Two Plus Two Poker Forums In how many ways can you fold a square piece of paper n times?
 Register FAQ Search Today's Posts Mark Forums Read Video Directory TwoPlusTwo.com

 Notices

 Science, Math, and Philosophy Discussions regarding science, math, and/or philosophy.

 11-03-2010, 10:48 PM #1 imfatandugly grinder   Join Date: Jul 2005 Location: boulder, co Posts: 673 In how many ways can you fold a square piece of paper n times? Trying to calculate this and it seems incredibly hard. I'm going by the rules of oragami, i.e. you can identify any edge with another edge (or crease) and any point where two edges meet to any other point where two edges meet. I'm actually not really sure on those rules, I just want each fold to be exactly reproducible and it seems like that would do it. Lets just say for simplicity sake that after every fold you have to unfold and use the creases as edges. While taking into account symmetries would be cool, i.e. two sequences of folds are equivilant iff they paper can be rotated or reflected to create the other one, it's prob too hard to start off that way. Any ideas about how to go about solving this? for n=1.... 4 possible ways for n=2.... a bunch
11-03-2010, 11:10 PM   #2
Aaron W.
Carpal \'Tunnel

Join Date: Sep 2002
Location: Henderson, NV
Posts: 27,803
Re: In how many ways can you fold a square piece of paper n times?

Quote:
 Originally Posted by imfatandugly Trying to calculate this and it seems incredibly hard. I'm going by the rules of oragami, i.e. you can identify any edge with another edge (or crease) and any point where two edges meet to any other point where two edges meet. I'm actually not really sure on those rules, I just want each fold to be exactly reproducible and it seems like that would do it. Lets just say for simplicity sake that after every fold you have to unfold and use the creases as edges. While taking into account symmetries would be cool, i.e. two sequences of folds are equivilant iff they paper can be rotated or reflected to create the other one, it's prob too hard to start off that way. Any ideas about how to go about solving this? for n=1.... 4 possible ways for n=2.... a bunch
I think with a lot of these combinatorial problems, the trick is to find some way of representing the folds, and then dealing with those rather than dealing with the pictures themselves.

Perhaps it might make sense to have some sort of "level k fold" where k is somehow the count of the depth of folds (how many folds it takes to create this fold), and then try counting from there. It will at least help you to wrap your mind around the possibilities.

For example...

There are 4 level 0 folds (two diagonal and two orthogonal).
There are 14 level 1 folds (4 for each diagonal fold, and 3 for each orthogonal fold)
Etc.

Then to find out how many ways you can have two folds, you take two level 0 folds, or you take one level 0 and one level 1 fold.

Hope this gives you a good start. (For all I know, it will crash and burn at level 2 folds!)

11-04-2010, 12:04 AM   #3
imfatandugly
grinder

Join Date: Jul 2005
Location: boulder, co
Posts: 673
Re: In how many ways can you fold a square piece of paper n times?

Quote:
 Originally Posted by Aaron W. I think with a lot of these combinatorial problems, the trick is to find some way of representing the folds, and then dealing with those rather than dealing with the pictures themselves. Perhaps it might make sense to have some sort of "level k fold" where k is somehow the count of the depth of folds (how many folds it takes to create this fold), and then try counting from there. It will at least help you to wrap your mind around the possibilities. For example... There are 4 level 0 folds (two diagonal and two orthogonal). There are 14 level 1 folds (4 for each diagonal fold, and 3 for each orthogonal fold) Etc. Then to find out how many ways you can have two folds, you take two level 0 folds, or you take one level 0 and one level 1 fold. Hope this gives you a good start. (For all I know, it will crash and burn at level 2 folds!)
This just got me thinking... maybe it's enough to know that you can make a new crease from any two preexisting creases uniquely. The problem is that sometimes you double count.
(Anyways this makes a relatively easy upper bound)
So when do you "accidentally" align two edges together when you are trying to align two other edges together?

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Two Plus Two     Two Plus Two Magazine Forum     The Best of Two Plus Two     The Two Plus Two Bonus Program     Two Plus Two Pokercast     Two Plus Two Videos     Marketplace         General Marketplace         Staking - Offering Stakes         Staking - Seeking Stakes         Staking - Selling Shares - Online         Staking - Selling Shares - Live         Staking Rails         Transaction Feedback & Disputes     Commercial Marketplace     Staking - Offering Stakes     About the Forums Fantasy Sports     Fantasy Sports         Sporting Events General Poker Discussion     Beginners Questions     Live Casino Poker         Poker Venues         Regional Communities     Poker Goals & Challenges     Books and Publications     Poker Theory     Poker Tells/Behavior, hosted by: Zachary Elwood     News, Views, and Gossip     Twitch - Watch and Discuss Live Online Poker     Televised Poker     Home Poker     Poker Legislation & PPA Discussion hosted by Rich Muny     That's What She Said!     Poker Beats, Brags, and Variance Coaching/Training     Coaching Advice     Cash Game Poker Coach Listings     Tournament/SNG Poker Coach Listings International Forums     Deutsch         BBV [German]     Français     Two Plus Two en Espańol No Limit Hold'em     Medium-High Stakes PL/NL     Micro-Small Stakes PL/NL     Medium-High Stakes Full Ring     Micro-Small Stakes Full Ring     Heads Up NL     Live Low-stakes NL Limit Texas Hold'em     Mid-High Stakes Limit     Micro-Small Stakes Limit Tournament Poker     STT Strategy     Heads Up SNG and Spin and Gos     Mid-High Stakes MTT     Small Stakes MTT     MTT Community     MTTc - Live         WPT.com Other Poker     High Stakes PL Omaha     Small Stakes PL Omaha     Omaha/8     Stud     Draw and Other Poker General Gambling     Backgammon Forum hosted by Bill Robertie.     Probability     Psychology     Sports Betting     Other Gambling Games Internet Poker     Internet Poker         Winning Poker Network         nj.partypoker.com         Global Poker     Commercial Software     Software         Commercial Software         Free Software     nj.partypoker.com         WPT.com 2+2 Communities     Other Other Topics         OOTV         Game of Thrones     The Lounge: Discussion+Review     EDF     Las Vegas Lifestyle     BBV4Life         omg omg omg     House of Blogs Sports and Games     Sporting Events         Single-Team Season Threads         Fantasy Sports     Wrestling     Golf     Pool, Snooker, and Billiards     Chess and Other Board Games     Video Games         League of Legends         Hearthstone     Puzzles and Other Games Other Topics     Politics         Economics     Business, Finance, and Investing     Travel     Science, Math, and Philosophy     History     Religion, God, and Theology     Health and Fitness     Student Life     The Studio     Laughs or Links!     Computer Technical Help     Programming

All times are GMT -4. The time now is 01:10 AM.

 Contact Us - Two Plus Two Publishing LLC - Privacy Statement - Top