Spiral, despite the simplicity of the image, is a complex and meaningful symbol. Even ancient people used it as a decorative symbol, a pattern easily applied to wood, stones, and clay. The shape of the spiral combines symmetry and the golden ratio; when visually perceived, it evokes a feeling of harmony and beauty. The spiral, associated with the symbolism of the center, has long been the beginning of beginnings, from where evolution, development, the movement of life starts. At one time, Archimedes drew attention to its form. An ancient Greek scientist from Syracuse studied the shape of a spirally twisted shell and deduced the spiral equation. The coil drawn by him according to this equation is named after him - the spiral of Archimedes.
Archimedes' coil
A curve described by a point moving at a constant speed along a beam rotating at a constant angular speed around its origin is called "Archimedes' spiral". Its construction is carried out as follows: its step is set - a, a circle is drawn from the center O with a radius equal to the step of the spiral, the step and the circle are divided into several equal parts, numbering the division points.
Archimedesin his treatise "On the Spiral" he studied 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. Displays the spiral of Archimedes formula r=atheta. The scientist knew that the increase in the pitch of the helix is always uniform.
Symbolism
The extraordinary variety of meanings of the spiral symbol is striking. It is perceived as the course and run 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, vitality given to us by nature. This is a desire for new levels, for your center, wisdom. The spiral is often associated with the snake, which, in turn, personifies the wisdom of the ancestors. After all, it is known that snakes love to curl up and look like spirals.
In nature, the spiral manifests itself in three main forms: frozen (snail shell), expanding (images of spiral galaxies) or contracting (similar to a whirlpool). Spiral forms are presented 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 spin their webs in a spiral, twisting the threads in a spiral around the center. Nature loves repetition, her creations use the samesame principles.
Archimedes spiral and Fibonacci sequence
Archimedes' spiral has a close relationship with the Fibonacci sequence. This law of mathematics describes the principle of the Archimedes spiral and the golden section. Their close connection can be observed in many phenomena and elements of nature - in the structure of shells of mollusks, inflorescences of sunflowers and succulent plants, fractal cabbage and pine cones, humans and entire galaxies.
Spiral symmetry
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.
Technical applications
Archimedes' spiral is currently widely used in engineering. One of the scientist's inventions - a screw (a prototype of a three-dimensional spiral) - was used as a mechanism for transferring water to irrigation canals from low-lying reservoirs. The Archimedes screw became the prototype of the screw ("snail") - a device widely used in various machines for mixing liquid, bulk and doughy materials. Its most common variety is the screw rotor in a conventional meat grinder. An example of an application in the technique of the Archimedean spiral is also a self-centering chuck. This mechanism is used in sewing machines forwinding thread evenly.
Now the Archimedes spiral deserves special attention when teaching computer graphics.
