GcatWiki - User contributions [en]

What other math problems (e.g. NP- complete) are accessible to us? Annie Siya Sun

2009-05-25T19:34:09Z

Antemmink:

'''Rigid fold''' origami may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

Problems according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli? -http://kahuna.merrimack.edu/~thull/rigid/rigid.html (the book is Oragami Design Secrets by Robert Lang- a leading math guy/origami designer)

''interesting topics and vocab:''

*circle river packing-a design technique for uniaxial bases (a base in which all flaps lie along a single axis and all hinges are perpendicular to the axis) that constructs the crease pattern by packing nonoverlapping circles and rivers into a square.

*box pleating-a style of folding characterized by all folds running at multiples of 45°, with the majority running at multiples of 0° and 90° on a regular grid.

*oragami bases- basic folds from which many other shapes can be folded

*crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes

*definitions taken from: http://www.langorigami.com/info/glossary.php4#tree%20graph

-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

Origami and NP Complete! apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this -from the book origami3 by Thomas Hull -google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1 this seems like a great collection of papers that relate all aspects of oragami to math

*This links to a paper showing/proving that flat fold problems can be NP complete. Very interesting
http://reference.kfupm.edu.sa/content/c/o/the_complexity_of_flat_origami__299207.pdf
more on np complete and flat folding
www.siam.org/pdf/news/579.pdf

*Link to information about 3 SAT problems (what they are) http://en.wikipedia.org/wiki/Boolean_satisfiability_problem

Retrieved from "http://gcat.davidson.edu/GcatWiki/index.php/What_other_math_problems_%28e.g._NP-_complete%29_are_accessible_to_us%3F_Siya_Sun"

What other math problems (e.g. NP- complete) are accessible to us? Annie Siya Sun

2009-05-19T19:43:04Z

Antemmink:

'''Rigid fold''' origami may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

Problems according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli? -http://kahuna.merrimack.edu/~thull/rigid/rigid.html (the book is Oragami Design Secrets by Robert Lang- a leading math guy/origami designer)

''interesting topics and vocab:''

*circle river packing-a design technique for uniaxial bases (a base in which all flaps lie along a single axis and all hinges are perpendicular to the axis) that constructs the crease pattern by packing nonoverlapping circles and rivers into a square.

*box pleating-a style of folding characterized by all folds running at multiples of 45°, with the majority running at multiples of 0° and 90° on a regular grid.

*oragami bases- basic folds from which many other shapes can be folded

*crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes

*definitions taken from: http://www.langorigami.com/info/glossary.php4#tree%20graph

-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

Origami and NP Complete! apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this -from the book origami3 by Thomas Hull -google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1 this seems like a great collection of papers that relate all aspects of oragami to math

*This links to a paper showing/proving that flatfold problems can be NP complete. Very interesting
http://reference.kfupm.edu.sa/content/c/o/the_complexity_of_flat_origami__299207.pdf

*Link to information about 3 SAT problems (what they are) http://en.wikipedia.org/wiki/Boolean_satisfiability_problem

Retrieved from "http://gcat.davidson.edu/GcatWiki/index.php/What_other_math_problems_%28e.g._NP-_complete%29_are_accessible_to_us%3F_Siya_Sun"

What other math problems (e.g. NP- complete) are accessible to us? Annie Siya Sun

2009-05-19T19:37:29Z

Antemmink:

Rigid fold origami may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

Problems according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli? -http://kahuna.merrimack.edu/~thull/rigid/rigid.html (the book is Oragami Design Secrets by Robert Lang- a leading math guy/origami designer)

interesting topics and vocab:

circle river packing-a design technique for uniaxial bases (a base in which all flaps lie along a single axis and all hinges are perpendicular to the axis) that constructs the crease pattern by packing nonoverlapping circles and rivers into a square.

box pleating-a style of folding characterized by all folds running at multiples of 45°, with the majority running at multiples of 0° and 90° on a regular grid.

