Interested in Artistic Patterns In Hyperbolic Geometry? On this page, we have collected links for you, where you will receive the most necessary information about Artistic Patterns In Hyperbolic Geometry.
https://www.d.umn.edu/~ddunham/dunbrid99.pdf
Artistic Patterns in Hyperbolic Geometry DouglasDunham DepartmentofComputerScience UniversityofMinnesota,Duluth Duluth,MN55812-2496,USA E-mail: [email protected] Abstract From antiquity, humans have created 2-dimensional art on flat …
http://t.archive.bridgesmathart.org/1999/bridges1999-239.pdf
To exhibit the true hyperbolic nature of such art, the pattern must exhibit symmetry and repetition. Thus, it is natural to use a computer to avoid the tedious hand constructions performed by Escher. We show a number of hyperbolic patterns, which are created by combining mathematics, artistic considerations, and computer technology. Introduction
https://www.semanticscholar.org/paper/Artistic-Patterns-in-Hyperbolic-Geometry-Dunham/2c635bab1ed1d235c52c506cc6c409cb0207d9da
Artistic Patterns in Hyperbolic Geometry. @inproceedings {Dunham1999ArtisticPI, title= {Artistic Patterns in Hyperbolic Geometry}, author= {D. Dunham}, year= {1999} } D. Dunham. Published 1999. Computer Science. From antiquity, humans have created 2-dimensional art on flat surfaces (the Euclidean plane) and on surfaces of spheres. However, it wasn't until recently that they have created art in the third "classical geometry", the hyperbolic …
https://www.d.umn.edu/~ddunham/isis4/index.html
Transformation of Hyperbolic Escher Patterns. Abstract: The Dutch artist M. C. Escher is known for his repeating patterns of interlocking motifs. Most of Escher's patterns are Euclidean patterns, but he also designed some for the surface of the sphere and others for the hyperbolic plane, thus making use of all three classical geometries: Euclidean, spherical, and hyperbolic.
https://www.d.umn.edu/~ddunham/dunbrid00.pdf
In the late 1950’s, the Dutch artist M. C. Escher became the fir st person to create hyperbolic art in his four Circle Limit patterns. The pattern of interlocking rings near the edge of his last woodcut Snakes (Catalog Number 448 of [6]) also exhibits hyperbolic symmetry. The goal of this paper is to take a first step toward combining Celtic knot art and hyperbolic geometry. Thus Celtic knot patterns will have …Cited by: 3
https://www.d.umn.edu/~ddunham/dunicgg08.pdf
USE OF MODELS OF HYPERBOLIC GEOMETRY IN THE CREATION OF HYPERBOLIC PATTERNS Douglas J. DUNHAM University of Minnesota Duluth, USA ABSTRACT: In 1958, the Dutch artist M.C. Escher became the first person to create artistic patterns in hyperbolic geometry. He used the Poincar é circle model of hyperbolic geometry.
http://pi.math.cornell.edu/~mec/Winter2009/Mihai/index.html
The Dutch artist M. C. Escher is known for his repeating patterns of interlocking motifs, tessellations of the Euclidean and the hyperbolic plane and his drawing representing impossible figures. Without having any mathematical knowledge, he managed to represent many mathematical concepts belonging to non-Euclidean geometry and many of his drawings are used by mathematicians to illustrate examples.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.3572
ABSTRACT: In 1958, the Dutch artist M.C. Escher became the first person to create artistic patterns in hyperbolic geometry. He used the Poincar é circle model of hyperbolic geometry. Slightly more than 20 years later, my students and I implemented a computer program that could draw repeating hyperbolic patterns in this model.
https://www.d.umn.edu/~ddunham/md04paper.pdf
Escher and others have used the Poincaré circle modelof hyperbolic geometry, which has two properties that are useful for artistic purposes: (1) it is conformal (i.e. the hyperbolic measure of an angle is equal to its Euclidean measure) – consequently a transformed object has roughly the same shape as the original, and (2) it lies entirely within a circle in the Euclidean plane – allowing the viewer to see the entire hyperbolic …
We hope you have found all the information you need about Artistic Patterns In Hyperbolic Geometry through the links above.
