# MoMA, Pop-Up Books, and A Game of Numbers

Welcome to this week’s Math Munch!

Thank you so much to everyone who participated in our Math Munch “share campaign” over the past two weeks. Over 200 shares were reported and we know that even more sharing happened “under the radar”. Thanks for being our partners in sharing great math experiences and curating the mathematical internet.

Of course, we know that the sharing will continue, even without a “campaign”. Thanks for that, too.

All right, time to share some math. On to the post!

To kick things off, you might like to check out our brand-new Q&A with Nalini Joshi. A choice quote from Nalini:

In contrast, doing math was entirely different. After trying it for a while, I realized that I could take my time, try alternative beginnings, do one step after another, and get to glimpse all kinds of possibilities along the way.

By Philippe Decrauzat.

I hope the math munches I share with you this week will help you to “glimpse all kinds of possibilities,” too!

Recently I went to the Museum of Modern Art (MoMA) in New York City. (Warning: don’t confuse MoMA with MoMath!) On display was an exhibit called Abstract Generation. You can view the pieces of art in the exhibit online.

As I browsed the galley, the sculptures by Tauba Auerbach particularly caught my eye. Here are two of the sculptures she had on display at MoMA:

Just looking at them, these sculptures are definitely cool. However, they become even cooler when you realize that they are pop-up sculptures! Can you see how the platforms that the sculptures sit on are actually the covers of a book? Neat!

Here’s a video that showcases all of Tauba’s pop-ups in their unfolding glory. Why do you think this series of sculptures is called [2,3]?

This idea of pop-up book math intrigued me, so I started searching around for some more examples. Below you’ll find a video that shows off some incredible geometric pop-ups in action. To see how you can make a pop-up sculpture of your own, check out this how-to video. Both of these videos were created by paper engineer Peter Dahmen.

Tauba Auerbach.

Tauba got me thinking about math and pop-up books, but there’s even more to see and enjoy on her website! Tauba’s art gives me new ways to connect with and reimagine familiar structures. Remember our post about the six dimensions of color? Tauba created a book that’s a color space atlas! The way that Tauba plays with words in these pieces reminds me both of the word art of Scott Kim and the word puzzles of Douglas Hofstadter. Some of Tauba’s ink-on-paper designs remind me of the work of Chloé Worthington. And Tauba’s piece Componants, Numbers gives me some new insight into Brandon Todd Wilson’s numbers project.

This piece by Tauba is a Math Munch fave!

For me, both math and art are all about playing with patterns, images, structures, and ideas. Maybe that’s why math and art make such a great combo—because they “play” well together!

Speaking of playing, I’d like to wrap up this week’s post by sharing a game about numbers I ran across recently. It’s called . . . A Game of Numbers! I really like how it combines the structure of arithmetic operations with the strategy of an escape game. A Game of Numbers was designed by a software developer named Joseph Michels for a “rapid” game competition called Ludum Dare. Here’s a Q&A Joseph did about the game.

A Game of Numbers.

If you enjoy A Game of Numbers, maybe you’ll leave Joseph a comment on his post about the game’s release or drop him an email. And if you enjoy A Game of Numbers, then you’d probably enjoy checking out some of the other games on our games page.

Bon appetit!

PS Tauba also created a musical instrument called an auerglass that requires two people to play. Whooooooa!

Reflection Sheet – MoMA, Pop-Up Books, and A Game of Numbers

### 63 responses »

1. Hello.

School was cancelled today because of the heat (a long story) so I had the time to sit and read your post. I’ve never really taken the time with it before. What beautiful stuff you’ve shared. Thank you and my sincere compliments for putting these posts together.

But I probably wouldn’t have commented unless I had a problem. (That’s kind of sad – I’ll have to think about that.)

Anyway, I played the Game of Numbers and loved it so I thought I’d purchase the enhanced version. I did and installed it on my MacBook. It wouldn’t run. I tried sending an email to the author with your link but that didn’t take me to a place to send an email. Can you check that link?

Thanks.

Seth Leavitt

PS A second thank you for sharing such great stuff.

• Hi Seth!
I’m glad you enjoyed the post, and I’m especially glad that you felt that way after having the chance to really dig into it. Awesome. It’s so nice to get that kind of positive feedback.
Isn’t A Game of Numbers cool? I haven’t played the full version yet, but maybe I’ll give it a go now that you’ve taken that step! I think the link is okay–it doesn’t lead you to a page where you can email Joseph, but his email address is on that page. It’s joe@joedev.net.
I hope you get your software issue resolved–let me know if you do–and that you continue to enjoy Math Munch. Are you a student, a teacher, or another flavor of math buff?

• Hi Marina. To make what? If you mean one of the pop-up sculptures, I can think of two good ways of finding out. You could ask someone who’s made one—maybe over email. Or you could try to make one yourself and keep track of how long it takes! Either way, let me know what you find out. 🙂

Or if you meant something else, just leave another comment. Cheers!

