摘要：Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq（x, y） between two vectors x and y in X, such that x is Birkhoff orthogonal to y if and only if Aq（x,y）=π/2. Some other properties of this angle are also discussed.

摘要：The piano teaching in the music education in normal universities can promote the students to feel the music, and improve the students＇ music qualities. The students can get the sense of the rhythm, the sense of harmony and the sense of pitch and other musical skills in the process of learning to play the piano, thus more accurate performing the music art. For the purpose, the piano teaching in the music education in the normal universities is for the purpose of cultivating the future piano teachers or performers. In this paper, the author carries out thediscussion with the dual nature of the piano teaching in the music education in normal colleges as the theme, in order to put forward some useful strategies for the piano teaching in eoUeges and universities.