2004-06-28
Fwd: NYTimes.com: Cones, Curves, Shells, Towers: He Made Paper Jump to Life
Look at the photographs in this newspaper article.
Is the universe just extremely intricate origami art?
http://www.nytimes.com/2004/06/22/science/22orig.html?ex=1089191452&ei=1&en=11df3feb4219df92
>Cones, Curves, Shells, Towers: He Made Paper Jump to Life
>
>June 22, 2004
> By MARGARET WERTHEIM
>
>Correction Appended
>
>SANTA CRUZ, Calif. - On the mantel of a quiet suburban home
>here stands a curious object resembling a small set of
>organ pipes nestled into a neat, white case. At first
>glance it does not seem possible that such a complex,
>curving form could have been folded from a single sheet of
>paper, and yet it was.
>
>The construction is one of an astonishing collection of
>paper objects folded by Dr. David Huffman, a former
>professor of computer science at the University of
>California, Santa Cruz, and a pioneer in computational
>origami, an emerging field with an improbable name but
>surprisingly practical applications.
>
>Dr. Huffman died in 1999, but on a recent afternoon his
>daughter Elise Huffman showed a visitor a sampling of her
>father's enigmatic models. In contrast to traditional
>origami, where all folds are straight, Dr. Huffman
>developed structures based around curved folds, many
>calling to mind seedpods and seashells. It is as if paper
>has been imbued with life.
>
>In another innovative approach, Dr. Huffman explored
>structures composed of repeating three-dimensional units -
>chains of cubes and rhomboids, and complex tesselations of
>triangular, pentagonal and star-shaped blocks. From the
>outside, one model appears to be just a rolled-up sheet of
>paper, but looking down the tube reveals a miniature spiral
>staircase. All this has been achieved with no cuts or glue,
>the one classic origami rule that Dr. Huffman seemed
>inclined to obey.
>
>Derived from the Japanese ori, to fold, and gami, paper,
>origami has come a long way from cute little birds and
>decorative boxes. Mathematicians and scientists like Dr.
>Huffman have begun mapping the laws that underlie folding,
>converting words and concepts into algebraic rules.
>Computational origami, also known as technical folding, or
>origami sekkei, draws on fields that include computational
>geometry, number theory, coding theory and linear algebra.
>This weekend, paper folders from around the nation will
>gather at the Fashion Institute of Technology in New York
>for the annual convention of Origami USA. At an adjacent
>conference on origami and education, Dr. Robert Lang, a
>leading computational origamist, will give a talk on
>mathematics and its application to origami design,
>including such real-world problems as folding airbags and
>space-based telescopes.
>
>Dr. Lang, a laser physicist in Alamo, Calif., who trained
>at the California Institute of Technology, gave up that
>career 18 months ago to become a full-time folder. "Some
>people are peculiarly susceptible to the charms of
>origami," he said, "and somewhere along the way the ranks
>of the infected were joined by mathematicians." Dr. Lang is
>the author of a recent book on technical folding, "Origami
>Design Secrets: Mathematical Methods for an Ancient Art."
>
>Most computational origamists are driven by sheer curiosity
>and the aesthetic pleasure of these structures, but their
>work is also finding application in fields like astronomy
>and protein folding, and even automobile safety. These days
>when Dr. Lang is not inventing new models using a
>specialized origami software package he has developed, he
>acts as an origami consultant. He has helped a German
>manufacturer design folding patterns for airbags and
>advised astronomers on how to fold up a huge flat-screen
>lens for a telescope based in space.
>
>Dr. Lang has been studying Dr. Huffman's models and
>research notes, and is amazed at what he has found.
>Although Dr. Huffman is a legend in the tiny world of
>origami sekkei, few people have seen his work. During his
>life he published only one paper on the subject. Dr.
>Huffman worked on his foldings from the early 1970's, and
>over the years, said Dr. Lang, "he anticipated a great deal
>of what other people have since rediscovered or are only
>now discovering. At least half of what he did is unlike
>anything I've seen."
