| Popis: |
Publisher Summary This chapter discusses symmetry of similarity. The idea of symmetry in relation to similarity, symmetry of likeness, originated long ago in the minds of artists, architects, and learned men generally. Only two types of equality as between figures are accepted in classical studies of symmetry, namely, equality allowing of coincidence—identity—and mirror symmetry—equality. By equal, it means not only figures that actually are identical but also all similar figures, that is, all figures of the same shape, including those of mirror similarity. The simplest similarity operation is that of transferring all similar parts of the figure into a parallel position, while enlarging or diminishing them and the distances between them by some specified factor. A group defined by one operation consists of a given operation, repetitions of that operation, or repetitions of the reverse operation. The treatment is being prepared in more detailed form and is being extended to three-dimensional figures. |
