• 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 Korea Computer Graphics Society
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• v.7 no.1
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• pp.19-25
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• 2001

In this paper, we study the special geometric reparametization of the (plane polynomial) Pythagorean Hodograph curves in the view point of their roots. The PH curves are completely determined by the roots of their hodographs. we show that the loci of roots of the PH curves satisfy some interesting geometric properties.

• 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 applied mathematics & informatics
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• v.14 no.1_2
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• pp.405-413
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• 2004

Rational parameterization of curves and surfaces is one of the main topics in computer-aided geometric design because of their computational advantages. Pythagorean hodograph (PH) curves and Minkowski Pythagorean hodograph (MPH) curves have attracted many researcher's interest because they provide for rational representation of their offset curves in Euclidean space and Minkowski space, respectively. In [10], Kim presented the characterization of the PH curves in the Euclidean space and analyzed the relation between the class of PH curves and the class of rational curves. In this paper, we extend the characterization of PH curves in [10] into that of MPH curves in the general Minkowski space and consider some generalized MPH curves satisfying this characterization.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.657-685
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• 2023

This paper aims to apply the concept of Pythagorean fuzzy soft sets (PFSSs) to UP-algebras. Then we introduce five types of PFSSs over UP-algebras, study their generalization, and provide illustrative examples. In addition, we study the results of four operations of two PFSSs over UP-algebras, namely, the union, the restricted union, the intersection, and the extended intersection. Finally, we will also discuss t-level subsets of PFSSs over UP-algebras to study the relationships between PFSSs and special subsets of UP-algebras.

• 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.

• 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.

• East Asian mathematical journal
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• v.26 no.1
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• pp.69-73
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• 2010

We invoke the characterization of Pythagorean-hodograph polynomial curves and prove that it is impossible to parameterize any real curves, other than a straight line, by rational functions of its arc length.

• 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.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.