“Spirals: Young Math Books”

Spirals are defined as a curve that emanate from a center point. (Sitomer; Mindel, 1974) The authors of the book, “Spirals” tell us that “typically, a spiral is a flat curve or a planer curve used in various forms of art and expressions” and that there is a variance in uses for these, where there are different types of spirals, such as two-dimensional spirals, three-dimensional spirals and spherical spirals.

The spiral is well associated with roles in symbolism and they sometimes appear in megalithic forms of art and a well known tomb, the Newgrange tomb which is decorated with spirals.

The author of the book, “Spirals: Young Math Books” tell us that “there is a long history into the study of spirals, sometimes called whorls, where they appear in many different objects in nature. Some common places to find them in nature are in the claws, plants and in horns from animals. Spirals are often found very often in plants”.

Spirals are found in Chinese Art and are used as an early symbol of our sun.

Relating back to the Tang Dynasty, spirals were used in roof tiles as decorations for their homes in China. If you pull a strip of paper between your thumb and the edge of a knife, while pulling tightly, you can create a spiral from paper and use in decorations for art projects. Many people use these spirals in decorating gifts for birthdays and holidays and for the use in decorating rooms for special occasions.

(Garndner, 1991) Very often, spirals are utilized in land art pieces.

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They are defined as geometrical loci of points that hold a certain set of properties and relations with a center point or focus area, such as sky spirals where the design comes from polar coordinate functions while the sky spirals show various levels of visual perception from the far distance.

The spiral’s characteristic of cyclic and linear expansion demonstrates one of the best metaphors for showing time. It is often used as symbolic for demonstrating this concept.

With sun spirals, there is a representation of the ultimate observatory, demonstrating various relations shared between the object of observation and the observer. The observer can walk in a concentrated path toward a linear path from the center point and move outward toward the edge of the spiral shape. The act of walking around in circles has been demonstrated during meditation and used in healing methods, as well. (Davis, 1993) Spirals are often used in mathematical equations and as symbols of mathematical equations.

A conical spiral is a space curve given by a parametric equation, while a cornuspiral is used to show a plot in the complex plane of points in mathematical equations.    Many artists use spirals forms in their projects to express themselves with the flow of the shape of the spiral that moves outward from the center point into a never ending flow, showing freedom in their art projects and pieces that demonstrated openness in their works of art.

A figure that resembles a daisy or sunflower which copies the geometric shape of a spiral because the form runs along the shape of the flowing spiral shape in creating the design. The shape is started in the center point of the design and arranged in an outward shape.

Richard Serra uses the spiral shape in creating pieces of art when he creates sculptures. He uses five torque spirals, where he bends his objects to represent a never ending path in his creations. In his work he uses the curves showing man as being curved and round and not standing upright in his creations.

Spiral shapes are often used in designing jewelry and crafts by many people creating various Celtic designs in their projects. Celtic spirals are second only to knot work designs as the symbols most associated with Celtic art. Like many other symbols associated with ancient Ireland, spirals held special meaning for the people who lived in Ireland.

Hurricanes are also formed in the shape of a spiral. The eye of the hurricane is the center point and origin of the hurricane, while the storm rotates out in a spiral shaped direction and moves across the land at various speeds. Where the hurricane originates, the general physics shows that there is typically little or nothing that binds the various spirals that have formed. The spiral shape, in which the hurricane moves, shows the shape of the earth’s spin in its rotating pattern.

There is a remarkable connection between avian flight patterns, stormy weather and the pinwheel. Each of these has a similar pattern which represents the shape of the spiral in their designs. Each demonstrate movement in their outwardly direction of movement.

In the Golden Ratio, we can also see that there is an expanding nature of what is termed as logarithmic, and it is not to be confused with other spiral shapes. The logarithmic spiral is a familiar shape in things that grows and logarithmic spirals appear in various forms. Spirals appear when a falcon dives in a forward motion in gaining his prey of choice. This spiraled flight pattern shows a constant pattern while the birds maintain an angular flow as he dives. This pattern allows the falcon to keep a constant watch on his target.

Galaxies, along with animals, plants and hurricanes, share in the similar design. They all share the equal trait in their shapes, where they show a spinning motion of movement in their forms. It is shown that galaxies rotate in the spiral direction which raised the question of why and in which direction it flows. It is understood that it does probably originate from a center point but the direction is unknown. It is often thought that it moves in the same direction as matter in the development of the creation of the universe and its surroundings.

Astronomers don’t exactly know for sure why and how the galaxies, such as the  Milky Way were formed, but they had an initial amount of angular momentum, which gave the spinning motion and causes the Milky Way to get its spiraled arms. Mindel Sitomer (Mindel, 1974) explains and defines spirals and discusses the usage of spirals in many areas of their usage from creating one‘s own projects of art, explaining the nature of plants and animals and in exploring the universe.

Using the spiral design is a unique way of demonstrating movement and showing direction and representing endless motions in many areas.