\input zb-basic
\input zb-matheduc
\iteman{ZMATH 06511323}
\itemau{Chung, Young Woo; Yoon, Kim Boo; Young, Kim Dong; Min, Ryu Dong; Hyung, Park Ju; Je, Jang Min}
\itemti{A study on the generalization of the Euclidean proof of the Pythagorean theorem.}
\itemso{East Asian Math. J. 31, No. 4, 459-481 (2015).}
\itemab
Summary: In this study, we investigate whether the theorem is established even if we replace a `square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. The Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.
\itemrv{~}
\itemcc{G40}
\itemut{Pythagorean theorem; generalization of the Euclidean proof of the Pythagorean theorem; Euclidean proof}
\itemli{}
\end