• I agree with Mister Lanier. Plus I think I’d like to try my best to make my own. I’ll give it a try. 😀

• i think what marina was trying to say how long does it take to make a pop up card

2. i really liked the video on the pop up card its really cool who of would known a beautiful piece of artwork has to do with a lot of math!!
how long does it take to make a pop up card

• Hi Brianna,
Yes, the connections that are possible—if only we look—between math and art blow me away time and time again.
I don’t know how long it takes to make a pop-up card yet—because I haven’t tried yet—but I’ll let you know if you let me know how it goes for you!
Best,
Justin

• hi Justin i tried doing a pop up card with just printer paper and scissors it was pretty cool

3. this was a great pop up video for the card. it was very interesting becuase it was cool that it made different shapes and it would make a great greeting card. im asure to try to make it.

• Awesome, Skylar! Go for it!
Justin

4. Where do you get the cut outs for these because i want to make one of these, but they do not look simple to make though. I almost think I enjoy watching some of them them open than any other part!

• Hi Ryan!
You can get the template for the pop-up in the how-to video mentioned in the post here. For the more complicated ones, you might try contacting the artist. Many folks who create wonderful mathematical objects are generous with their time and resources. I bet they’d be happy to help you if they can.
I hope you’re able to make a pop-up of your own. Send us a photo if you do!
Justin

5. Hello my name is Juliann, when I saw the pop up card I was woudering how long it took you guys to do the huge flower one and how you did it if you guys get back to me that would be wonderful Thanks
Juliann Herrera

• Hi Juliann!
Thanks for dropping by Math Munch. That huge flower pop-up sure is amazing! I don’t know how long it took to make, though, because I didn’t make it. Most of what you’ll find on Math Munch isn’t made by me or Paul or Anna. It’s made by other people. We’re just fortunate enough to find it all and share it with you!
In the post, I mentioned that the person who made that flower pop-up is Peter Dahmen. You can check out more of his artwork on his website. If you want to ask him how long it took him to make the flower pop-up, maybe you or your class could email him! You can find his contact information here.
Have fun!
Justin

• sorry Justin I didn’t see this post that you replayed and sorry to respond so late but Thanks 🙂 and I will tell my math teacher if our class could email him and just to let you now my math teacher is Mrs.Ngyen!! And she would to here about this so thanks again Justin!!

• I have two more qustions for you Justin “If we made our own pop up how will be able to show you our pop up?” And my second question for you Justin is “And is it ok if we mad our pop up with simple materials?”

• Hi Max,
I don’t know anything about. Just try again.
You do have to click on the first page of her website to get the menu to load, so make sure to do that.
Good luck,
Justin

6. That is so crazy how they can just use card stock paper to make a greeting card that can pop up and make diffrent shapes.I also think it is cool because you can make a flower or other shapes.

• Natalie,
Totally crazy and cool. Glad you enjoyed it. 🙂
Justin

7. I think that it is amazing how you can make an amazing pop-up card just out of paper.It looks really challening but alot of my classmates have made them. I am going to start one tomorrow.

• That sounds great, Shelby. Good luck making your pop-up. Let us know how it goes!
Justin

8. I think it is amazing how someone can do a pop-up card by using math! Some of the other designs were awesome too!

9. Do you think someone can come up with their own popup. And if so, what elements of math would be used?

• Hi Noah,

I’m definitely sure that someone can come up with their own pop-up. After all, pop-ups have to come from somewhere! 😀 It’s pretty mind-blowing, I admit—all of the cool stuff in the world was made by someone. Someone just like you, maybe.

In terms of math, there’s definitely some geometry and spatial reasoning involved in designing pop-ups. I hope you’ll try to make a pop-up of your own. I bet there are some good resources out there to help you if you look around. Here’s one article to get you started: http://ohhappyday.com/2011/05/diy-pop-up-cards/

Good luck, and let us know what you make!
Justin

10. These pop up cards are amazing! I never knew they included math. I tried to do the other pop up card in the link and it was confusing. I wonder how complex the pop up cards in the video.

• Hi Sammy,
I’m glad you enjoyed the cards. I bet you’re right—that the complex pop-ups in the video are probably even harder to make than the one in the tutorial.
I hope you’ll try the tutorial again, or maybe try designing a pop-up of your own. Good luck!
Justin

11. these pop up cards are amazing i thought this website was going to be boring but my teacher for math inspired me to like math i would love to learn how to make this thank you making this site incredible!!!!!

• Hi Alyssa,
Ha! Well I’m glad we exceeded your expectations. We try to share great math on Math Munch, and I hope that you’ll find more stuff that you love on the site in the future. I’m glad your teacher has inspired you to like math, and you are certainly most welcome for Math Munch! 😀
Justin

12. the pop-ups were amazing. I didn’t even know you could make things like this. Before I watched this video I thought math was just about numbers. But know I know that you could be created with math and have fun while doing it. Thanks for this amazing video. You inspired me to try to make one to.

• Hi Skylar,
There are lots of ways to be creative and have fun while doing mathematics. Math Munch shares lots of ways you can do this! You might enjoy checking out our Math Art Tools page: https://mathmunch.org/math-art-tools/
Justin

13. These pop-up cards are amazing to look at. I didn’t know that math was a part of art. I always thought that math involved only numbers include letters only. Thanks to you guys I look at math in a whole new way.

