题目：Mathematics in Music & Design
报告人：SHIN Hyunyong(韩国国立教育大学)
时间：5月21日8:50~9:50
地点：天元讲堂
摘要：?
Introduction
We may consider cognitive and affective aspects in mathematics education. Korean students are not bad on cognitive aspects. However, they are not good on affective aspects.
We may approach music and design with mathematics. Mathematical presentation of patterns seems to be possible. In other words, we can hear design and look at music. In this talk, we propose a teaching and learning material for integrating mathematics with music and design.
This proposal seems to results in better affective understanding of mathematics.
Proposal
1. We meet Pythagoras in the painting ‘School of Athens’ by Raphael. What could be the symbol for Pythagorean school? Not right triangle, but tetraktys. Tetraktys mainly represents arithmetic and harmonic means. Pythagoras has used arithmetic and harmonic means for Pythagorean Scale, a music theory. For Pythagoras, the numbers were rational.
2. Pythagoras could not solve the problem “Pythagoras Comma” proposed by himself. The problem has required about 2,000 years to be solved. The key was “irrational number.” It was mathematics
that has solved the musical problem. The new theory is called “Equal Temperament”.
3. We may notice mathematics in guitar. More mathematics has been needed for guitar. In fact, mathematics is useful for enjoying and producing music.
4. Mathematics is also useful for designs. In this case, symmetry is another important concept. There are only seven types of frieze patterns on group theoretic point of view. We may represent all these frieze patterns by music through mathematics. Mathematics is playing as the coordinator between music and design.
5. Based on traditional 7 frieze patterns of Korea, we produce a music. We may hear design and look at music through mathematics. Various smart equipments will help mathematics.
Concluding Remarks
This proposal is
1. not for regular curriculum of mathematics.
2. a special program for mathematics integrated with arts.
3. utilizing smart circumstances like computers, internet, apps, smart phones, etc.
4. developed for vocational high schools in Korea.
5. for producing their own patterns of students.
6. for composing their own music of students.
7. suitable for one hour per week.