Mathematics of landscape design
The Mathematics of landscape design integrates mathematical concepts with architectural and horticultural practices to create aesthetically pleasing and functional outdoor spaces. This field requires knowledge from various disciplines, including engineering, visual arts, and horticulture, with mathematics playing a crucial role in aspects such as plant placement, erosion resistance, and geometric design elements. Landscape architects often employ principles of symmetry and geometric shapes to achieve visual harmony, while advanced mathematical concepts, like fractals, may be used in specific designs.
Design elements in landscape architecture revolve around lines, shapes, sizes, textures, and colors, expressed through natural and human-made materials. Patterns and principles like repetition and balance are essential for creating focal points, such as sculptures and flower beds. Additionally, cultural practices, such as feng shui and ancient Egyptian geometry, highlight the historical connection between mathematics and landscape design, illustrating how spirituality and practicality intertwine in shaping environments.
Financial considerations also play a role, as well-designed landscapes can significantly enhance property value. As a result, mathematical calculations are essential for budgeting landscaping projects, making this field not only an artistic endeavor but also a financially strategic one.
Mathematics of landscape design
Summary: Landscape design is an application of geometry, shaping an outdoor environment to something pleasing.
Landscape design is the combination of gardening and architecture for making outdoors environments more aesthetically pleasing, ergonomic, and useful.
It is a synthetic occupation, requiring the knowledge and skills of horticulturists, engineers, architects, and visual artists.
Mathematical calculations underlie many aspects of landscape design, such as how many plants are needed to fill a bed or landscape or how to build a landscaped terrace that will resist erosion. Landscape architects often include design elements based on symmetry and other geometric features of areas, surfaces, and three-dimensional elements. More advanced mathematical forms, such as fractals or labyrinths, are incorporated in some landscapes, like crop circles. Peter Schaar was an applied mathematician for many years before turning to a career as a landscape designer. He noted that the notion of an elegant solution is common to both mathematics and garden design.
Design Elements and Principles
Landscape design, like other forms of design and decorating, uses design principles and elements that are mathematical in their nature. The Western traditions of landscape design typically use lists of elements, including the following:
- Line
- Shape
- Size
- Texture
- Color
Every element is expressed through natural or architectural media, including plants, stones, and ground shapes. Straight or curved lines and shapes are created using hedges, paths, flower borders, and shapes of bushes and trees. Sizes of landscape elements, including stones, plants, and built structures, can match or contrast. Textures and color can be natural, such as foliage, water, grass, and stone, or modified by people, such as cut bushes, polished stones, and painted structures.
Likewise, the artistic principles, such as repetition, balance, and focal points, are achieved with the combination of human-made and natural elements. For example, traditional landscaping focal points include sculptures, fountains, and flower beds.
Sacred Traditions and the Development of Mathematics
Building, gardening, and designing landscapes were connected to spiritual practices by many cultures around the world. The resulting complexity of habitats often elevated mathematical and scientific knowledge, as well as the arts within the cultures practicing these traditions.
For example, feng shui is the Chinese design tradition connected with the development of astronomy and precise measurement instruments, such as magnetic compasses and astrolabes. Mathematical ideas involved in feng shui symbols include binary numbers, powers, and combinatorics.
Some mid-African cultures use fractal structures in village design, where the shape of the village is repeated in shapes of house clusters, then houses, then rooms within houses. The shape is connected to the beliefs of the people and reflected in the lore while at the same time being practical for the needs of the village.
Ancient Egyptians used the concept of gnomon, which is a specially constructed geometric shape corresponding to a regular polygon, in their area and architecture calculations. When a gnomon is added, the ratio of polygon sides is maintained. Osiris was associated with this idea of the constant ratio, in the myth as the God of Sun, growth, and constant change, and was often drawn on a square throne expanded with the L-shaped gnomon. These geometric traditions were inherited by the Greeks, formalized as Euclid’s geometry, and entered the Western knowledge base.
Budgets and Rates
Landscaping expenses include the price of material and labor for construction and maintenance. It is estimated that in the United States, a house with its landscape design rated “excellent” by experts can sell for 5% to 10% more than the same house with its design rated “good.” Therefore, it may make financial sense to spend money landscaping the property. These calculations are performed by developers and real estate agents when deciding landscaping budgets.
Bibliography
Agnew, Michael, Nancy Agnew, Nick Christians, and Ann VanDerZanden. Mathematics for the Green Industry: Essential Calculations for Horticulture and Landscape Professionals. Hoboken, NJ: Wiley, 2008.
Ferrater, Borja, and Carlos Ferrater. Synchronizing Geometry: Landscape, Architecture & Construction. New York: Actar, 2006.
Winn, Becky. “The Mathematician’s Garden.” Dhome, February 2006. http://www.dmagazine.com/Home/2006/02/16/The‗Mathematicians‗Garden.aspx.