| Search results - "origami" |
Spiked Rhombic EnneacontahedronThis structure was conceived by taking a 90-sided polyhedron, whose faces are made from two types of rhombi, and placing a pyramid on each face. The construction uses 180 small squares of paper, all folded and interlocked together without glue. See more models on the Origami Gallery.
--- Thomas Hull. Photograph by Nancy Rose Marshall.
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Professor Tom HullTom Hull took his Ph.D. in mathematics at the University of Rhode Island in 1997. His dissertation was on list coloring bipartite graphs, now he mostly studies the mathematics of origami (paper folding).
Tom Hull is an associate professor in the Department of Mathematics at Merrimack College in North Andover, MA.
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Nested Hexogonal CollapseThis model is a series of concentric hexagons with "zig-zag" creases coming from the center-most hexagon out to the midpoints of the paper's sides. It can be collapsed in many different ways and twisted into interesting shapes, as done here. See more geometrics and tesselations on the Origami Gallery.
--- Thomas Hull. Photograph by Nancy Rose Marshall.
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Five Intersecting TetrahedraThis is a version of the Ow-Hull "Five Intersecting Tetrahedra." The visually stunning object should be a familiar sight to those who frequent the landscapes of M.C. Escher or like to thumb through geometry textbooks. Read about the object and how it is constructed on the Origami Gallery.
--- Thomas Hull. Photograph by Nancy Rose Marshall.
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"2 Circles in a bi-pentagon pattern," by Bradford Hansen-SmithThe symbol of the circle is used as metaphor for nothing and for everything, and endless parts in-between. Folding circles appears to have little history: Somewhere in the history of origami lies the circle, unrecognized and discarded in favor of the square; Buckminster Fuller also folded the circle, with informational intent. Fuller is the inspiration for my own exploration into geometry and provided the seed for folding and joining circles-9" paper plates.
-- Bradford Hansen-Smith, Wholemovement
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"80 circles in an icosahedron pattern," by Bradford Hansen-SmithYou can also see many hexagonal and pentagonal shapes in this pattern. The symbol of the circle is used as metaphor for nothing and for everything, and endless parts in-between. Folding circles appears to have little history: Somewhere in the history of origami lies the circle, unrecognized and discarded in favor of the square; Buckminster Fuller also folded the circle, with informational intent. Fuller is the inspiration for my own exploration into geometry and provided the seed for folding and joining circles-9" paper plates.
-- Bradford Hansen-Smith, Wholemovement
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"36 circles in a dual tetrahedron pattern" by Bradford Hansen-SmithThe tetrahedron has four faces. The symbol of the circle is used as metaphor for nothing and for everything, and endless parts in-between. Folding circles appears to have little history: Somewhere in the history of origami lies the circle, unrecognized and discarded in favor of the square; Buckminster Fuller also folded the circle, with informational intent. Fuller is the inspiration for my own exploration into geometry and provided the seed for folding and joining circles-9" paper plates.
-- Bradford Hansen-Smith, Wholemovement
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"20 circles in an icosahedron pattern" by Bradford Hansen-SmithAn icosahedron is a solid with 20 faces. This solid has hexagons on its surface with pentagonal indentations. The symbol of the circle is used as metaphor for nothing and for everything, and endless parts in-between. Folding circles appears to have little history: Somewhere in the history of origami lies the circle, unrecognized and discarded in favor of the square; Buckminster Fuller also folded the circle, with informational intent. Fuller is the inspiration for my own exploration into geometry and provided the seed for folding and joining circles-9" paper plates.
--Bradford Hansen-Smith, Wholemovement
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"Fiddler Crab, opus 446," by Robert J. Lang. Medium: One uncut square of Origamido paper, composed and folded in 2004, 4". Image courtesy of Robert J. Lang. Photograph by Robert J. Lang.The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. Origami, like music, also permits both composition and performance as expressions of the art. Over the past 35 years, I have developed over 480 original origami compositions. About a quarter of these have been published with folding instructions, which, in origami, serve the same purpose that a musical score does: it provides a guide to the performer (in origami, the folder) while allowing the performer to express his or her own personality through interpretation and variation.
