How to find a symmetry axis

How to find a symmetry axis

The concept of symmetry plays the leader, though not always a conscious role in modern science, art, the equipment and the life surrounding us. It penetrates literally everything around, occupying, apparently, unexpected areas and objects. In mathematics the word ""symmetry"" has not less than seven values (among them there are symmetric polynoms, symmetric matrixes).


1. Let's consider mirror symmetry. It is easy to establish that each symmetric flat figure can be combined by means of a mirror with itself. Adequately surprises that such difficult figures as a five-pointed star or an equilateral pentagon, are symmetric too. And it is not so simple to understand why such, apparently, correct figure as an oblique-angled parallelogram, is asymmetrical. At first it is represented that parallel to one of you the parties could pass you a symmetry axis. But once you mentally try to use it, at once make sure that it not so.

2. Some children write the letters ""topsy-turvy"". Latin N looks at them as well as, and S and Z turn out on the contrary. If we attentively look at letters of the Latin alphabet, then we will see among them symmetric and asymmetrical. Such letters as N, S, Z, have no axis of symmetry (as well as at F, G, J, L, P, O, R). But N, S, and Z are especially easily written ""on the contrary"" as have the center of symmetry. At other capital letters is at least on one axis of symmetry. Letters A, M, T, U, V, W, Y can be halved a longitudinal axis of symmetry. Letters B, C, D, E, I, K - a cross axis of symmetry. At letters H, O, X is available on two co-perpendicular axes of symmetry. The same experiment can be made with any alphabet of the European group. If you place letters in front of the mirror, having arranged it parallel to a line, then will notice that those from them at which the axis of symmetry passes horizontally can be read also in a mirror. And here at what the axis is located vertically or is absent at all, become ""unreadable""

3. In architecture of an axis of symmetry are used as means of expression of an architectural plan. In the equipment of an axis of symmetry are most accurately designated where it is required to estimate a deviation from zero situation, for example on a wheel of the truck or on a ship steering wheel. If we more attentively look narrowly at the objects (pipe, a glass) surrounding us, then we will notice that all of them anyway consist of a circle through which infinite set of axes of symmetry there passes the infinite number of the planes of symmetry. The majority of such bodies (they are called rotation bodies) have also the center of symmetry (center of a circle) through which pass though you one axis of symmetry.

Author: «MirrorInfo» Dream Team