*oragami bases- basic folds from which many other shapes can be folded

*crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes

*definitions taken from: http://www.langorigami.com/info/glossary.php4#tree%20graph

-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

Origami and NP Complete! apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this -from the book origami3 by Thomas Hull -google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1 this seems like a great collection of papers that relate all aspects of oragami to math

This links to a paper showing/proving that flatfold problems can be NP complete. Very interesting
http://reference.kfupm.edu.sa/content/c/o/the_complexity_of_flat_origami__299207.pdf

Link to information about 3 SAT problems (what they are) http://en.wikipedia.org/wiki/Boolean_satisfiability_problem

Retrieved from "http://gcat.davidson.edu/GcatWiki/index.php/What_other_math_problems_%28e.g._NP-_complete%29_are_accessible_to_us%3F_Siya_Sun"

Missouri Western/Davidson iGEM2009

2009-05-19T19:29:47Z

Antemmink:

This space will be used starting April, 2009 for brainstorming and a shared whiteboard space.

[http://gcat.davidson.edu/GcatWiki/index.php/Davidson_Missouri_W/Davidson_Protocols Davidson Lab Protocols] 
[http://gcat.davidson.edu/GcatWiki/index.php/Davidson_Missouri_W/MWSU_protocols MWSU Lab Protocols] 
[http://gcat.davidson.edu/sybr-u/bmc.html BioMath Connections Page] 
[http://gcat.davidson.edu/GCATalog-r2.1/GCATalog.htm GCAT-alog Freezer Stocks] 

We need to learn more about these topics:
<center>'''Biology-based'''</center>

#[[What is msDNA?]]
#[[How is msDNA normally produced?]] Olivia/Alyndria
#[[How many copies are carried per cell?]] Alyndria
#[[What would we need to do to turn this into a BioBrick device?]] Romina
#[[ How could we swap out msDNA sequences?]] Shamita
#[[What role can physical modeling of protein structure play in our project?]]
#[[What role can physical modeling of proteins play in our project? Eric Sawyer]]
#[[What other cool reporters are there? (Discrete On/Off or Continuous) Bryce Szczepanik]]
#[[Can we use promoter strength/opposite directions to subtract? Clif Davis]]
#[[Can we use suppressor tRNAs to encode logical operators (suppressor suppressor logic, SSL)?]]
#[[How is msDNA stored in E. coli?]] Olivia
#[[What is the sequence of bacterial reverse transcriptase and can we clone that gene?]] Shamita
#[[Can we redesign the normal msDNA pathway to produce new segments of DNA of our choosing?]] All
#[[What are other available reverse transcriptases?]] Leland
#[[What other math problems (e.g. NP- complete) are accessible to us? Annie Siya Sun]]
#[[What is the relationship between 3-SAT and map coloring? Ashley Schnoor]]
#[[What activators are there that turn on a promoter without any help?]]
#[[Can we use protein interactions to compute? (Post-translation, proteases, quaternary structure) Will Vernon]]
#[[Could we do something with clocks/counting?]]
#[[Could we have/use multiple synthetic organelles in a cell?]]
#[[What ideas from previous iGEM teams are useful to us?]]

<center>'''Math-based'''</center>
#[[Can we get bacteria to solve a problem large enough to challenge a person?]]
#[[What interesting challenges or problems does origami offer?]]
#[[Can we produce a series of increasingly difficult goals that might be possible to produce in the lab?]]
#[[What has been done before and how can we improve upon that?]]
#[[We can perform some pilot experiments using synthesized DNA and later switch to msDNA (maybe).]]
#[[Can we address the Boolean Satisfiability (SAT) problem with a bacterial computer?]]
#[[How has 3SAT been addressed with a DNA computer? Can we use those methods?]]

#Can we get bacteria to solve a problem large enough to challenge a computer (probably not, but it is fun to think about)?
#[[What are some linear algebra applications for DNA origami?]]
#[[How can we use origami to solve 3-SAT problems?]]

<center>'''Behavior-based'''</center>
#[[What constructs are we testing?]]
#[[What school districts do we have access to?]]
#[[Where is the Synthetic Biology page we want high school teachers to use after the survey?]]
#[[Do you need any more input from the veterans before the survey is ready?]]

