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Recent documents in The Open Repository @ Binghamton (The ORB)en-usThu, 14 Dec 2017 02:07:40 PST3600Ultra Frosted Detail Curved Trivalent Tree Pendant
http://orb.binghamton.edu/mathematical_sculptures/482
http://orb.binghamton.edu/mathematical_sculptures/482Fri, 08 Dec 2017 12:35:15 PST
Curved Trivalent Tree Pendant, made by 3D printing at Shapeways.com.
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Alex J. FeingoldPolished Bronze Steel Curved Trivalent Tree Pendant
http://orb.binghamton.edu/mathematical_sculptures/481
http://orb.binghamton.edu/mathematical_sculptures/481Fri, 08 Dec 2017 12:35:11 PST
Curved Trivalent Tree Pendant, made by 3D printing at Shapeways.com.
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Alex J. FeingoldRhodium Plated Brass Curved Trivalent Tree Pendant
http://orb.binghamton.edu/mathematical_sculptures/480
http://orb.binghamton.edu/mathematical_sculptures/480Fri, 08 Dec 2017 12:35:07 PST
Curved Trivalent Tree Pendant, made by 3D printing at Shapeways.com.
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Alex J. FeingoldTimborana Wood (3,5) Torus Knot , Figure 2
http://orb.binghamton.edu/mathematical_sculptures/479
http://orb.binghamton.edu/mathematical_sculptures/479Fri, 08 Dec 2017 12:35:03 PST
A (3,5) torus knot carved from a 3"x8"x8" block of timborana wood. The size of this torus knot is approximately 3" deep and 8" in diameter.
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Alex J. FeingoldTimborana Wood (3,5) Torus Knot , Figure 1
http://orb.binghamton.edu/mathematical_sculptures/478
http://orb.binghamton.edu/mathematical_sculptures/478Fri, 08 Dec 2017 12:34:59 PST
A (3,5) torus knot carved from a 3"x8"x8" block of timborana wood. The size of this torus knot is approximately 3" deep and 8" in diameter.
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Alex J. FeingoldCast bronze bell
http://orb.binghamton.edu/mathematical_sculptures/477
http://orb.binghamton.edu/mathematical_sculptures/477Fri, 08 Dec 2017 12:34:55 PST
Cast bronze bell on a small wooden base, hung from a bronze rod arch
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Alex J. FeingoldBronze Kinetic Sound Sculpture. Figure 2
http://orb.binghamton.edu/mathematical_sculptures/476
http://orb.binghamton.edu/mathematical_sculptures/476Fri, 08 Dec 2017 12:34:51 PST
A bronze kinetic sound sculpture with 13 rods arranged in a G2 pattern (Star of David).
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Alex J. FeingoldBronze Kinetic Sound Sculpture. Figure 1
http://orb.binghamton.edu/mathematical_sculptures/475
http://orb.binghamton.edu/mathematical_sculptures/475Fri, 08 Dec 2017 12:34:47 PST
A bronze kinetic sound sculpture with 13 rods arranged in a G2 pattern (Star of David).
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Alex J. FeingoldCocobolo Wood (3,5) Torus Knots, Figure 3
http://orb.binghamton.edu/mathematical_sculptures/474
http://orb.binghamton.edu/mathematical_sculptures/474Fri, 08 Dec 2017 12:34:44 PST
A pair of (3,5) Torus Knots carved from two pieces of cocobolo wood. One of them is about 3.5" in diameter, and the other is about 3.8" in diameter.
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Alex J. FeingoldCocobolo Wood (3,5) Torus Knots, Figure 2
http://orb.binghamton.edu/mathematical_sculptures/473
http://orb.binghamton.edu/mathematical_sculptures/473Fri, 08 Dec 2017 12:34:40 PST
A pair of (3,5) Torus Knots carved from two pieces of cocobolo wood. One of them is about 3.5" in diameter, and the other is about 3.8" in diameter.
