spiral, despite the simplicity of the image - is a complex and capacious symbol of value.The ancient people used it as a decorative symbol, pattern, easily applied to the wood, stone, clay.Shape spiral combines symmetry and golden section, with visual perception, it is a sense of harmony and beauty.Spiral associated with symbols of the center, has long been the beginning started, starts from the evolution, development, movement of life.At one time, it drew attention to the shape of Archimedes.Ancient Greek scientist from Syracuse learned form helically twisted shell, and derived an equation of the spiral.Drawn to them in this equation round named after him - the spiral of Archimedes.
Revolution Archimedes
curve that describes a point moving at a constant velocity along the line, rotating with a constant angular velocity about its origin, the so-called "spiral of Archimedes."Building it is carried out as follows: asking her step - and, hold the center of the circle with a radius about equal to the pitch of the helix pitch and a circle divided into several equal parts, numbering point of division.Archimedes in his treatise "On the spiral" investigated the properties of the form, using polar coordinates, he recorded a characteristic property of its points, gave the construction of a tangent to the helix and defined its area.Displays Archimedean spiral formula r = a * theta.Scientists have known that increasing the pitch of the helix are always evenly.
symbolism
striking extraordinary diversity values of the symbol of the spiral.He is perceived as running and running time (cyclic rhythms, changing solar and lunar phases, the course of history, human life).Spiral is considered a sign of vitality, given to us by nature.This commitment to new levels, to its center, wisdom.The spiral is often associated with the snake, which embodies, in turn, the wisdom of their ancestors.It is known that snakes love to curl rings and looks like a spiral.
spiral in nature manifests itself in three main forms: frozen (snail shells), expanding (images of spiral galaxies) or contract (similarity whirlpool). Spiral forms are represented by evolutionary depths (DNA molecule) to the laws of dialectics.
spiral close to the rim - the most ideal form of all that nature has created.Indeed, natural and natural elements having a spiral shape, it is very common in nature.This spiral nebulae, galaxies, whirlpools, tornadoes, tornado device plants.Even spiders weave a spiral web, spinning yarn in a spiral around the center.Nature loves repetition, in her writings used the same principles.
Archimedean spiral and Fibonacci sequence
Archimedean spiral has a close relationship with the Fibonacci sequence.This law describes the principle of mathematics Archimedes spiral and the golden section.Their close relationship can be observed in many phenomena and elements of nature - the device mollusk shells, sunflower inflorescences and succulent plants, fractal cabbage and pine cones, human and entire galaxies.
spiral symmetry I
time factor, combined with the rotation and direction of movement, forms the shape of a spiral.Spirals are present in the structure of works of art have to do with time, not in space.They are present mainly in the pattern, at least - in arhitekture.Eto cathedral spiers and spiral staircases.
Application technique
spiral of Archimedes is now widely used in the art.One of the inventions of the scientist - the screw (a prototype bulk helix) - were used as a mechanism for the transfer of water in the irrigation channels of the low-lying lakes.The Archimedes screw was the prototype of the screw ("snail") - the device is widely used in various machines for mixing liquid, granular and pasty materials.The most common kind of it - in a conventional screw rotor grinder.An example of the application of the technique as an Archimedean spiral is self-centering chuck.This mechanism is used in sewing machines for uniform winding thread.
Now spiral of Archimedes deserves special attention in the training computer graphics.
