Folds, GIMPS, and More Billiards

Welcome to this week’s Math Munch!

First up, we’ve often featured mathematical constructions made of origami. (Here are some of those posts.) Origami has a careful and peaceful feel to it—a far cry from, say, the quick reflexes often associated with video games. I mean, can you imagine an origami video game?

heartfolds

One of Fold’s many origami puzzles.

Well, guess what—you don’t have to, because Folds is just that! Folds is the creation of Bryce Summer, a 21-year-old game designer from California. It’s so cool. The goal of each level of its levels is simple: to take a square piece of paper and fold it into a given shape. The catch is that you’re only allowed a limited number of folds, so you have to be creative and plan ahead so that there aren’t any loose ends sticking out. As I’ve noted before, my favorite games often require a combo of visual intuition and careful thinking, and Folds certainly fits the bill. Give it a go!

Once you’re hooked, you can find out more about Bryce and how he came to make Folds in this awesome Q&A. Thanks so much, Bryce!

gimpsNext up, did you know that a new largest prime number was discovered less than a month ago? It’s very large—over 17 million digits long! (How many pages would that take to print or write out?) That makes it way larger than the previous record holder, which was “only” about 13 million digits long. Here is an article published on the GIMPS website about the new prime number and about the GIMPS project in general.

What’s GIMPS you ask? GIMPS—the Great Internet Mersenne Primes Search—is an example of what’s called “distributed computing”. Testing whether a number is prime is a simple task that any computer can do, but to check many or large numbers can take a lot of computing time. Even a supercomputer would be overwhelmed by the task all on its own, and that’s if you could even get dedicated time on it. Distributed computing is the idea that a lot of processing can be accomplished by having a lot of computers each do a small amount of work. You can even sign up to help with the project on your own computer. What other tasks might distributed computing be useful for? Searching for aliens, perhaps?

GIMPS searches only for a special kind of prime called Mersenne primes. These primes are one less than a power of two. For instance, 7 is a Mersenne prime, because it’s one less that 8, which is the third power of 2. For more on Mersenne primes, check out this video by Numberphile.

Finally, we’ve previously shared some resources about the math of billiards on Math Munch. Below you’ll find another take on bouncing paths as Michael Moschen combines the math of billiards with the art of juggling.

So lovely. For more on this theme, here’s a second video to check out.

Bon appetit!

35 responses »

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  3. I thought this was amazing!! How was the guy able to catch them so fast and then have to throw the balls right after. But I was getting pretty confused becasue sometimes it looked liked he was hitting the ball instead of catching and throwing them. I wonder how long this took him to master bouncing the balls with his feet ,without even messing up once!

  4. Im still in shock of how he did this! I kind of got lost during some parts of it because the balls were going so fast and it was hard to keep track of where they were but it was very interesting. I cant wait to see more videos of him bouncing the balls and maybe he will use different techniques and use different shapes of walls. 🙂

  5. This was very awesome and interesting. I like the speed the ball went ,even though I will lose it sometimes. I will like to ask a few questions. How do you know where to hit the ball and where to receive it? Will it have the same effect if that frame was a different shape, for example, a hexagon?Does the weight of the ball effect where you’ll throw and receive it?

  6. This is very interesting and awesome video. I like the speed the ball went, even though I will lose it sometimes. I will like to ask a few questions . How do you know where to hit and receive the ball. Will it still have the same effect if the shape of the frame was different, for example, a hexagon. Does the weight of the ball effect where you’ll throw and receive the ball?

  7. This is an interesting and awesome video. I like the speed the ball went, even though I will lose it sometimes. I have a few questions. How do you know where to throw and receive the ball. Will it still have the same effect if the frame wasn’t a triangle, for example, will it work if it was a hexagon. Does the weight of the ball effect where you’ll receive and throw the ball?

  8. This is an interesting and awesome video. I like the speed the ball went, even though I will lose it sometimes. I have a few questions. How do you know where to throw and receive the ball. Will it still have the same effect if the frame wasn’t a triangle, for example, will it work if it was a hexagon. Does the weight of the ball effect where you’ll receive and throw the ball?

  9. I liked the origami game. I got stuck on level 12, because the folds necessary became less obvious. I liked that when you folded the paper, the color became darker. I disliked how the background had lines on it because it influenced my folds. overall, it was a good game.

