가우스 정수를 활용한 교수－학습 자료 개발 연구

다국어 초록 (Multilingual Abstract)

In environment for excessive competition for entrance exams, the high school students do not
touch the interesting issues or concepts in mathematics and has been devoted to problem-solving.
To resolve this situation, club activities and after-school programs that provide various types of
training programs outside the regular curriculum are operated at schools. This paper, according to
this trend, to develop teaching and learning materials that can be applied to the club activities and
after-school program, allow students to bring several effects.
John Machin first computed 100 decimal digits of π in 1706 using his arctangent identity. The
existence of this identity is closely related to equations over the Gaussian integers. The existence
of single-angle identities has several applications to geometry. For instance, this leads to a very simple
and intuitive proof that if the side lengths of a triangle form a Pythagorean triple, then its acute angles have irrational degree measures. Ultimately, theorems and facts in this teaching and learning materials let students feel the variety
of mathematics, improve logical reasoning and problem-solving, and are expected to bring positive effect for students to know the meaning of mathematics.