| Search results - "makin" |
8-torus.jpg"The 8-Crossing Torus Knot T(4,3)," by Dror Bar-Natan (University of Toronto, Canada)
This is an example of a torus knot. A torus is a surface best described as a doughnut. A torus knot can be thought of as looping around and through the torus. The symbol T(4,3) means that the string making the knot loops through the hole of the torus 4 times, making 3 revolutions. This knot is drawn with TubePlot.
--- Dror Bar-Natan
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27-torus.jpg"The 27-Crossing Torus Knot T(9,4)," by Dror Bar-Natan (University of Toronto, Canada)
This is an example of a torus knot. A torus is a surface best described as a doughnut. A torus knot can be thought of as looping around and through the torus. The symbol T(9,4) means that the string making the knot loops through the hole of the torus 9 times, making 4 revolutions. This knot is drawn with TubePlot.
--- Dror Bar-Natan
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"The Susurrus of the Sea," by George W. Hart (www.georgehart.com)Soft waves, suggestive of both sky and water, travel around the globe along six different criss-crossing equators. The susurrus (murmur) of the sea is suggested as a sense of harmony in this sphere. Technically difficult, the 60 transparent blue acrylic plastic components had to be made very precisely to fit together. Heat-formed, the components were formed and assembled on special jigs which imparted the proper dimensions and angles. Mathematically, the blue spirals are helixes that follow the edges of an icosidodecahedron. This is a polyhedron that was known to the ancient Greeks, but the oldest known drawing of it is by Leonardo da Vinci. Formally constructed of triangles and pentagons (which show up here as the openings) it can also be seen as an arrangement of six equatorial regular decagons. Each equator makes ten twists in a complete path, crossing the other five equators at two opposite points. If one "walks along" a dark blue edge, making right-angle turns where edges meet, one traces a large five-pointed star before returning to one’s starting point.
--- George W. Hart (www.georgehart.com)
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"The Net," by Mehrdad Garousi (2008)Digital art print, 24" x 18.5". "This image exhibits a very complex, yet ordered series of lonely fibers that are woven in each other. This generated lacy net is not flat and goes to infinity at the center and also many times in each of its main arms. Another wonderful mathematical and artistic representation is where hexaploid weaving is modified into a triple one without cutting or deleting any fibers. Self similarity is the main property of this work, as any small hole in the main arms is nearly similar to the whole image. Having experimented with other media, I chose mathematical fractal image making as one of the newest and most wonderful common areas between mathematics and art." --- Mehrdad Garousi, Freelance fractal artist, painter and photographer, Hamadan, Iran
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"Starfruit," by David MakinDavid Makin is a British computer programmer born in North Wales, who loves fractal geometry and science fiction. The majority of his work comes from his investigations into the use of coloring algorithms. In this case he employed three algorithms applied to a Julia set. The first of his algorithms, named "MMF3-Turning Points," generated the starred forms that characterize the image and suggested the title of the shape immediately to him (the starfruit is a tropical fruit whose cross section produces a five-pointed star). With the second algorithm, "MMF3-Orbital Waves," he used the idea of complementing the first layer with the handsome curved lines that accentuate the set. At this point he proceeded to include the third algorithm, "MMF3-Alternative fBm II," which provides a more organic texture. Finally, David Makin took considerable time in combining the three layers with color palettes and the algorithms described that produced the final result.
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"Five Left Tetrahedral Cosets," by Francisco Lara-Dammer, Indiana University, Bloomington (2008)Digital print, 20" x 20". "This is a Klein diagram (named after the nineteenth-century German mathematician Felix Klein) that represents A5, the group of symmetries of the icosahedron. Another way of describing A5 is as the alternating group on five elements, namely, the group of all even permutations of five entities. This diagram emphasizes A5's tetrahedral subgroup A4 (the group of symmetries of the tetrahedron, also the group of even permutations of four entities), which has twelve elements, plus the four left cosets of A4. The general diagram is obtained by centrally projecting an icosahedron onto a sphere (with the center of one face projected onto the north pole) and then making a stereographic projection of the sphere down onto a horizontal plane. Each coset has been identified with one color. The circle contains a hundred and twenty regions from which sixty correspond to the dark blue background, and the other sixty are split with the five left cosets. The reason I have realized Klein diagrams is to understand more clearly the beauty of Group Theory." --- Francisco Lara-Dammer, Research assistant. Center for Research on Concepts and Cognition, Indiana University, Bloomington, IN
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