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Alex J. FeingoldCocobolo Wood (3,5) Torus Knots, Figure 1
http://orb.binghamton.edu/mathematical_sculptures/472
http://orb.binghamton.edu/mathematical_sculptures/472Fri, 08 Dec 2017 12:34:37 PST
A pair of (3,5) Torus Knots carved from two pieces of cocobolo wood. One of them is about 3.5" in diameter, and the other is about 3.8" in diameter.
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Alex J. FeingoldBrazilian Cherry Wood Genus 3 Knot, Figure 4
http://orb.binghamton.edu/mathematical_sculptures/471
http://orb.binghamton.edu/mathematical_sculptures/471Fri, 08 Dec 2017 12:34:32 PST
The Brazilian Cherry wood carving was made from a block of size 3"x10"x10" and the completed piece is 9.5" in diameter and 2.75" deep. This carving was inspired by a design of an artist from Shapeways. During the carving process the curves going through the three holes were made more shallow, so they ended up forming a single long curve that passed through each hole twice (once going up and once going down).
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Alex J. FeingoldBrazilian Cherry Wood Genus 3 Knot, Figure 3
http://orb.binghamton.edu/mathematical_sculptures/470
http://orb.binghamton.edu/mathematical_sculptures/470Fri, 08 Dec 2017 12:34:29 PST
The Brazilian Cherry wood carving was made from a block of size 3"x10"x10" and the completed piece is 9.5" in diameter and 2.75" deep. This carving was inspired by a design of an artist from Shapeways. During the carving process the curves going through the three holes were made more shallow, so they ended up forming a single long curve that passed through each hole twice (once going up and once going down).
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Alex J. FeingoldBrazilian Cherry Wood Genus 3 Knot, Figure 2
http://orb.binghamton.edu/mathematical_sculptures/469
http://orb.binghamton.edu/mathematical_sculptures/469Fri, 08 Dec 2017 12:34:26 PST
The Brazilian Cherry wood carving was made from a block of size 3"x10"x10" and the completed piece is 9.5" in diameter and 2.75" deep. This carving was inspired by a design of an artist from Shapeways. During the carving process the curves going through the three holes were made more shallow, so they ended up forming a single long curve that passed through each hole twice (once going up and once going down).
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Alex J. FeingoldBrazilian Cherry Wood Genus 3 Knot, Figure 1
http://orb.binghamton.edu/mathematical_sculptures/468
http://orb.binghamton.edu/mathematical_sculptures/468Fri, 08 Dec 2017 12:34:22 PST
The Brazilian Cherry wood carving was made from a block of size 3"x10"x10" and the completed piece is 9.5" in diameter and 2.75" deep. This carving was inspired by a design of an artist from Shapeways. During the carving process the curves going through the three holes were made more shallow, so they ended up forming a single long curve that passed through each hole twice (once going up and once going down).
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Alex J. FeingoldBlack Palm Wood (3,5) Torus Knot, Figure 3
http://orb.binghamton.edu/mathematical_sculptures/467
http://orb.binghamton.edu/mathematical_sculptures/467Fri, 08 Dec 2017 12:34:17 PST
A (3,5) torus knot carved from Black Palm wood. The original block of wood was 2"x4"x4" but the completed piece is approximately 3.75" in diameter and 1.75" deep.
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Alex J. FeingoldBlack Palm Wood (3,5) Torus Knot, Figure 2
http://orb.binghamton.edu/mathematical_sculptures/466
http://orb.binghamton.edu/mathematical_sculptures/466Fri, 08 Dec 2017 12:34:12 PST
A (3,5) torus knot carved from Black Palm wood. The original block of wood was 2"x4"x4" but the completed piece is approximately 3.75" in diameter and 1.75" deep.
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Alex J. FeingoldBlack Palm Wood (3,5) Torus Knot, Figure 1
http://orb.binghamton.edu/mathematical_sculptures/465
http://orb.binghamton.edu/mathematical_sculptures/465Fri, 08 Dec 2017 12:34:09 PST
A (3,5) torus knot carved from Black Palm wood. The original block of wood was 2"x4"x4" but the completed piece is approximately 3.75" in diameter and 1.75" deep.