<center>'''Solving The 3SAT Problem Using Suppressor Logic'''</center>
#[[Can we solve a 3-SAT problem with supressor logic?]]

Help:Contents

2009-05-19T15:43:31Z

Antemmink:

http://meta.wikimedia.org/wiki/Help:Editing

Missouri Western/Davidson iGEM2009

2009-05-19T15:41:12Z

Antemmink:

This space will be used starting April, 2009 for brainstorming and a shared whiteboard space.

[http://gcat.davidson.edu/GcatWiki/index.php/Davidson_Missouri_W/Davidson_Protocols Davidson Lab Protocols] 
[http://gcat.davidson.edu/GcatWiki/index.php/Davidson_Missouri_W/MWSU_protocols MWSU Lab Protocols] 
[http://gcat.davidson.edu/sybr-u/bmc.html BioMath Connections Page] 
[http://gcat.davidson.edu/GCATalog-r2.1/GCATalog.htm GCAT-alog Freezer Stocks] 

We need to learn more about these topics:
<center>'''Biology-based'''</center>

#[[What is msDNA?]]
#[[How is msDNA normally produced?]] Olivia/Alyndria
#[[How many copies are carried per cell?]] Alyndria
#[[What would we need to do to turn this into a BioBrick device?]] Romina
#[[ How could we swap out msDNA sequences?]] Shamita
#[[What role can physical modeling of protein structure play in our project?]]
#[[What role can physical modeling of proteins play in our project? Eric Sawyer]]
#[[What other cool reporters are there? (Discrete On/Off or Continuous) Bryce Szczepanik]]
#[[Can we use promoter strength/opposite directions to subtract? Clif Davis]]
#[[Can we use suppressor tRNAs to encode logical operators (suppressor suppressor logic, SSL)?]]
#[[How is msDNA stored in E. coli?]] Olivia
#[[What is the sequence of bacterial reverse transcriptase and can we clone that gene?]] Shamita
#[[Can we redesign the normal msDNA pathway to produce new segments of DNA of our choosing?]] All
#[[What are other available reverse transcriptases?]] Leland
#[[What other math problems (e.g. NP- complete) are accessible to us? Siya Sun]]
#[[What is the relationship between 3-SAT and map coloring? Ashley Schnoor]]
#[[What activators are there that turn on a promoter without any help?]]
#[[Can we use protein interactions to compute? (Post-translation, proteases, quaternary structure) Will Vernon]]
#[[Could we do something with clocks/counting?]]
#[[Could we have/use multiple synthetic organelles in a cell?]]
#[[What ideas from previous iGEM teams are useful to us?]]

<center>'''Math-based'''</center>
#[[Can we get bacteria to solve a problem large enough to challenge a person?]]
#[[What interesting challenges or problems does origami offer?]]
#[[Can we produce a series of increasingly difficult goals that might be possible to produce in the lab?]]
#[[What has been done before and how can we improve upon that?]]
#[[We can perform some pilot experiments using synthesized DNA and later switch to msDNA (maybe).]]
#[[Can we address the Boolean Satisfiability (SAT) problem with a bacterial computer?]]
#[[How has 3SAT been addressed with a DNA computer? Can we use those methods?]]

#Can we get bacteria to solve a problem large enough to challenge a computer (probably not, but it is fun to think about)?
#[[What are some linear algebra applications for DNA origami?]]
#[[How can we use origami to solve 3-SAT problems?]]

<center>'''Behavior-based'''</center>
#[[What constructs are we testing?]]
#[[What school districts do we have access to?]]
#[[Where is the Synthetic Biology page we want high school teachers to use after the survey?]]
#[[Do you need any more input from the veterans before the survey is ready?]]

<center>'''Solving The 3SAT Problem Using Suppressor Logic'''</center>
#[[Can we solve a 3-SAT problem with supressor logic?]]