I'm especially pleased with this model, which involves a combination of symmetry with one distinctly non-symmetric element. The base is quite irregular, but its asymmetry is mostly concealed. The crease pattern is here.
--- Robert J. Lang
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"Fiddler Crab, opus 446" crease pattern, by Robert J. Lang. Copyright Robert J. Lang (www.langorigami.com).Crease patterns (CPs) provide a one-step connection from the unfolded square to the folded form, compressing hundreds of creases, and sometimes hours of folding, into a single diagram! A CP can sometimes be more illuminating than a detailed folding sequence, conveying not just "how to fold," but also how the figure was originally designed. Mathematical and geometric CPs usually show all the creases, but representational origami rarely shows every crease in the finished form, as it would make the crease pattern impossibly busy. Instead, the crease pattern gives the creases needed to fold the "base," that is, a geometric shape that has the right number and arrangements of flaps. It is still left up to the folder to add thinning and shaping folds. See the final "Fiddler Crab" origami work in this album.
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"Night Hunter, opus 469," by Robert J. Lang. Medium: One uncut square of Korean hanji, composed and folded in 2003, 18". Image courtesy of Robert J. Lang. Photograph by Robert J. Lang.The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. Origami, like music, also permits both composition and performance as expressions of the art. Over the past 35 years, I have developed over 480 original origami compositions. About a quarter of these have been published with folding instructions, which, in origami, serve the same purpose that a musical score does: it provides a guide to the performer (in origami, the folder) while allowing the performer to express his or her own personality through interpretation and variation.
--- Robert J. Lang
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"Night Hunter, opus 469" crease pattern, by Robert J. Lang. Copyright Robert J. Lang (www.langorigami.com).Crease patterns (CPs) provide a one-step connection from the unfolded square to the folded form, compressing hundreds of creases, and sometimes hours of folding, into a single diagram! A CP can sometimes be more illuminating than a detailed folding sequence, conveying not just "how to fold," but also how the figure was originally designed. Mathematical and geometric CPs usually show all the creases, but representational origami rarely shows every crease in the finished form, as it would make the crease pattern impossibly busy. Instead, the crease pattern gives the creases needed to fold the "base," that is, a geometric shape that has the right number and arrangements of flaps. It is still left up to the folder to add thinning and shaping folds. See the final "Night Hunter" origami work in this album.
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"Bull Moose, opus 413," by Robert J. Lang. Medium: One uncut square of Nepalese lokta, composed and folded in 2002, 6". Image courtesy of Robert J. Lang. Photograph by Robert J. Lang.The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. Origami, like music, also permits both composition and performance as expressions of the art. Over the past 35 years, I have developed over 480 original origami compositions. About a quarter of these have been published with folding instructions, which, in origami, serve the same purpose that a musical score does: it provides a guide to the performer (in origami, the folder) while allowing the performer to express his or her own personality through interpretation and variation.
--- Robert J. Lang
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"Tree Frog, opus 280," by Robert J. Lang. Medium: One uncut square of Origamido paper, composed in 1993, folded in 2005, 5". Image courtesy of Robert J. Lang. Photograph by Robert J. Lang.The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. Origami, like music, also permits both composition and performance as expressions of the art. Over the past 35 years, I have developed over 480 original origami compositions. About a quarter of these have been published with folding instructions, which, in origami, serve the same purpose that a musical score does: it provides a guide to the performer (in origami, the folder) while allowing the performer to express his or her own personality through interpretation and variation.
--- Robert J. Lang
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"African Elephant, opus 322," by Robert J. Lang. Medium: One uncut square of watercolor paper, composed and folded in 1996, 8". Image courtesy of Robert J. Lang. Photograph by Robert J. Lang.The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. Origami, like music, also permits both composition and performance as expressions of the art. Over the past 35 years, I have developed over 480 original origami compositions. About a quarter of these have been published with folding instructions, which, in origami, serve the same purpose that a musical score does: it provides a guide to the performer (in origami, the folder) while allowing the performer to express his or her own personality through interpretation and variation.
--- Robert J. Lang
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