• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.493-499
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• 2014

The Pythagorean won-loss formula postulated by James (1980) indicates the percentage of games as a function of runs scored and runs allowed. Several hundred articles have explored variations which improve RMSE by original formula and their fit to empirical data. This paper considers a variation on the formula which allows for variation of the Pythagorean exponent. We provide the most suitable optimal exponent in the Pythagorean method. We compare it with other methods, such as the Pythagenport by Davenport and Woolner, and the Pythagenpat by Smyth and Patriot. Finally, our results suggest that proposed method is superior to other tractable alternatives under criterion of RMSE.

• The Mathematical Education
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• v.57 no.2
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• pp.93-110
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• 2018

One of the biggest changes in the 2015 revised mathematics curriculum is shifting to the second year of middle school in Pythagorean theorem. In this study, the following subjects were studied. First, Pythagoras theorem analyzed the expected problems caused by the shift to the second year middle school. Secondly, we have researched the reconstruction method to solve these problems. The results of this study are as follows. First, there are many different ways to deal with Pythagorean theorem in many countries around the world. In most countries, it was dealt with in 7th grade, but Japan was dealing with 9th grade, and the United States was dealing with 7th, 8th and 9th grade. Second, we derived meaningful implications for the curriculum of Korea from various cases of various countries. The first implication is that the Pythagorean theorem is a content element that can be learned anywhere in the 7th, 8th, and 9th grade. Second, there is one prerequisite before learning Pythagorean theorem, which is learning about the square root. Third, the square roots must be learned before learning Pythagorean theorem. Optimal positions are to be placed in the eighth grade 'rational and cyclic minority' unit. Third, Pythagorean theorem itself is important, but its use is more important. The achievement criteria for the use of Pythagorean theorem should not be erased. In the 9th grade 'Numbers and Calculations' unit, after learning arithmetic calculations including square roots, we propose to reconstruct the square root and the utilization subfields of Pythagorean theorem.

• 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.

• 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.

• 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 of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1477-1485
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• 2016

The Pythagorean theorem for baseball based on the number of runs they scored and allowed has been noted that in many baseball leagues a good predictor of a team's end of season won-loss percentage. We study the convergence characteristics of the Pythagorean expectation formula during the baseball game season. The three way ANOVA based on main effects for year, rank, and baseball processing rate is conducted on the basis of using the historical data of Korean professional baseball clubs from season 2005 to 2014. We perform a regression analysis in order to predict the difference in winning percentage between teams. In conclusion, a difference in winning percentage is mainly associated with the ranking of teams and baseball processing rate.

• 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.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.381-393
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• 2012

In this paper, we show two ways of the time reparametrization of piecewise Pythagorean-hodograph $C^1$ Hermite interpolants. One is the time reparametrization with no shape change, and the other is that with shape change. We show that the first reparametrization does not depend on the boundary data and that it is uniquely determined by the size of parameter domain, up to the general cases. We empirically show that the second parametrization can cause the change of the shape of interpolant.

• 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.

• 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.