Geometry, Symmetry and Architecture
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| Taken from Bovill, C. (2012) Fractal Geometry in Architecture and Design. New York, NY, United States: Springer-Verlag New York. |
Reading 1: Geometry Concepts in Architectural Design by Cornelie Leopold
Geometry is the fundamental science of forms and their order. Geometric figures, forms and transformations build the material of architectural design. In the history of architecture, geometric rules based on the ideas of proportions and symmetries formed fixed tools for architectural design. Proportions were analysed in nature and found as general aesthetic categories across nature and art. Therefore proportions such as the golden section were seen as the power to create harmony in architecture as well as in art and music. According to Pythagoras, there were general principles for harmony. They were also applied in architecture and they found a further development especially in the renaissance.
(p. 1)
The concept of symmetry is combined with the idea of harmony and proportion. Symmetry operations are concerned with motions of figures and shapes. Geometry can be seen also as a structural science. The architectural design is based on geometric structures developed out of the idea of transformations. The symmetry transformations are visible as design concepts throughout the history of architecture. In contemporary architecture, there are no fixed rules about design concepts. But there are still relations to geometric space concepts.
(p. 1)
The notion of harmony is seen as a fundamental principle of composition within the history of architecture. Composition is based on harmony and order as aesthetic categories. The understanding of harmony is based on the mythological person “Harmonia”, the goddess of harmony, who was seen as the daughter of Ares, the god of war, and Aphrodite, the goddess of love and beauty. Harmonia is the symbol of the union of antagonisms. Harmony means the connection of different or opposed things to an arranged whole. The antiquity science itself is conducted by principles of harmony and order.
(p. 2)
Another fundamental notion in the history of architecture is the concept of symmetry closely connected with the idea of harmony. “Symmetry”, derived from the Greek “syn” which means together and “metron” which means measure, is understood as the harmony between the parts of an object and the way of the combination of several parts.
(p. 4)
By remembering the historical relations between geometry and architectural design we help to keep the background of our culture but also to understand the fruitful combination between geometrical thinking and architectural designing. By integrating experiments on using geometric structures for designing in the architecture curriculum we should reflect this relationship and try to develop new impulses for geometrical based designing in architecture.
(p. 8)
Reading 2: Geometric Shapes and Frank Lloyd Wright by Matthew Drutt
The architect known as Frank Lloyd Wright developed a system of rotating geometric forms that became one of his principal methods of design. Wright believed that geometry had cosmic meaning and that its use as the means of ordering design connected man to the cosmos. In this idealistic and romantic view, architecture could provide a means of harmony between the individual, society, and the universe.
Most buildings contain interior spaces that are rectilinear. Frank Lloyd Wright thought in curves and straight lines—triangles, circles, ovals, squares, and spirals—as well as shapes adapted from nature. For Wright, geometry was the basic building block of nature. Geometric forms also held symbolic significance. The circle, he said, suggested infinity; the triangle, structural unity; the spire, aspiration; the spiral, organic progress; and the square, integrity. Nearly all of these forms can be found in the architecture of the Guggenheim Museum.
Reading 3: It’s All in the Pattern: Recognizing Symmetry in Architecture by Stephen J. Farenga and Daniel Ness
The ability to detect symmetric relations is a cognitive process that is encountered by nearly all individuals (Rosen 1998; Weyl 1980). Few curriculum programs, however, have implemented a detailed study of symmetry for students to develop geometric thinking before middle school. Genkins (1971, 1975) studied how the concept of symmetry is learned among children. Through paper-folding exercises, her results show that students are able to classify point-symmetric (mirror image of an object is a point) figures and asymmetric (no symmetry existing) figures as nonbilaterally symmetric (mirror image of an object is not a line) figures.
From both a social and anthropological perspective, Mapapá (1994) examined symmetries in the everyday context of merchants and artisans in Maputo, Mozambique. He found that these skilled workers, particularly metal grate workers, have an adept sense of symmetric relations, a necessary skill for their source of revenue. Clearly, symmetric relations have been shown to play an important role in our daily lives. Likewise, it is important to examine the nature of students’ symmetric thinking with regard to their everyday knowledge. The study of symmetry can provide a bridge to unify sciences, mathematics, humanities, and the arts.
Architecture fosters spatial and geometric concepts in the study of physical science. The intimate connection between symmetry and architecture had been noted for centuries; it is clearly and explicitly illustrated in the writings of Marcus Vitruvius Pollio, a Roman architect and engineer who lived in the first century BC, as well as in the first of eight books on the architecture of Sebastiano Serlio, written in 1545.
For architects from antiquity to the present, the relationship between geometry and architecture is clear (Blackwell 1984); geometric reasoning is an essential component for determining form and function of a structure before its construction, and the finished product possesses characteristics that stimulate geometric thinking. An architect, for example, cannot dismiss the role that symmetry plays in the construction of a suspension bridge or the building of a skyscraper. Moreover, she cannot ignore shape and contour when dealing with a building’s aesthetic quality or a client’s interests.
At the same time, we see these ideas clearly emerge in the thinking and cognitive processes of students as they construct models of bridges, buildings, tracks, and roads. A number of sources shed light on how architectural principles, along with their spatial and geometric underpinnings, are essential to ensuring a structure’s durability and strength, its aesthetic design, and its usefulness (Allen 1995; Ching 1996; O’Gorman 1998; Salvadori 1980, 1990). In addition, a number of resources are geared toward students’ actual involvement in architectural design (Abhau, Copeland, and Greenberger 1986; Lupton and Miller 1991; New York State Education Department 1982; Slafer and Cahill 1995)
ReferencesAllen, E. 1995. How buildings work: The natural order of architecture. 2nd ed. New York: Oxford University Press.Blackwell, W. 1984. Geometry in architecture. Berkeley, CA: Key Curriculum Press.