    • Hi Ashely,
      I’m glad you enjoyed Folds. I hope you’ll return to it to conquer level 12 sometime. True story: after starting Light-bot a few years ago, I only recently completed it! A good game is worth coming back to.
      And so is a good website. I hope you’ll be back to Math Munch soon! 🙂
      Justin

  10. I seriously LOVED this game! It makes my brain work hard and it’s fun. It gets more difficult as you go, but I enjoy the challenge! I hate having to buy paper and make the origami myself. This game seems realistic and it gives you a sense of accomplishment, I do think that if it didn’t have the transparency of the folds, it would make the levels be easier. Although, if there wasn’t a hard part to a game, it would seem boring and lifeless. I like games with a challenge, and this totally made me happy!!! Thank you for showing me this game, I really liked it.

  11. Wow, that video was really awesome. I got confused at some parts when the balls were going really fast in different directions, it was hard to keep track of. How did he keep track of them and know where to throw them?

  12. That man is very skilled in order to do that. I could only imagine how long it would’ve taken him to master an act like that.

  13. I think that the reason the ball bonces really fast in some places and slow in other is because of the gravitational pull on the ball. Also when it hits the walls sometimes the angle is different so it makes the ball move into a different place on the wall. The reason it has to do with math is because it is showing you how the angle on something makes a difference on the overall shape of the object.

  14. I thought the video was very interesting. Its really cool how he threw the balls and they were going fast I got lost sometimes. It must of took him forever to practice all of this.

  15. I’m amazed of how he did this! I wonder how long it took him to practice and memorized it? It got me kind of dizzy after awhile because of all the balls were going everywhere.

  16. i’m amazed of how he did this! I wonder how long it took him to practice? it got me kind of dizzy after awhile because all of the balls were going everywhere.

  17. The balls bouncing everywhere started to get confusing until he stopped for a short while, this must have taken a lot of practice and precise calculation to create! I have one question, how bouncy were those balls when he threw them because he could bounce them with his feet! Did it have to do with something about the structure of the triangle? Or was it a specific material that was used?

  18. The game Folds was very addicting and confusing(especially the final level) but after me getting over my bitter frustration i completed the level

  19. I was really impressed with the juggler, he must have spent numerous hours to figure out the angles he has to throw the balls at to catch them on key. Throwing and catching one ball seems hard enough, but to do it with 3, that real skill!

  20. I watched the video of the juggler and the triangle and I was truly shocked. Not only was the video fun to watch but listening to it was just as amazing. I wonder how many times he practiced until he could catch every throw. Throwing just one ball would have been impressive, but throwing three was truly worth watching. I wonder how much harder the balls would be to follow if they were thrown into different shapes with more sides.

  21. That must of been hard and tooken a long and patient time to know where and when the ball will be and I wonder if he used a different shape would it be the same for him example circle because it has no edges would that be easier or harder but overall I liked the video.

  22. Folds I got stuck on level 11 im still trying to figure it out it is a cool game how you only get 3 chances but you can go back and every level the paper changes and it will get harder

  23. This video was super cool! It’s really amazing how Michael act like he is just figuring this out! I think Michael did a great job of performing, but I am still asking myself how he could stand up to such pressure. Those balls could have flown off course at anytime. this would have effected his performance and his composure. All-in-all, this was an amazing performance that would be tricky for anybody to replicate whatsoever! 🙂

  24. The game was amazing! I’m a fan of origami so this game really caught my eye! I got stuck on the level called ‘Precise Reduction’. I believe I could have made it if I had 1 or 2 more moves, but I guess that’s what makes this game fun-because it’s challenging!

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  26. that video was soo cool. I realized through this video that math isn’t just on paper. Also, i really want one of those bouncy balls!

    • Hi!
      I’m glad the video helped you to see that math is not just on paper. Hopefully, keeping this in mind, you’ll start seeing math pop up all over the place!
      Thanks for reading and commenting,
      Justin

  27. This video is one of the most amazing mathematical performances I have ever seen!!! I’m surprised that he can do that with more than three balls. You would have to have numerous balls in one hand and focus on more than one ball per eye. I assume he learned to juggle first as I would think that would make it easier. Just out of curiosity, how big is the width of the triangle. How much margin of error would you need to hit the edge every single time? The game Folds is also a really fun game. I am terrible at origami and this game made me feel not so bad about my swans that look like pointy blobs. I only made it to level 11 but I am very proud of my self as I thought I would only made it to 6 at the highest!

  28. My critique about the game is that is fun, love how its a challenging brain game, and fun if you are good at origami. My dislikes are that its hard on the finger tips and it was hard acquiring miss folds.A suggestion would be to have two sheets of paper that make two different objects that go together.

  29. Pingback: Nice Neighbors, Spinning GIFs, and Breakfast | Math Munch

  30. WOW! He must have had a LOT of concentration and a lot of practice to not mess up. that was the best mathematicalskit I have ever seen

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