Axis of symmetry.

Life is full of people symmetry.This is convenient, beautiful, it does not need to invent new standards.But what it really is and it is beautiful in nature, as is commonly believed?


Since ancient times, people tend to organize the world around them.Therefore, something is considered beautiful, but something not very much.From an aesthetic point of view as attractive and are considered the gold silver ratio, as well as, of course, symmetry.This term is of Greek origin and literally means "proportionate".Of course, it's not just about the coincidence on this basis, but also on some other.In a general sense symmetry - it is a property of the object, as a result of various structures, the result is the original data.It is found in the living and inanimate nature, as well as objects made by man.

First of all, the term "symmetry" is used in geometry, but is used in many scientific fields, and its value remains generally unchanged.This phenomenon is quite common and is considered interesting because it varies a few species, and the elements.Using the symmetry is also interesting because it is found not only in nature but also in the ornaments on the cloth, curbs buildings and many other man-made objects.It is necessary to examine this phenomenon in detail, because it is extremely exciting.

use of the term in other scientific fields

Later symmetry will be considered in terms of geometry, but it is worth mentioning that the word is used not just here.Biology, virology, chemistry, physics, crystallography - all non-exhaustive list of areas in which this phenomenon is studied from different angles and in different conditions.From that to which science is the term, depends, for example, classification.Thus, the separation of the types of serious varies, although some of the basic, perhaps, remain the same everywhere.


There are several basic types of symmetry, of which the most common are three:

  • Mirror - observed with respect to one or more planes.Also, the term used to designate the type of symmetry when used this transformation as a reflection.
  • Radial, axial or radial - there are several options in a variety of sources, in a general sense - the symmetry with respect to a straight line.It can be considered as a special case of rotational variations.
  • Central - there is symmetry with respect to a certain point.

In addition, the geometry distinguish the following types, they are much less common, but no less curious:

  • moving;
  • rotational;
  • point;
  • progressive;
  • spiral;
  • fractal;
  • and so on. D.

In biology, all types are called a little differently, but in fact may be the same.The division into certain groups occurs on the basis of the presence or absence and the amount of some elements such as points, planes and axes of symmetry.They should be considered separately and in detail.

basic elements

isolated phenomenon in some of the features, one of which is necessarily present.So called basic elements include a plane, the centers and the axis of symmetry.It is in line with their presence, absence and the amount is determined by the type.

center of symmetry is called a point inside the shape or crystal, in which converge the lines connecting all pairs parallel to each other party.Of course, it does not always exist.If there is a party to which no parallel pair, a point can not be found because it is not.In accordance with the definition, it is obvious that the center of symmetry - is that through which the figure can be reflected on itself.An example is, for example, a circle and a point in the middle thereof.This element is commonly referred to as C.

plane of symmetry, of course, an imaginary, but that it divides the shape into two equal parts to each other.It can pass through one or more parties, be parallel to it and can share them.For the same figure may exist several planes.These elements are usually referred to as P.

But perhaps the most common is what is called "the axis of symmetry."It is not uncommon you can see in geometry and nature.And it is worthy of separate consideration.


part of the elements, on which the figure can be called symmetric,
acts directly or segment.In any case, it is not a point not on the plane.Then we considered the axis of symmetry of figures.There may be a lot, and they can be arranged as you like: Share a party or be parallel to them, as well as cross the corners or not to do so.The axis of symmetry is usually referred to as L.

Examples are isosceles and equilateral triangles.In the first case is the vertical axis of symmetry, on both sides of which are equal to the edge, and in the second line will intersect each corner and all coincide bisectors, medians and heights.The usual triangles do not possess it.

By the way, the collection of all the above elements in crystallography and solid geometry is called the degree of symmetry.This figure depends on the number of axes, planes, and points.

Examples in geometry

can be divided all the many objects in the study of mathematics shape having an axis of symmetry, and those in which it is not.The first category includes all automatically regular polygons, circles, ellipses, as well as some special cases, the others fall into the second group.

As in the case, when he talked about the axis of symmetry of the triangle, the quadrilateral element for does not always exist.For square, rectangle, rhombus or a parallelogram it is, but for the wrong figures, respectively, no.For the circumference of the axis of symmetry - a set of straight lines that pass through its center.

is also interesting to consider the volume and shape at this point.At least one axis of symmetry in addition to all regular polygons and the ball will have some cones and pyramids, parallelograms, and several others.Each case must be considered separately.

Examples in nature

mirror symmetry in life is called bilateral, it occurs most often
.Anyone and many animals is an example.Axial and radial also called much rarer, usually in the plant world.And yet they are.For example, consider how many axes of symmetry has a star, and whether it is at all?Of course, we are talking about marine life, and is not the subject matter of astronomers.And the correct answer would be: it depends on the number of points in the star, such as five, if it is a five-pointed.

In addition, the radial symmetry is observed in many flowers: daisies, cornflowers, sunflowers, and so on. D. Examples of a huge number, they are literally all around.


This term, first of all, most reminiscent of medicine and cardiology, but he initially has a slightly different meaning.In this case, it would be synonymous with "asymmetry", that is, the absence or violation of regularity in one form or another.It can be seen as a coincidence, but sometimes it can be a wonderful reception, for example, clothing or architecture.For symmetrical buildings a lot, but the famous Leaning Tower of Pisa leaned, and though it is not the only one, but it is the most famous example.We know that it happened by chance, but it has its own charm.

Furthermore, it is obvious that the face and body of humans and animals is also not completely symmetrical.Even conducted studies, according to which the "right" person regarded as inanimate or simply unattractive.Still, the perception of symmetry and this phenomenon is surprising and not yet fully understood, and therefore extremely interesting.