Concept Of Symmetry Group Research Articles

KEMAMPUAN MAHASISWA PGSD DALAM MENGONSTRUKSI PEMAHAMAN KONSEP ALJABAR BERDASARKAN TEORI APOS

The purpose of this study is to describe the ability of students in constructing the concept of symmetry group. This research was conducted in STKIP PGRI Tulungagung, subjek in this research is PGSD student of Semester VI, Data collection with written test, interviews and documentation. Written tests and interviews were conducted to obtain student data in building understanding of the concept of symmetry group, While documentation is used to record all activities in building understanding of the concept of Symmetry group. The results of this study indicate that At the stage of action the subject is able to show the next steps of showing the permutation link with an equilateral triangle, At the stage of the process is able to show the next steps of imagining the reflection of the triangle, And determine reflection, At the stage of the subject object is confident with the done and able to explain the next steps of imagining the reflection properties of the triangle wake up, and determine the reflection From the nature of the reflection is changed again into a transformation composition, At the subject schema stage can already explain if the triangle is altogether converted into a rectangular or pentagonal wake, then the reflection and composition of its transformation will change, it indicates that the subject already has a scheme about symmetry group.

Group Symmetries Connect Art and History with Mathematics

Throughout history, different cultures have produced designs to be used as ornamentation, as part of ceremonies, and as religious symbols. Many of these designs are mathematical in nature, and their bases are often the transformations of reflection and rotation in the plane. The images form groupings that appear to have an underlying unity. Thus, history and art merge to create a medium through which students can study the concrete operations of reflection and rotation in the plane, as well as the more abstract concept of symmetry groups. The resulting patterns give students a sense of the potential for creativity inherent in mathematics.

Qualitative treatment of nonrigid motions in the HOOH molecule

Internal motion in the hydrogen peroxide (HOOH) molecule is analyzed qualitatively with inclusion of trans- and cis-type transitions between its two independent, energetically equivalent equilibrium configurations and with the use of the chain concept of symmetry groups. The analysis involves the classification of stationary states and construction of effective operators of physical parameters which characterize the rotational spectrum of the molecule in the presence of nonrigid motions in an arbitrary order of perturbation theory. The set of necessary equilibrium configurations is specified using the coordinate spin operator. An effective Hamiltonian is used as an example to show that the simplicity of the description and its operator form for all types of motion under study are the important advantages of this approach.