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Alex J. FeingoldRight Regular Rigid 3D Hexagon
http://orb.binghamton.edu/mathematical_sculptures/464
http://orb.binghamton.edu/mathematical_sculptures/464Fri, 08 Dec 2017 12:34:05 PST
A distinguished professor at the Institut des Hautes Etudes Scientifiques (IHES) demonstrated an interesting mathematical toy. It consisted of 6 L-shaped pieces, each of which could be attached to one end of another, making a 3D polygon where all angles were 90 degree angles (at the elbows of each L). At the points of contact, where two legs of different L's form a straight line, the only motion possible was a twisting rotation. When arranged initially as 6 edges of a cube (each edge being two legs of two different L's), there were two possible choices. For the choice of initial position, shown in the second picture below, the object is rigid, and will not flex at all. The version of this toy was made using wooden dowels, PVC pipe corners and tubes, and strong neodymium magnets and steel washers. 10 L's were made to experiment with these right regular 3D polygons with 6, 7, 8, 9 or 10 edges. The motion can be quite complex for larger polygons! Analysis of the possible positions leads to some rather deep mathematics.
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Alex J. FeingoldSycamore Wood (3,5) Torus Knot, Figure 3
http://orb.binghamton.edu/mathematical_sculptures/463
http://orb.binghamton.edu/mathematical_sculptures/463Fri, 08 Dec 2017 12:34:01 PST
Ccarved from a 2"x4"x4" piece of Sycamore wood, and is a (3,5) Torus Knot
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Alex J. FeingoldSycamore Wood (3,5) Torus Knot, Figure 2
http://orb.binghamton.edu/mathematical_sculptures/462
http://orb.binghamton.edu/mathematical_sculptures/462Fri, 08 Dec 2017 12:33:57 PST
Ccarved from a 2"x4"x4" piece of Sycamore wood, and is a (3,5) Torus Knot
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Alex J. FeingoldSycamore Wood (3,5) Torus Knot, Figure 1
http://orb.binghamton.edu/mathematical_sculptures/461
http://orb.binghamton.edu/mathematical_sculptures/461Fri, 08 Dec 2017 12:33:53 PST
Ccarved from a 2"x4"x4" piece of Sycamore wood, and is a (3,5) Torus Knot
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Alex J. FeingoldAmazakoue Wood Genus 3 Triple Link, Figure 4
http://orb.binghamton.edu/mathematical_sculptures/460
http://orb.binghamton.edu/mathematical_sculptures/460Fri, 08 Dec 2017 12:33:49 PST
Carved from a 2"x6"x6" piece of Amazakoue wood. It has three holes, making a genus 3 surface. The raised edges form three separate curves, each of which pass through a pair of holes. It is called a Genus 3 Triple Link. It was inspired by a surface made by another artist on Shapeways.com, but it is not hollow since it was carved from one piece of wood.
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Alex J. FeingoldAmazakoue Wood Genus 3 Triple Link, Figure 3
http://orb.binghamton.edu/mathematical_sculptures/459
http://orb.binghamton.edu/mathematical_sculptures/459Fri, 08 Dec 2017 12:33:46 PST
Carved from a 2"x6"x6" piece of Amazakoue wood. It has three holes, making a genus 3 surface. The raised edges form three separate curves, each of which pass through a pair of holes. It is called a Genus 3 Triple Link. It was inspired by a surface made by another artist on Shapeways.com, but it is not hollow since it was carved from one piece of wood.
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Alex J. FeingoldAmazakoue Wood Genus 3 Triple Link, Figure 2
http://orb.binghamton.edu/mathematical_sculptures/458
http://orb.binghamton.edu/mathematical_sculptures/458Fri, 08 Dec 2017 12:33:41 PST
Carved from a 2"x6"x6" piece of Amazakoue wood. It has three holes, making a genus 3 surface. The raised edges form three separate curves, each of which pass through a pair of holes. It is called a Genus 3 Triple Link. It was inspired by a surface made by another artist on Shapeways.com, but it is not hollow since it was carved from one piece of wood.
