• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1585-1592
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• 2016

Estimation of winning percentage in baseball has always been particularly interesting to many baseball fans. We have fitted models including linear regression and Pythagorean formula to the Korean baseball data of seasons from 1982 to 2015. Using RMSE criterion for both the linear formula and the Pythagorean formula, we compared two models in predicting the actual winning percentage. Pythagorean expectation is superior to linear formula when there is either high or low winning percentage. Two methods yield very similar efficiencies when the actual winning percentage is about 50%. To understand and use for estimating winning percentage, it is easier linear formula as estimated equations.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.309-316
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• 2017

In baseball, estimation of winning percentage is critical and many studies for this topic have been actively performed. Pairwise winning percentage estimation using Pythagorean winning percentages of individual teams against other individual teams has the property that the sum of estimated winning percentage totals must be a constant. In this paper, we consider two types of pairwise estimation including linear formula and Pythagorean formula to the Korean baseball data of seasons from 2013 to 2016 under the criterions of RMSE and MAD. In conclusion, pairwise Pythagorean methods have the smaller RMSE and MAD than traditional Pythagorean methods. We suggest the optimal pairwise Pythagorean formula with a fixed exponent. Also we show that there are very little differences of RMSE and MAD between variation in exponent values.

• 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.

• 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.

• 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 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.

• East Asian mathematical journal
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• v.28 no.4
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• pp.419-433
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• 2012

In this paper, by using the inductive method, recurrence relation, the unit circle, circle to inscribe a right-angled triangle, formula of multiple angles, solution of quadratic equation and Fibonacci numbers, we study various problem solving methods to find pythagorean triple.

• Imaging Science in Dentistry
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• v.51 no.4
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• pp.373-382
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• 2021

Purpose: Cone-beam computed tomography (CBCT) reconstructions were analysed to elucidate factors affecting the anatomical relationship between tooth roots and the mandibular canal(MC). Materials and Methods: Images of 300 volumetric tomography scans of patients aged between 20 and 79 years old (167 women and 133 men) were analysed. The mean distances between 2,053 dental root apices and the internal border of the MC were obtained by measuring the horizontal and vertical distances on coronal CBCT images. The actual distance was then calculated mathematically with the Pythagorean formula. The statistical significance of differences between men and women was assessed using the Mann-Whitney test. Correlations with patient age were evaluated with the Spearman rank correlation coefficient. Results: The mean distances ranged from 2.17 mm, for single right third molar roots in women, to 8.02 mm for single left third molar mesiolingual roots in men. The mean distances measured for the mandibular right second molar mesial roots and the right second premolar roots were larger in men than in women. Age showed a significant positive correlation with the measured distances for mesial and distal roots of the first and second molar on both sides and the right third molar, mesiolingual roots of the left third molar, and single roots of the right third molar. Conclusion: The root-to-mandibular canal distance depended on age and the type of tooth. In 2 root types, this distance was impacted by sex.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.401-418
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• 2018

The current geometric and vector textbooks focus on the mechanical activities of finding focus, corner, etc. through elliptic equations. In this paper, we propose a process in which analogy and analytical methods are used in reversible activities of focusing from a given elliptic graph without a coordinate plane. The exploratory tool was used as Geogebra. At first, students tried to find the focus of the ellipse by randomly constructing the major a is and the minor a is in the given ellipse. However, we have experienced a method of constructing the circle of symmetry and analyzed this principle and deduced it to the ellipse. As a result, we could construct the center, long a is and short a is of the ellipse. Then, using the analytical method, the focus formula was recognized as the Pythagorean theorem, and the ellipse's focus was constructed by using the original drawing. Therefore, it is confirmed that analogy and analytical method can positively affect the elliptical focus.