Search results
Results from the WOW.Com Content Network
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically . Natural patterns include symmetries , trees , spirals , meanders , waves , foams , tessellations , cracks and stripes. [ 1 ]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art, and music. The opposite of symmetry is asymmetry, which refers to the absence of symmetry.
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.
Self-similarity can be found in nature, as well. To the right is a mathematically generated, perfectly self-similar image of a fern, which bears a marked resemblance to natural ferns. Other plants, such as Romanesco broccoli, exhibit strong self-similarity.
According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein. [5] Many forms observed in nature can be related to geometry; for example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape.
In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged.
Examples of the use of mathematics in the visual arts include applications of chaos theory and fractal geometry to computer-generated art, symmetry studies of Leonardo da Vinci, projective geometries in development of the perspective theory of Renaissance art, grids in Op art, optical geometry in the camera obscura of Giambattista della Porta ...