minkowski spaces $\mathbf{R}^{n+1,m}$. For an polynomial curves $\mathbf{s}(t)=(x_1(t),...,\;x_{n+m}(t))$, we also find Minkowski Pythagorean-hodograph curves $\mathbf{r}(t)=(x_0(t),\;x_1(t),...,\;x_{n+m}(t))$. In case m=0, Minkowski Pythagorean-hodograph curves become Pythagorean-hodograph curves in the Euclidean spaces $\mathbf{R}^{n+1}$ and Theorems in this paper hold for these Pythagorean-hodograph curves.