• Hi Nico!
I’m glad your idea of math has grown by reading Math Munch. I hope you’ll find more math that’s exciting and mind-expanding on the site in the weeks ahead. Happy exploring!
Justin

14. I just have to show my family this it is awesome!!!!! I wish I was that talented, to make such beautiful pop-up cards.

15. this video is amazing I really liked the one of the flower! the pop-up cards look very difficult to make but with math I guess it is possible! I would really like to know how to make them.

16. The Pop-up art video is so mind blowing! I cant believe those things are pop ups. I have always enjoyed math and this type of art and when you add them both together its really amazing. I have already recreated one of these pop ups and had a lot of fun doing so and was wondering if you can tell me where more of these templates are because I really want to try the more complex pop ups. Thanks for posting. P.S. (the pop up dome is my favorite!)

17. I have a question for Tauba, was there much trial and error when making the pop-ups? Also which one is your personal favorite? I love the pop-ups and I am hoping to make one myself soon.

• Hi Luke,
Great questions. I’m not in contact with Tauba, but I bet you could get in touch with her through her website. I’m sure she’d be happy to answer your questions! It’s always fun to hear from people who are interested in your work.
Good luck,
Justin

18. This video was absolute amazing.I’m so eager to make one.Whoever made these pop up cards are very creative.I wonder how long it took for them to make them.My favorite was the last pop up card. this video really inspired me to make one no! more than one.This video was amazing and I’m going to make my own!

• Hi Jacob,
I’m so glad you’re feeling inspired by those pop-ups! Please send us pictures or video of your projects:
mathmunchteam@gmail.com
Cheers!
Justin

19. The pop up cards were so amazing! I really want to make one. I didn’t know the pop up cards had anything to do with math. Before I watched this video, I thought only artist can make it. My favorite one was the flower. It must have token so long to make all of them. Hope I could do one like that!

• Nina,
I bet you could make a great pop-up if you put your mind and heart to it!
Something that’s very interesting to me is how the easy categories that we sometimes think in—artist, mathematician, scientist, historian, teacher—often break down in the lives of real people. It’s possible for a person to be all of those things in different ways, at different times, and with different emphases. Actually, it’s the unexpected combinations that can make for the best results!
That’s a great incentive to keep trying new things and finding out as much as you can about the world. 🙂
Best,
Justin

20. The pop up cards were beautiful creations of art. I will definitely try to make one for a birthday card or something. Thanks for putting the video on Math Munch, it made me see that art is created by math and creativity:) My favorite one was the last one, the globe shaped object, I need to make one A. S. A. P.

• Hi Rebeckah,
I hope you do make one! If you do, send us a photo or video:
mathmunchteam@gmail.com
Also, we’re very happy to share awesome and creative math with you. Come back by!
Justin

21. The pop up cards were really amazing and I liked how such a huge and big object can fit in just a piece of paper that is not as big as it. I would really like to make one of thes it seems really complex. These are really amazing peices or art I would really like to see more posts about this topic.

• Hi Anthony,
I’m glad that you enjoyed the video and post! I hope that you do try to make a pop-up, either from a template or one of your own. Peter Dahmen shares some how-to’s on his site.
And I’ll see what I can do about making another post about pop-ups!
Cheers,
Justin

22. I have played the game A Game of Numbers and I enjoyed playing it. Also I was struggling when I got to a problem and I tried it about 8 times until I got it. Each time it got harder and harder and it got me very frustrated and annoyed, but at the beginning of the game I didn’t know how to play, and I didn’t understand how to play until the third level; then I got the hang of the game and it was fun.

23. This game is so cool. It was so fun and I liked it. This game really helped me learn.

• Cool, Alex! I’m glad you liked it. What do you feel like you learned by playing it? Also, did you beat it?
Justin

24. These pop-up art structures are amazing! I really like the flower pop-up. How long did it take you to build them? How did you get this idea?

25. I think the pop up video will give me ideas that will help me with my math munch paper. about how long did it take you to make the pop up papers.

26. the game of numbers was soo cool it was easy but as I past the levels I was restarting the level it was hard but then when I found the answer I was like wow that was so easy and I had to restart the level but it was fun thanks for the amazing games thanks for giving us history behind the math.

27. The game of numbers was way more fun than I thought. I liked trying to figure out the path your number was supposed to go.

28. i tried a game of numbers it was easy until i got to the loop
that was when it got tricky

29. the pop up cards are AMAZING!!! The designs are awesome and how they are made looks like it would take major concentration and patience. I think that this could result in gift card ideas.

30. All these pop ups were great! They were so amazing to just watch go up. Its so cool that its just paper.

31. . First of all I thought the video was awesome because well I think it is cool how art is related to math and so are lots of other thing like when you go to the store and shop there are number all around us everywhere.

32. I watched the pop up card video it was very creative. The one pop up card I liked was the flower one. It must have taken a long time to just get all those layers of the flower. If I were the one to do that card I wouldn’t mind how long it would take. I would go for it.

33. How do you open it and something new comes out of all the time.