Related Research Articles
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.
William Kingdon Clifford was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to mathematical physics, geometry, and computing. Clifford was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression mind-stuff.
In botany, phyllotaxis or phyllotaxy is the arrangement of leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature.
Jay Hambidge (1867–1924) was an American artist who formulated the theory of "dynamic symmetry", a system defining compositional rules, which was adopted by several notable American and Canadian artists in the early 20th century.
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry which, in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books. These dynamic rectangles begin with a square, which is extended to form the desired figure, which can be the golden rectangle, the 2:3 rectangle, the double square (1:2), or a root rectangle.
Islamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Denis Louis Blackmore was an American mathematician and a full professor of the Department of Mathematical Sciences at New Jersey Institute of Technology. He was also one of the founding members of the Center for Applied Mathematics and Statistics at NJIT. Dr. Blackmore was mainly known for his many contributions in the fields of dynamical systems and differential topology. In addition to this, he had many contributions in other fields of applied mathematics, physics, biology, and engineering.
Anne Macaulay was a Scottish musicologist, author and lecturer.
Wasma'a Khalid Chorbachi is an American-Iraqi artist.
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. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
Vera Martha Winitzky de Spinadel was an Argentine mathematician. She was the first woman to gain a PhD in mathematics at the University of Buenos Aires, Argentina, in 1958. Between 2010 and 2017, she was full Emeritus Professor in the Faculty of Architecture, Design and Urban Planning of the University of Buenos Aires. In 1995, she was named Director of the Centre of Mathematics and Design. In April 2005 she inaugurated the Laboratory of Mathematics & Design, University Campus in Buenos Aires. From 1998 to her death she was the President of the International Mathematics and Design Association, which organizes international congresses every 3 years and publishes a Journal of Mathematics & Design. She was the author of more than 10 books and published more than 100 research papers. Spinadel was a leader in the field of metallic mean and in the development of the classical Golden Ratio and got wide international recognition.
Muthusamy Lakshmanan is an Indian theoretical physicist currently working as Professor of Eminence at the Department of Nonlinear Dynamics of Bharathidasan University. Presently he is the DST-SERB National Science Chair awarded by the Science and Engineering Research Board, Department of Science and Technology. He has held several research fellowships which included Raja Ramanna fellowship of the Department of Atomic Energy, Alexander von Humboldt fellowship, Japan Society for the Promotion of Science fellowship, Royal Society Nuffield Foundation fellowship, and NASI-Senior Scientist Platinum Jubilee Fellowship. In the year 2021, on August 15, he was conferred with the Dr. A. P. J Abdul Kalam Award by the Government of Tamil Nadu.
In the mathematics of circle packing, a Doyle spiral is a pattern of non-crossing circles in the plane in which each circle is surrounded by a ring of six tangent circles. These patterns contain spiral arms formed by circles linked through opposite points of tangency, with their centers on logarithmic spirals of three different shapes.
Elizabeth Whiteley is an American fine artist and designer.
Slavik Vlado Jablan was a Serbian mathematician and crystallographer. Jablan is known for his contributions to antisymmetry, knot theory, the theory of symmetry and ornament, and ethnomathematics.
References
- ↑ Sol, Levinson. "Funeral home". Sol Levinson funeral home. Retrieved 1 February 2024.
- 1 2 Jay Kappraff (2001). Connections: The Geometric Bridge Between Art and Science. World Scientific. ISBN 978-981-02-4585-6.
- ↑ Bruno Gruber; Giuseppe Marmo; Naotaka Yoshinaga (2004). Symmetries in science XI. Springer. pp. 228 & 238. ISBN 978-1-4020-2633-1.
- ↑ Jay Kappraff (2002). Beyond measure: a guided tour through nature, myth, and number. World Scientific. p. 264. ISBN 978-981-02-4702-7.
