Symmetry

Symmetry. Two objects which are related to each other, as the right hand is to the left, are said to be symmetrical. The one is, in fact, the image of the other. In the case of the two hands the svmmetry is, of course, not faultless; but we can take any object we like and place it in front of a plane mirror, and we shall see behind the mirror an object exactly the reverse of the real one in front. Every point or line in the object has its representative in the image, and the two corresponding details are at the same distance from the reflecting surface. This surface is therefore a plane of symmetry. In considering a cube carefully we notice that there are several methods of dividing it into two symmetrical parts. There are, in fact, nine such methods, and the dividing planes are the nine planes of symmetry possessed by a cube. An octahedron, however, has the same number of planes of symmetry, while a hexagonal prism has seven. In no science, perhaps, does symmetry play so important a part as in that branch of mineralogy known as crystallography. Crystals are divided into families, according as they possess this characteristic in a greater or less degree. [CRYSTALLOGRAPHY.] A sphere is a solid possessing an infinite number of planes of symmetry. Any plane passing througb its centre divides it into two exactly egual and similar parts. If we are dealing with plane figures, the circle possesses greatest symmetry. Any diameter is an axis of symmetry dividing the circle into two halves, of which each is the image of the other. An ordinary isosceles triangle has one axis of symmetry - the line through the apex bisecting the base. This is multiplied by three when the isosceles is specialised into an equilateral triangle.