Geometric Design - Assignment Example

The paper "Geometric Design" is a wonderful example of an assignment on design and technology. The origin function of Navajo of weaving was to produce clothing, with designs of shoulder robes, rectangular panel or wrap around dresses, semi-tailored shirts and designs of different kind of belts. The weaving began in the mid-1800s during the trade with the white settlers. Same designs have been developed and improved geometrically to assist in mathematical fields. The woven designs that were developed prior to the 1970s in Zapotec are much similar to the ones developed by the Navajo designs-tapestry weaving have been also developed to create geometric designs because of the relationship of the loom’s vertical wrap to horizontal wefts, and they contain the early designs and carving made on stones on Zapotec building.

  In relationship to the interpretations, Witherspoon (1987), claimed that Navajo weaving women have woven archetypal symbols of Navajo cosmology with rugs pattern. Every culture had two sets of symbols by which it codifies and communicates its concept. He links techniques, symbols and processes them together with cosmology to form a semiotic geometry. The main focus of geometry of Navajo was the art of rug-making. Zaslavsky (1991), states the rug patterns have been widely used in the mathematical field as a basis of understanding of geometry and symmetry.

The same designs can be created geometrically to incorporate the notion of the context.When fractals are mentioned, the only type that comes into mind is the Mandelbrot set. Simple fractal does not go on indefinitely, but it demonstrates or displays a few iterations of congruent shapes. Limited and simple fractals are not similar in that a fern’s mimic cannot perfectly mimic the shape of the larger frond and therefore lack of self-similarity. They may not be mathematically exact and lack self-similarity, but they share the same fractal nature.

Form the fractal pattern the early Africans and Navajo artists the beauty in the recursive and soughed to emulate them including art and town planning that is currently used by architectures in the development of urban areas.During the period of 1820, Leonardo Da Vinci after seeing patterns in tree branches, in which a Japanese artist Kanagawa created, the great wave off in which resembles large ocean wave the top breaks off into smaller bits. In the early 19th century, mathematicians started developing an interest in the patterns used and developed and used by the Navajo community.

In the 20th century, Gaston Julia devised the idea of using a feedback loop to enable produce the repeating pattern that she experimented with properties of a recursive and self-similar set of fractals. People like Koch published the concept of an infinite curve, using approximately the same technique as the Navajo weaving designs in the 1880s but he used continuous lines. These explorations into such complex mathematics were mostly theoretical, however. Looking at the time there was no machine capable of performing the grunt work of so many mathematical calculations in a reasonable amount of time to find out where these ideas really led.

As the power of computers evolved, so too did the ability of mathematicians to test these theories. In the next section, we'll look at the mathematics behind fractal geometry.A morphing was a singe geometric transformation that captured the imagination of the special industrial effects in the 1990s. When morphing the arbitrate shapes transforms dynamically to take on the appearance of some other different shapes. No mathematician can call morphing a rigid transformation since the conventional human forms emerge dramatically from shapeless blobs to more understanding shape.

Geometers Sketchpad includes the traditional Euclidean tools of classical geometric constructions; that is to mean if a figure such as a pentagon can be constructed using a compass and straight edge, it can also be constructed using the designs used by the Navajo weavers. The only problem with the designs developed by this program is that it allows room for cheating, for instant creating figures that are impossible to construct under normal traditional compass and straight edge rules like nonagon.

In Sketchpad, the mid-image corresponding to a given point Twin (on the segment between Pre and Post-construction) can be generated by constructing the locus of Twin as Pre travels about the pre-image. If Twin is an arbitrary point on the segment between Pre and Post (as opposed to some specific point, such as the midpoint), then it can be dragged freely between the segment's endpoints. Correspondingly, the locus of Twin morphs smoothly between the point of origin and the final destination. The use of dynamic geometry software like Geometers Sketchpad allows you to construct and manipulate geometric figures.

Such software can help you discover relationships among geometric figures, search for invariants (properties that do not change), and clarify the beginning stages of geometric proof. You can use the tools of Geometers Sketchpad to construct geometric figures and explore their properties and patterns.Works CitedJungnickel, Dieter. "Characterizing geometric designs, II." Journal of Combinatorial Theory, Series A 118.2 (2011): 623-633. Print.Usiskin, Zalman. Geometry. 2nd ed. Glenview, Ill.: Scott Foresman/Addison-Wesley, 1998. Print.Witherspoon, David. Patterns. Crystal Lake, IL: Rigby Interactive Library, 1987. Print.