Vector graphics is a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as points, lines, curves and polygons. The associated mechanisms may include vector display and printing hardware, vector data models and file formats, as well as the software based on these data models. Vector graphics is an alternative to raster or bitmap graphics, with each having advantages and disadvantages in specific situations.
Origami is the Japanese art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word kirigami to refer to designs which use cuts.
The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability, and the use of paper folds to solve up-to cubic mathematical equations.
Peter Engel is an American origami artist and theorist, science writer, graphic designer, and architect. He has written several books on Origami, including Origami from Angelfish to Zen, 10-Fold Origami: Fabulous Paperfolds You Can Make in Just 10 Steps!, and Origami Odyssey.
Erik D. Demaine is a professor of computer science at the Massachusetts Institute of Technology and a former child prodigy.
Robert J. Lang is an American physicist who is also one of the foremost origami artists and theorists in the world. He is known for his complex and elegant designs, most notably of insects and animals. He has studied the mathematics of origami and used computers to study the theories behind origami. He has made great advances in making real-world applications of origami to engineering problems.
In geometry, a hendecagram is a star polygon that has eleven vertices.
Origamic architecture is a form of kirigami that involves the three-dimensional reproduction of architecture and monuments, on various scales, using cut-out and folded paper, usually thin paperboard. Visually, these creations are comparable to intricate 'pop-ups', indeed, some works are deliberately engineered to possess 'pop-up'-like properties. However, origamic architecture tends to be cut out of a single sheet of paper, whereas most pop-ups involve two or more. To create the three-dimensional image out of the two-dimensional surface requires skill akin to that of an architect.
Godfried Theodore Patrick Toussaint was a Canadian computer scientist, a professor of computer science, and the head of the Computer Science Program at New York University Abu Dhabi (NYUAD) in Abu Dhabi, United Arab Emirates. He is considered to be the father of computational geometry in Canada. He did research on various aspects of computational geometry, discrete geometry, and their applications: pattern recognition, motion planning, visualization, knot theory, linkage (mechanical) reconfiguration, the art gallery problem, polygon triangulation, the largest empty circle problem, unimodality, and others. Other interests included meander (art), compass and straightedge constructions, instance-based learning, music information retrieval, and computational music theory.
Thomas C. Hull is an associate professor of mathematics at Western New England University and is known for his expertise in the mathematics of paper folding.
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.
The Vegreville egg is a giant sculpture of a pysanka, a Ukrainian-style Easter egg. The work by Paul Maxym Sembaliuk is built of an intricate set of two-dimensional anodized aluminum tiles in the shape of congruent equilateral triangles and star-shaped hexagons, fashioned over an aluminum framework. The egg is 31 ft (9 m) long and three and a half storeys high, weighing in at 2.5 t (5,512 lb). It is the second largest pysanka in the world.
Jay Kappraff is an American professor of mathematics at the New Jersey Institute of Technology and author.
David Albert Huffman was an American pioneer in computer science, known for his Huffman coding. He was also one of the pioneers in the field of mathematical origami.
Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding, and polyhedral nets, by Erik Demaine and Joseph O'Rourke. It was published in 2007 by Cambridge University Press (ISBN 978-0-521-85757-4). A Japanese-language translation by Ryuhei Uehara was published in 2009 by the Modern Science Company (ISBN 978-4-7649-0377-7).
Rona Gurkewitz is an American mathematician and computer scientist, known for her work on modular origami. She is a professor emerita of computer science at Western Connecticut State University, and the former head of the department of computer science there.
Tomohiro Tachi is a Japanese academic who studies origami from an interdisciplinary perspective, combining approaches from the mathematics of paper folding, structural rigidity, computational geometry, architecture, and materials science. His work was profiled in "The Origami Revolution" (2017), part of the Nova series of US science documentaries. He is a professor at the University of Tokyo.
Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger and published by Arbelos Publishing in 2008. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