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Alex J. FeingoldAmazakoue Wood Genus 3 Triple Link, Figure 1
http://orb.binghamton.edu/mathematical_sculptures/457
http://orb.binghamton.edu/mathematical_sculptures/457Fri, 08 Dec 2017 12:33:37 PST
Carved from a 2"x6"x6" piece of Amazakoue wood. It has three holes, making a genus 3 surface. The raised edges form three separate curves, each of which pass through a pair of holes. It is called a Genus 3 Triple Link. It was inspired by a surface made by another artist on Shapeways.com, but it is not hollow since it was carved from one piece of wood.
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Alex J. FeingoldTransparent Acrylic Material Saddle Trivalent Tree Pendant
http://orb.binghamton.edu/mathematical_sculptures/456
http://orb.binghamton.edu/mathematical_sculptures/456Fri, 08 Dec 2017 12:33:33 PST
Saddle Trivalent Tree Pendant, 3D printed by Shapeways.com in transparent acrylic material. In this design the tree is draped on a ``saddle surface", that is, a hyperbolic paraboloid, z = x2 - y2, like a potato chip. The previous version was draped on the cap of a sphere. The curvature is rather gentle, so it does not show very clearly in these pictures.
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Alex J. FeingoldRhodium Plated Brass Saddle Trivalent Tree Pendant
http://orb.binghamton.edu/mathematical_sculptures/455
http://orb.binghamton.edu/mathematical_sculptures/455Fri, 08 Dec 2017 12:33:29 PST
Saddle Trivalent Tree Pendant, 3D printed by Shapeways.com in Rhodium plated brass. In this design the tree is draped on a ``saddle surface", that is, a hyperbolic paraboloid, z = x2 - y2, like a potato chip. The previous version was draped on the cap of a sphere. The curvature is rather gentle, so it does not show very clearly in these pictures.
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Alex J. FeingoldSpalted Tamarind Block Twist and
http://orb.binghamton.edu/mathematical_sculptures/454
http://orb.binghamton.edu/mathematical_sculptures/454Fri, 08 Dec 2017 12:33:26 PST
A small ``Twist" sculpture next to the torus knot, for comparison of sizes. The Twist scuplture is approximately 1.75" in diameter and 2" tall.
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Alex J. FeingoldSpalted Tamarind Block Twist, Figure 3
http://orb.binghamton.edu/mathematical_sculptures/453
http://orb.binghamton.edu/mathematical_sculptures/453Fri, 08 Dec 2017 12:33:23 PST
A small ``Twist" sculpture made from the center cylinder of the Spalted Tamarind block. It is approximately 1.75" in diameter and 2" tall.
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Alex J. FeingoldSpalted Tamarind Block Twist, Figure 2
http://orb.binghamton.edu/mathematical_sculptures/452
http://orb.binghamton.edu/mathematical_sculptures/452Fri, 08 Dec 2017 12:33:19 PST
A small ``Twist" sculpture made from the center cylinder of the Spalted Tamarind block. It is approximately 1.75" in diameter and 2" tall.
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Alex J. FeingoldSpalted Tamarind Torus Knot and Spalted Tamarind Block Twist
http://orb.binghamton.edu/mathematical_sculptures/451
http://orb.binghamton.edu/mathematical_sculptures/451Fri, 08 Dec 2017 12:33:15 PST
A small ``Twist" sculpture made from the center cylinder of the Spalted Tamarind block. It is approximately 1.75" in diameter and 2" tall.
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Alex J. FeingoldSpalted Tamarind Wood (3,5) Torus Knot, Figure 2
http://orb.binghamton.edu/mathematical_sculptures/450
http://orb.binghamton.edu/mathematical_sculptures/450Fri, 08 Dec 2017 12:33:12 PST
Torus knot carved from a 2"x6"x6" block of spalted tamarind wood.
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Alex J. FeingoldSpalted Tamarind Wood (3,5) Torus Knot, Figure 1
http://orb.binghamton.edu/mathematical_sculptures/449
http://orb.binghamton.edu/mathematical_sculptures/449Fri, 08 Dec 2017 12:33:08 PST
Torus knot carved from a 2"x6"x6" block of spalted tamarind wood.
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Alex J. Feingold