>
>One of Dr. Huffman's main interests was to calculate
>precisely what structures could be folded to avoid putting
>strain on the paper. Through his mathematics, he was trying
>to understand "when you have multiple folds coming into a
>point, what is the relationship of the angles so the paper
>won't stretch or tear,'' said Dr. Michael Tanner, a former
>computer science colleague of Dr. Huffman who is now
>provost and vice chancellor for academic affairs at the
>University of Illinois in Chicago.
>
>What fascinated him above all else, Dr. Tanner said, "was
>how the mathematics could become manifest in the paper.
>You'd think paper can't do that, but he'd say you just
>don't know paper well enough."
>
>One of Dr. Huffman's discoveries was the critical "pi
>condition." This says that if you have a point, or vertex,
>surrounded by four creases and you want the form to fold
>flat, then opposite angles around the vertex must sum to
>180 degrees - or using the measure that mathematicians
>prefer, to pi radians. Others have rediscovered that
>condition, Dr. Lang said, and it has now generalized for
>more than four creases. In this case, whatever the number
>of creases, all alternate angles must sum to pi. How and
>under what conditions things can fold flat is a major
>concern in computational origami.
>
>Dr. Huffman's folding was a private activity.
>Professionally he worked in the field of coding and
>information theory. As a student at M.I.T. in the 1950's,
>he discovered a minimal way of encoding information known
>as Huffman Codes, which are now used to help compress MP3
>music files and JPEG images. Dr. Peter Newman of the
>Computer Science Laboratory at the Stanford Research
>Institute said that in everything Dr. Huffman did, he was
>obsessed with elegance and simplicity. "He had an ability
>to visualize problems and to see things that nobody had
>seen before," Dr. Newman said.
>
>Like Mr. Resch, Dr. Huffman seemed innately attracted to
>elegant forms. Before he took up paper folding, he was
>interested in what are called "minimal surfaces," the
>shapes that soap bubbles make. He carried this theme into
>origami, experimenting with ways that pleated patterns of
>straight folds can give rise to curving three-dimensional
>surfaces. Dr. Erik Demaine of M.I.T.'s Laboratory for
>Computer Science, who is now pursuing similar research,
>described Dr. Huffman's work in this area as "awesome."
>
>Finally, Dr. Huffman moved into studying models in which
>the folds themselves were curved. "We know almost nothing
>about curved creases," said Dr. Demaine, who is using
>computer software to simulate the behavior of paper under
>the influence of curving folds. Much of Dr. Huffman's
>research was based on curves derived from conic sections,
>such as the hyperbola and the ellipse.
>
>His marriage of aesthetics and science has grown into a
>field that goes well beyond paper. Dr. Tanner noted that
>his research is relevant to real-world problems where you
>want to know how sheets of material will behave under
>stress. Pressing sheet metal for car bodies is one example.
>"Understanding what's going to happen to the metal,'' which
>will stretch, "is related to the question of how far it is
>from the case of paper," which will not, Dr. Tanner said.
>
>The mathematician G. H. Hardy wrote that "there is no
>permanent place in the world for ugly mathematics." Dr.
>Huffman, who gave concrete form to beautiful mathematical
>relations, would no doubt have agreed. In a talk he gave at
>U.C. Santa Cruz in 1979 to an audience of artists and
>scientists, he noted that it was rare for the two groups to
>communicate with one another.
>
>"I don't claim to be an artist. I'm not even sure how to
>define art," he said. "But I find it natural that the
>elegant mathematical theorems associated with paper
>surfaces should lead to visual elegance as well."
>
>An article in Science Times on Tuesday about Dr. David
>Huffman, a pioneer in the application of math to origami,
>misspelled the surname of a computer scientist who praised
>Dr. Huffman's ability to visualize problems. He is Dr.
>Peter G. Neumann, not Newman. The article also used an
>outdated name for the institution where Dr. Neumann conducts research. It
>is SRI International, no longer the Stanford Research Institute.