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T03:28:59Z

Antemmink:

'''Rigid fold origami''' may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html
(the book is Oragami Design Secrets by Robert Lang- a leading math guy/origami designer)

[[interesting topics and vocab:]]

'''circle river packing'''-a design technique for uniaxial bases (a base in which all flaps lie along a single axis and all hinges are perpendicular to the axis) that constructs the crease pattern by packing nonoverlapping circles and rivers into a square.

'''box pleating'''-a style of folding characterized by all folds running at multiples of 45°, with the majority running at multiples of 0° and 90° on a regular grid.

'''oragami bases'''- basic folds from which many other shapes can be folded

'''crease patterns'''- really interesting patterns start to show up on paper when you unfold complex oragami shapes

definitions taken from: http://www.langorigami.com/info/glossary.php4#tree%20graph

-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Origami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this
-from the book origami3 by Thomas Hull
-google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1
this seems like a great collection of papers that relate all aspects of oragami to math

Link to information about 3 SAT problems (what they are)
http://en.wikipedia.org/wiki/Boolean_satisfiability_problem

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T03:12:27Z

Antemmink:

'''Rigid fold origami''' may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html
(the book is Oragami Design Secrets by Robert Lang- a leading math guy/origami designer)

[[interesting topics:]]
'''circle river packing'''-a design technique for uniaxial bases (a base in which all flaps lie along a single axis and all hinges are perpendicular to the axis) that constructs the crease pattern by packing nonoverlapping circles and rivers into a square.

'''box pleating'''-a style of folding characterized by all folds running at multiples of 45°, with the majority running at multiples of 0° and 90° on a regular grid.

'''tree theory'''-
'''oragami bases'''- basic folds from which many other shapes can be folded

''crease patterns''- really interesting patterns start to show up on paper when you unfold complex oragami shapes

-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Origami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this
-from the book origami3 by Thomas Hull
-google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1
this seems like a great collection of papers that relate all aspects of oragami to math

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T03:10:24Z

Antemmink:

'''Rigid fold origami''' may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html
(the book is Oragami Design Secrets by Robert Lang- a leading math guy/origami designer)
[[interesting topics:]]
''circle river packing''-a design technique for uniaxial bases (a base in which all flaps lie along a single axis and all hinges are perpendicular to the axis) that constructs the crease pattern by packing nonoverlapping circles and rivers into a square.
''box pleating''-a style of folding characterized by all folds running at multiples of 45°, with the majority running at multiples of 0° and 90° on a regular grid.
''tree theory''-
''oragami bases''- basic folds from which many other shapes can be folded

''crease patterns''- really interesting patterns start to show up on paper when you unfold complex oragami shapes

-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Origami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this
-from the book origami3 by Thomas Hull
-google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1
this seems like a great collection of papers that relate all aspects of oragami to math

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T03:00:02Z

Antemmink:

'''Rigid fold origami''' may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html
(the book is Oragami Design Secrets by Robert Lang- a leading math guy/origami designer)
[[interesting topics:]]
circle river packing-
box pleating-
tree theory-
oragami bases- basic folds from which many other shapes can be folded

crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes

-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Origami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this
-from the book origami3 by Thomas Hull
-google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1
this seems like a great collection of papers that relate all aspects of oragami to math

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T02:59:11Z

Antemmink:

'''Rigid fold origami''' may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html
(the book is Oragami Design Secrets by Robert Lang- a leading math guy/origami designer)
interesting topics:
circle river packing-
box pleating-
tree theory-
oragami bases- basic folds from which many other shapes can be folded
crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes
-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Origami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this
-from the book origami3 by Thomas Hull
-google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1
this seems like a great collection of papers that relate all aspects of oragami to math

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T02:52:15Z

Antemmink:

'''Rigid fold origami''' may pose interesting problems. Most origami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds.(most research has been about analysing crease patterns to determine flatfoldability, but it would be interesting to examine a 3d shape instead. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html

(book is Oragami Design Secrets by Robert Lang- a leading math guy/orgmi designer)
interesting topics:
circle river packing-
box pleating-
tree theory-
oragami bases- basic folds from which many other shapes can be folded
crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes
-google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Oragami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this
-from the book oragami3 by Thomas Hull
-google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1
this seems like a great collection of papers that relate all aspects of oragami to math