Ching, F.D.K. 1996. Architecture: Form, space, and order. New York: Wiley.
Genkins, E.F. 1971. A comparison of two methods of teaching the concept of bilateral symmetry to young children. EdD diss., Teachers College, Columbia University
Genkins, E.F. 1975. The concept of bilateral symmetry in young children. In Children’s mathematical concepts: Six Piagetian studies in mathematics education, ed. M.F. Rosskopf, 3–41. New York: Teachers College Press.
Lupton, E., and J.A. Miller. 1991. The ABC’s of ??¢: The Bauhaus and design theory from preschool to postmodernism. Princeton, NJ: Princeton Architectural Press.
Mapapá, A. 1994. Symmetries and metal grates in Maputo-Didactic experimentation. In Explorations in ethnomathematics and ethnoscience in Mozambique, ed. P. Gerdes, 49–55. Maputo: Instituto Superior Pedagógico Moçambique.
Ness, D., and S.J. Farenga. 2007. Knowledge under construction: The importance of play in developing children’s spatial and geometric thinking. Lanham, MD: Rowman & Littlefield.
New York State Education Department. 1982. Mathematics/architecture related activities. Albany, NY: The State Department Bureau of Curriculum Development.
O’Gorman, J.F. 1998. ABC of architecture. Philadelphia: University of Pennsylvania Press.
Rosen, J. 1998. Symmetry discovered: Concepts and applications in nature and science. New York: Dover Publications.
Salvadori, M. 1980. Why buildings stand up: The strength of architecture. New York: Norton.
Salvadori, M. 1990. The art of construction: Projects and principles for beginning engineers and architects. Chicago: Chicago Review Press.
Slafer, A., and K. Cahill. 1995. Why design? Activities and projects from the National Building Museum. Chicago: Chicago Review Press.
Weyl, H. 1980. Symmetry. Princeton, NJ: Princeton University Press.
Ching, F.D.K. 1996. Architecture: Form, space, and order. New York: Wiley.
Genkins, E.F. 1971. A comparison of two methods of teaching the concept of bilateral symmetry to young children. EdD diss., Teachers College, Columbia University
Genkins, E.F. 1975. The concept of bilateral symmetry in young children. In Children’s mathematical concepts: Six Piagetian studies in mathematics education, ed. M.F. Rosskopf, 3–41. New York: Teachers College Press.
Lupton, E., and J.A. Miller. 1991. The ABC’s of ??¢: The Bauhaus and design theory from preschool to postmodernism. Princeton, NJ: Princeton Architectural Press.
Mapapá, A. 1994. Symmetries and metal grates in Maputo-Didactic experimentation. In Explorations in ethnomathematics and ethnoscience in Mozambique, ed. P. Gerdes, 49–55. Maputo: Instituto Superior Pedagógico Moçambique.
Ness, D., and S.J. Farenga. 2007. Knowledge under construction: The importance of play in developing children’s spatial and geometric thinking. Lanham, MD: Rowman & Littlefield.
New York State Education Department. 1982. Mathematics/architecture related activities. Albany, NY: The State Department Bureau of Curriculum Development.
O’Gorman, J.F. 1998. ABC of architecture. Philadelphia: University of Pennsylvania Press.
Rosen, J. 1998. Symmetry discovered: Concepts and applications in nature and science. New York: Dover Publications.
Salvadori, M. 1980. Why buildings stand up: The strength of architecture. New York: Norton.
Salvadori, M. 1990. The art of construction: Projects and principles for beginning engineers and architects. Chicago: Chicago Review Press.
Slafer, A., and K. Cahill. 1995. Why design? Activities and projects from the National Building Museum. Chicago: Chicago Review Press.
Weyl, H. 1980. Symmetry. Princeton, NJ: Princeton University Press.
Reading Reflection Notes:
After reading up about the importance geometry has in regards to design, I reminded me of a photo shoot I carried out before the start of term at the Alhambra Palace in Granada, Spain.
I went back over my photographs I took on that particular shoot and realised that Alhambra Palace was a heaven of geometric patterns with its architectural designs. As you can see from the contact sheets I have included after this section of the process book, there is a wide array of complex geometric designs in the photographs and all possess some form of symmetry in its design or composition.
With the readings, it made me consider what forms of symmetry I wanted to establish in my photographs, particularly in regards to bilateral and point symmetry. These were types of symmetry I knew would encourage me to take up unique standpoints in order to create these types of symmetrical compositions. Although, now I'm thinking about the message my photographs sends out through what it depicts. I know that they will provide viewers with visual pleasure through the symmetrical composition and geometric shapes present in the architectural subject's construction that I chose to photograph, but I want to develop on this. I wanted to find the hidden beauty in a style of architectures construction, maybe one that certain societies dislike. This is something I will research into later in the term.
Reading Sources:
1. Leopold, C. (2006) ‘Geometry Concepts in Architectural Design’ in Journal of Geometry and Graphics [Conference Document]. pp. 1–8. Available at: https://www.researchgate.net/publication/237544451_GEOMETRY_CONCEPTS_IN_ARCHITECTURAL_DESIGN (Accessed: November 2013).
2. Drutt, M. (2010) Geometric Shapes: The Architecture of the Solomon R. Guggenheim Museum [Website]. Available at: https://www.guggenheim.org/arts-curriculum/topic/geometric-shapes (Accessed: November 2016).
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