• Journal of the Korea Computer Graphics Society
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• v.6 no.1
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• pp.37-50
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• 2000

Using the complex formulation of plane curves which R. T. Farouki introduced, we can identify any plane polynomial curve with only a polynomial with complex coefficients. In this paper, using the well-known fundamental theorem of algebra, we completely factorize the polynomial over the complex number field C and from the completely factorized form of the polynomial, we find a new necessary and sufficient condition for a plane polynomial curve to be a Pythagorean-hodograph curve, obseving the set of all roots of the complex polynomial corresponding to the plane polynomial curve. Applying this method to space polynomial curves in the three dimensional Minkowski space $R^{2,1}$, we also find the necessary and sufficient condition for a polynomial curve in $R^{2,1}$ to be a PH curve in a new finer form and characterize all possible curves completely.

• 한국체육학회지인문사회과학편
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• v.55 no.6
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• pp.361-373
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• 2016

The winning rate is the most important indicator for running a professional baseball team because it directly affects the spectator. James(1980) suggests that the Pythagorean method is almost identical to the actual winning rate, which is known as a way of helping to establish a team strategy. In this study, it was analyzed what kind of detail difference produced difference between real winning rate and winning rate based on Pythagorean method for 10 years from 2005 to 2014. The purpose of this study is to derive a plan to improve the performance of Korean professional baseball team. The results show that the expected winning rate differs from the actual winning rate by +.062 to -.054. In the process of this result, records of base on balls of the hitter, strikeout of the hitter, base on balls of the pitcher, batting average, sacrifice fly, etc. were found to affect the performance of professional baseball team. Therefore professional baseball teams should improve their batting eye so they can get a base on balls and reduce strikeouts. In the case of a pitcher, it should be instructed to reduce the base on balls by improving the control.

• Journal for History of Mathematics
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• v.29 no.5
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• pp.257-266
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• 2016

This paper is a sequel to our paper [3]. Although polynomials in the tianyuanshu induce perfectly the algebraic structure of polynomials, the tianyuan(天元) is always chosen by a specific unknown in a given problem, it can't carry out the role of the indeterminate in ordinary polynomials. Further, taking the indeterminate as a variable, one can study mathematical structures of polynomials via those of polynomial functions. Thus the theory of polynomials in East Asian mathematics could not be completely materialized. In the previous paper [3], we show that Jeong Yag-yong disclosed in his Gugo Wonlyu(勾股源流) the mathematical structures of Pythagorean polynomials, namely polynomials p(a, b, c) where a, b, c are the three sides gou(勾), gu(股), xian(弦) of a right triangle, respectively. In this paper, we show that Jeong obtained his results through his recognizing Pythagorean polynomials as polynomial functions of three variables a, b, c.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.251-274
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• 2020

We study a dynamical system that was originally defined by Romik in 2008 using an old theorem of Berggren concerning Pythagorean triples. Romik's system is closely related to the Farey map on the unit interval which generates an additive continued fraction algorithm. We explore some number theoretical properties of the Romik system. In particular, we prove an analogue of Lagrange's theorem in the case of the Romik system on the unit quarter circle, which states that a point possesses an eventually periodic digit expansion if and only if the point is defined over a real quadratic extension field of rationals.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.469-482
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• 2006

It ill give much interest both to the teacher and student that paper crane makes interesting mathematical investment possible. It is really possible for the middle school students to invest mathematical activity such as the things about triangle and square, resemblance, Pythagorean theorem. I reserched how this mathematical investment possible through folding and unfolding paper crane and analyzed the mathematical meaning.

• Journal of the Korean Society of Clothing and Textiles
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• v.27 no.6
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• pp.665-674
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• 2003

The purpose of this study was to develop a grading increment at armhole area by apparel CAD(Computer Aided Design) system. In developing a grading increment at armhole area, we analyzed ease values of armhole area in bodice and sleeve by manual drafting patterns of five sizes. We suggested grading increments applied Pythagorean theorem to development the grading increment of the armhole of sleeve. The results and discussions of this study were as follows: 1. In drafting each size, the ease values were not identical. It was difficult to draft perfectly the same armhole line shape between sizes. 2. According to our developed grading increments applied Pythagorean theorem, the ease values were identical between sizes and difference of the armhole length between sizes was also identical. 3. The grading formulas were made out for apparel CAD system. Once grading increment or formula is set in the computer, it can be easily altered to various clothing items at any time. The efficiency of grading work will be also improved and grading time will be reduced.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.17-24
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• 2003

The Pythagorean equation $x^2{＋}y^2{=}z^2$ and Pythagorean triple had appeared in the Babylonian clay tablet made between 1900 and 1600 B. C. Another quadratic equation called Pell equation was implicit in an Archimedes' letter to Eratosthenes, so called ‘cattle problem’. Though elliptic equation were contained in Diophantos’ Arithmetica, a substantial progress for the solution of cubic equations was made by Bachet only in 1621 when he found infinitely many rational solutions of the equation $y^2{=}x^3{-}2$. The equation $y^2{=}x^3{+}c$ is the simplest of all elliptic equations, even of all Diophantine equations degree greater than 2. It is due to Bachet, Dirichlet, Lebesque and Mordell that the equation in better understood.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.175-195
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• 2012

Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki's double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general $C^1$ Hermite interpolation problems. We also extend the UJP method to solve $C^2$ Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with $C^1$ junction points. Further generalizing the UJP method, we go on to solve $C^2$ Hermite interpolation problems using two PH quintics with a $C^1$ junction point, and we also show the possibility of applying the modi e UJP method to $G^2[C^1]$ Hermite interpolation.

• Journal of Integrative Natural Science
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• v.9 no.1
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• pp.10-15
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• 2016

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.