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T02:45:11Z

Antemmink:

'''Rigid fold oragmi''' may pose interesting problems. Most oragami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html

(book is Oragami Design Secrets by Robert Lang- a leading math guy/orgmi designer)
interesting topics:
circle river packing-
box pleating-
tree theory-
oragami bases- basic folds from which many other shapes can be folded
crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes

google book preview: http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Oragami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this
-from the book oragami3 by Thomas Hull
-google book preview: http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1
this seems like a great collection of papers that relate all aspects of oragami to math

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T02:43:28Z

Antemmink:

'''Rigid fold oragmi''' may pose interesting problems. Most oragami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html

(book is Oragami Design Secrets by Robert Lang- a leading math guy/orgmi designer)
interesting topics:
circle river packing-
box pleating-
tree theory-
oragami bases- basic folds from which many other shapes can be folded
crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes

http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Oragami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonal creases can fold by a series of simple folds is NP complete"...need more info on this

-http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1
this seems like a great collection of papers that relate all aspects of oragami to math

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T02:41:33Z

Antemmink:

'''Rigid fold oragmi''' may pose interesting problems. Most oragami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html

(book is Oragami Design Secrets by Robert Lang- a leading math guy/orgmi designer)
interesting topics:
circle river packing-
box pleating-
tree theory-
oragami bases- basic folds from which many other shapes can be folded
crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes

http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

'''Oragami and NP Complete!'''
apparently slight generalizations of map folding problems are np complete (pages 10-11 of this book)"deciding whether a rectangle with horixontal, vertical and diagonalcreases can fold by a series of simple folds is NP complete"

this seems like a great collection of papers that relate all aspects of oragami to math
http://books.google.com/books?id=_Nw4Hg89qxoC&pg=PA1&lpg=PA1&dq=linear+algebra+in+orgigami&source=bl&ots=0Usk4d8xHc&sig=-Hh8gFCSJHHcDn3C0MN0vmTXjAA&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=8#PPA10,M1

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T02:18:36Z

Antemmink:

'''Rigid fold oragmi''' may pose interesting problems. Most oragami is not made with rigid folds(making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- no bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.

linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

[[Problems]]
according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding- could be of interest. Maybe we could figure out, given a shape, if and how it can be broken down into rigid folds. Maybe there could be a way to categorize the simple shapes that make up complex shapes that could be modled and tested by ecoli?
-http://kahuna.merrimack.edu/~thull/rigid/rigid.html

(book is ''Oragami Design Secrets'' by Robert Lang- a leading math guy/orgmi designer)
interesting topics:
circle river packing-
box pleating-
tree theory-
oragami bases- basic folds from which many other shapes can be folded
crease patterns- really interesting patterns start to show up on paper when you unfold complex oragami shapes

http://books.google.com/books?id=tqGm8LeomyYC&pg=PT4&lpg=PT4&dq=linear+algebra+in+orgigami&source=bl&ots=XpHe8Zp205&sig=fV-izurvanpIUxqC30RnesVfd0E&hl=en&ei=Pd0RSrXmNYqMtgeW0YCICA&sa=X&oi=book_result&ct=result&resnum=5#PPT265,M1

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T01:31:59Z

Antemmink:

What other math problems (e.g. NP- complete) are accessible to us? Siya Sun

2009-05-19T01:27:20Z

Antemmink:

Rigid fold oragmi may pose interesting problems. Most oragami is not made with rigid fold oragami (making it a more unusual phenomenon) a rigid fold is one that could be made with sheet metal and hinges- not bending or twisting just a simple hinge fold from flat to not flat. these folds are of interest to industrial designers/manufactures/package designers and are also becoming useful for solarpanels in space (Miura map fold was one used for sending solarpanels into space)/telescope folding etc.
linear algebra could be used in modeling these kinds of folds particularly using isometry rotation (rotations that preserve distance, thus insuring that folds are rigid....because a bend/crease would not preserve distance)

according to this site not much research has been done on the field, particularly when there is more than one vertex involved in the folding. p