Is the universe just extremely intricate origami art?
http://www.nytimes.com/2004/06/22/science/22orig.html?ex=1089191452&ei=1&en=11df3feb4219df92
>Cones, Curves, Shells, Towers: He Made Paper Jump to Life
>
>June 22, 2004
> By MARGARET WERTHEIM
>
>Correction Appended
>
>SANTA CRUZ, Calif. - On the mantel of a quiet suburban home
>here stands a curious object resembling a small set of
>organ pipes nestled into a neat, white case. At first
>glance it does not seem possible that such a complex,
>curving form could have been folded from a single sheet of
>paper, and yet it was.
>
>The construction is one of an astonishing collection of
>paper objects folded by Dr. David Huffman, a former
>professor of computer science at the University of
>California, Santa Cruz, and a pioneer in computational
>origami, an emerging field with an improbable name but
>surprisingly practical applications.
>
>Dr. Huffman died in 1999, but on a recent afternoon his
>daughter Elise Huffman showed a visitor a sampling of her
>father's enigmatic models. In contrast to traditional
>origami, where all folds are straight, Dr. Huffman
>developed structures based around curved folds, many
>calling to mind seedpods and seashells. It is as if paper
>has been imbued with life.
>
>In another innovative approach, Dr. Huffman explored
>structures composed of repeating three-dimensional units -
>chains of cubes and rhomboids, and complex tesselations of
>triangular, pentagonal and star-shaped blocks. From the
>outside, one model appears to be just a rolled-up sheet of
>paper, but looking down the tube reveals a miniature spiral
>staircase. All this has been achieved with no cuts or glue,
>the one classic origami rule that Dr. Huffman seemed
>inclined to obey.
>
>Derived from the Japanese ori, to fold, and gami, paper,
>origami has come a long way from cute little birds and
>decorative boxes. Mathematicians and scientists like Dr.
>Huffman have begun mapping the laws that underlie folding,
>converting words and concepts into algebraic rules.
>Computational origami, also known as technical folding, or
>origami sekkei, draws on fields that include computational
>geometry, number theory, coding theory and linear algebra.
>This weekend, paper folders from around the nation will
>gather at the Fashion Institute of Technology in New York
>for the annual convention of Origami USA. At an adjacent
>conference on origami and education, Dr. Robert Lang, a
>leading computational origamist, will give a talk on
>mathematics and its application to origami design,
>including such real-world problems as folding airbags and
>space-based telescopes.
>
>Dr. Lang, a laser physicist in Alamo, Calif., who trained
>at the California Institute of Technology, gave up that
>career 18 months ago to become a full-time folder. "Some
>people are peculiarly susceptible to the charms of
>origami," he said, "and somewhere along the way the ranks
>of the infected were joined by mathematicians." Dr. Lang is
>the author of a recent book on technical folding, "Origami
>Design Secrets: Mathematical Methods for an Ancient Art."
>
>Most computational origamists are driven by sheer curiosity
>and the aesthetic pleasure of these structures, but their
>work is also finding application in fields like astronomy
>and protein folding, and even automobile safety. These days
>when Dr. Lang is not inventing new models using a
>specialized origami software package he has developed, he
>acts as an origami consultant. He has helped a German
>manufacturer design folding patterns for airbags and
>advised astronomers on how to fold up a huge flat-screen
>lens for a telescope based in space.
>
>Dr. Lang has been studying Dr. Huffman's models and
>research notes, and is amazed at what he has found.
>Although Dr. Huffman is a legend in the tiny world of
>origami sekkei, few people have seen his work. During his
>life he published only one paper on the subject. Dr.
>Huffman worked on his foldings from the early 1970's, and
>over the years, said Dr. Lang, "he anticipated a great deal
>of what other people have since rediscovered or are only
>now discovering. At least half of what he did is unlike
>anything I've seen."
