The spiral, despite the simplicity of the image, is a complex and capacious in meaning symbol. Even ancient people used it as a decorative symbol, a pattern that is easily applied to wood, stones, clay. The shape of the spiral combines symmetry and the golden ratio, with visual perception it causes a sense of harmony and beauty. The spiral associated with the symbolism of the center has long been the beginning of the beginnings, from where evolution, development, the movement of life starts. At one time, Archimedes paid attention to her form. An ancient Greek scientist from Syracuse studied the shape of a spirally twisted shell and derived the equation of a spiral. The coil drawn by him according to this equation is named after him - the Archimedes spiral.
Revolution of Archimedes
The curve described by a point moving at a constant speed along a ray rotating at a constant angular velocity around its origin is called the “Archimedes spiral”. Its construction is carried out as follows: set its step - and, draw a circle from the center O with a radius equal to the spiral step, the step and circle are divided into several equal parts, numbering the division points.
Archimedes in his treatise "On the spiral" investigated the properties of this form using polar coordinates, he wrote down the characteristic property of its points, gave the construction of a tangent to the spiral and determined its area. The spiral of Archimedes displays the formula r = a * theta. The scientist knew that the increase in the pitch of the spiral is always uniform.
Symbolism
The extraordinary variety of meanings of the spiral symbol is striking. It is perceived as the passage and flight of time (cyclic rhythms, the change of solar and lunar phases, the course of history, human life). The spiral is considered a sign of development, the life force given to us by nature. This is a striving for new levels, for its center, wisdom. The spiral is often associated with a snake, personifying, in turn, the wisdom of the ancestors. After all, it is known that snakes are very fond of folding rings and look like spirals.
In nature, a spiral manifests itself in three main forms: frozen (snail shells), expanding (images of spiral galaxies), or contracting (a kind of whirlpool).
Spiral forms range from evolutionary depths
(DNA molecules) to the laws of dialectics.
The spiral is close to a circle - the most ideal form of all that nature has created. Indeed, elemental and natural elements in the form of a spiral are very common in nature. These are spiral nebulae, galaxies, whirlpools, tornadoes, tornadoes, plant devices. Even spiders weave cobwebs in a spiral fashion, twisting the threads in a spiral around the center. Nature loves repetition, the same principles are used in her creations.
Archimedean spiral and Fibonacci sequence
The Archimedes spiral has a close relationship with
the Fibonacci sequence. This law of mathematics describes the principle of the spiral of Archimedes and the golden ratio. Their close connection can be observed in many natural phenomena and elements - in the arrangement of mollusk shells, inflorescences of sunflowers and succulent plants, fractal cabbage and pine cones, humans and whole galaxies.
Spiral symmetry i
The time factor, combined with rotation and directional movement, forms the shape of a spiral. The spirals present in the structure of works of art are related to time, not to space. They are present mainly in patterns, less often in architecture.
These are cathedral spiers and
spiral staircases.Application in technology
The Archimedes spiral is now widely used in technology. One of the scientist's inventions - a screw (prototype of a volumetric spiral) - was used as a mechanism for transferring water to irrigation canals from low-lying reservoirs. The Archimedes screw has become the prototype of the screw (“snail”) - a device widely used in various machines for mixing liquid, bulk and pasty materials. Its most common variety is a screw rotor in a conventional meat grinder. An example of application in the Archimedean spiral technique is also a self-centering cartridge. This mechanism is used in sewing machines for uniform winding of threads.
Nowadays, the Archimedes spiral deserves special attention when teaching computer graphics.