>
>One of Dr. Huffman's main interests was to calculate
>precisely what structures could be folded to avoid putting
>strain on the paper. Through his mathematics, he was trying
>to understand "when you have multiple folds coming into a
>point, what is the relationship of the angles so the paper
>won't stretch or tear,'' said Dr. Michael Tanner, a former
>computer science colleague of Dr. Huffman who is now
>provost and vice chancellor for academic affairs at the
>University of Illinois in Chicago.
>
>What fascinated him above all else, Dr. Tanner said, "was
>how the mathematics could become manifest in the paper.
>You'd think paper can't do that, but he'd say you just
>don't know paper well enough."
>
>One of Dr. Huffman's discoveries was the critical "pi
>condition." This says that if you have a point, or vertex,
>surrounded by four creases and you want the form to fold
>flat, then opposite angles around the vertex must sum to
>180 degrees - or using the measure that mathematicians
>prefer, to pi radians. Others have rediscovered that
>condition, Dr. Lang said, and it has now generalized for
>more than four creases. In this case, whatever the number
>of creases, all alternate angles must sum to pi. How and
>under what conditions things can fold flat is a major
>concern in computational origami.
>
>Dr. Huffman's folding was a private activity.
>Professionally he worked in the field of coding and
>information theory. As a student at M.I.T. in the 1950's,
>he discovered a minimal way of encoding information known
>as Huffman Codes, which are now used to help compress MP3
>music files and JPEG images. Dr. Peter Newman of the
>Computer Science Laboratory at the Stanford Research
>Institute said that in everything Dr. Huffman did, he was
>obsessed with elegance and simplicity. "He had an ability
>to visualize problems and to see things that nobody had
>seen before," Dr. Newman said.
>
>Like Mr. Resch, Dr. Huffman seemed innately attracted to
>elegant forms. Before he took up paper folding, he was
>interested in what are called "minimal surfaces," the
>shapes that soap bubbles make. He carried this theme into
>origami, experimenting with ways that pleated patterns of
>straight folds can give rise to curving three-dimensional
>surfaces. Dr. Erik Demaine of M.I.T.'s Laboratory for
>Computer Science, who is now pursuing similar research,
>described Dr. Huffman's work in this area as "awesome."
>
>Finally, Dr. Huffman moved into studying models in which
>the folds themselves were curved. "We know almost nothing
>about curved creases," said Dr. Demaine, who is using
>computer software to simulate the behavior of paper under
>the influence of curving folds. Much of Dr. Huffman's
>research was based on curves derived from conic sections,
>such as the hyperbola and the ellipse.
>
>His marriage of aesthetics and science has grown into a
>field that goes well beyond paper. Dr. Tanner noted that
>his research is relevant to real-world problems where you
>want to know how sheets of material will behave under
>stress. Pressing sheet metal for car bodies is one example.
>"Understanding what's going to happen to the metal,'' which
>will stretch, "is related to the question of how far it is
>from the case of paper," which will not, Dr. Tanner said.
>
>The mathematician G. H. Hardy wrote that "there is no
>permanent place in the world for ugly mathematics." Dr.
>Huffman, who gave concrete form to beautiful mathematical
>relations, would no doubt have agreed. In a talk he gave at
>U.C. Santa Cruz in 1979 to an audience of artists and
>scientists, he noted that it was rare for the two groups to
>communicate with one another.
>
>"I don't claim to be an artist. I'm not even sure how to
>define art," he said. "But I find it natural that the
>elegant mathematical theorems associated with paper
>surfaces should lead to visual elegance as well."
>
>An article in Science Times on Tuesday about Dr. David
>Huffman, a pioneer in the application of math to origami,
>misspelled the surname of a computer scientist who praised
>Dr. Huffman's ability to visualize problems. He is Dr.
>Peter G. Neumann, not Newman. The article also used an
>outdated name for the institution where Dr. Neumann conducts research. It
>is SRI International, no longer the Stanford Research Institute.
Subscribe to Posts [Atom]