Celebration of Mind, Cutouts, and the Problem of the Week

Welcome to this week’s Math Munch! We’re going to revisit the work of Martin Gardner, look at some beautiful mathematical art, and see if we can dig into a college’s “problem of the week” program.

Martin Gardner

Last October, I wrote about Martin Gardner. He is one of the great popularizers of mathematics, known for his puzzles, columns in Scientific American, and over 100 books. Around the time of his birthday, October 21st, each year, people around the world participate in a global “Gathering4Gardner” — a so-called Celebration of Mind.

One of Martin Gardner’s many puzzles

These are gatherings of two or more people taking time to dig into the kinds of mathematics that Martin Gardner loved so much. Below you can find lots of ways to participate and share with family, friends, or strangers.

First, If you want to learn more about Gardner himself, here’s a very detailed interview. You can also try solving some of Gardner’s great puzzles. We featured both of these last year, but I recently found a whole new page of resources and activities for the Celebration of Mind.

In the video on the left you can see a geometric vanish like those we’ve previously featured (Get off the Earth, and Chocolate). The second is a surprising play on the Möbius Strip which we’ve also featured before (Art and Videos + Möbius Hearts). I hope you’ll find some time this week to celebrate Martin Gardner’s love of math and help grow your own. (Though, I guess if you’re reading this, you already are!)

Up next, check out the work of artist Elena Mir. This video shows a series of artworks she created over the last four years. They feature stacks of cut paper to form geometric shapes, and they make me wonder what I could make out of cut paper. If you make something, please let us now.

It reminds me of the work of Matt Shlian that we featured in our very first post. You can watch Matt’s TED Talk or visit his website to see all sorts of cutouts and other paper sculptures, plus incredible videos like the one below. It might be my favorite video I’ve ever posted on Math Munch.

Finally, Macalester College in St. Paul, Minnesota has a weekly problem that they offer to their students, and the problem archives can be found online. These are for college students, so some of them are advanced or phrased in technical language, but I think we can find some that all of us can dig in to. Give these a try:

I read Martin Gardner’s long interview. It is interesting to know that his hobby in magic, his love for math and his writing for children’s and scientific magazines led him to creating mathematical games and puzzles. My two questions are: What are your first steps to creating a new puzzle or game? What age group do you like to make games for (children, teenagers or adults)? Thank you.

Hey Sophia. Thanks for your questions. Were they for me (author of this blog post) or Martin Gardner? Unfortunately, Martin Gardner died in 2010, so he won’t be able to answer your question.

I think the key to creating new puzzles and games is trying to clever, imaginative, and tricky. I don’t think that’s very clear, but a lot of it is just playing around and seeing what works.

I think a really good puzzle is good for any age group! Here’s a link to a page of puzzles I wrote that I think are good for a lot of different age ranges. My goal was to write a puzzle that used tipping scales. I had to figure out what would make a good question and how I could design them to sneakily reveal information.

Well first of all I though the interview was intresting because I found out that the way he decided to create mathamatical games. Also I would like to ask if he did all those games and puzzles to make the viewer get intrested to all the those games and puzzles? If you get to answer my question I will be happy and Thank You.

You know, I can’t really speak for Martin Gardner, but I think his major motivation was curiosity and enjoyment. He liked the puzzles and games that he worked on. I also imagine he took pleasure in sharing math with other people, but again, I can’t really speak for him.

Just when I thought I’ve seen everything about the mobius strip this little gem comes along. How have I never seen this before? I’m getting out my scissors and tape now…GTG

I looked into Martin Gardner’s dollar bill geometric vanish and found it quite unique. Instead of relying on a trick of the eyes to distract the audience from the cuts, the edges get closer in. If you make a big show of measuring the borders people will be less likely to see the edges shrink. Keep up the great work!

That video of geometrical spaces is one of the most incredible things that I’ve seen in a while. It’s interesting to think that someone can be so accurate with cutting that they can create the masterpieces shown. Although I know that I could never compete with such magnificent work, it does inspire me to pick up some paper and an x-acto knife and just start experimenting with making shapes. At first glance, I thought that in the second video it was a three dimensional paper ball-like figure, but once I watched it several more times, I realized that it was, instead, a stop motion video of many different paper made cutouts. It really makes me wonder how long it would take to make all of those various configurations. Through and through it was an excellent display that really made me think about all of the different everyday items that could be used for a plethora of uses.

I read the geometrical spaces video by Elena Mir. It was very interesting looking at the paper cut outs. The cot outs were very detailed and had looked like it was a flat surface in front of me.

I thought that the geometric figures was really cool. It inspired me into trying to do that myself. You cannot wonder how many pieces of paper it takes to make ONE of those. Is there a certain template you use to make that or do you just freestyle it? Elena Mir is very talented in make wonderful projects. I can’t wait to see more of her work!

It actually says in the video how many sheets each one uses. “Hojas” is Spanish for “sheets.” You’ll see things that say “30 hojas.”

I know Matt Shlian has these things planned out and uses a computer to do the patterns. You could definitely do it “freestyle” though. I hope you give it a try.

I liked playing Martin Gardner’s puzzle games on http://www.puzzles.com/puzzleplayground/Authors/MartinGardner.htm
His puzzles are really fun and interesting! I like his logic puzzles the best! What are your favorite puzzles?
A set of five different letters can be arranged in such a way that to produce the name of an animal. What familiar animal should it be?
A C E L W
I also liked finding out that even Martin Gardner had problems with Calculus! Even if math is hard he still had fun with it!

I love these little flip books! They looks like it would be pretty simple to make a tiny one but these big ones would take a ton of time and skill. I am so doing a few!

I really liked the video about the the flip book. I watched it a few times and it really does look like a three dimensional figure. I think that its amazing that someone cut all of those papers. How long did this take? These seem like they take so long to only have a few seconds. Another question is how many papers were in the book?

I really liked the video about the flip book. I watched this a few times and it doesn’t look like paper it looks like a three dimensional figure. I love flip books. These take so long and you only get a few seconds. How long did it take? Also how many pieces of paper were in this?

I really like the Geometrical Spaces video. I love the music that went with it and I love how the its a shape in the spaces. In one of them, I thought it looked like a diamond. It was really cool. I got really fascinated by it. I was enjoying it, a lot actually. 🙂 🙂

This was very interesting, I thought it was a drawn figure, but i now think it’s actual paper i’m still not sure, but it was really interesting, i believe my favorite figure was #12, i wonder what other notebook figures he could make.

this was a really cool video. I thought it was a drawing but it was a figure cut out to a shape. i had to watch it again because i couldn’t believe that it was a cut out figure made out of paper. i cant wait to see another video of this.

i love how has wrote over a hundred books. And what i thibk is carzy is that we have the same birthday October 21. i checked out one his puzzels. its really cool. what i was always wonderig is hwo does he make up his remarkable and fun puzzels. and the videos of the paper making those patterns brilliant.

even though the video was very short it was amazing on how the diamond was a 3D shape I’ve tried to make a 3D shape but the shape never came out the way as planed :[

I did the puzzle The Two Spirals and at first it was hard, but then with my eyes i trieed to trace the figures and i got the answer. It was the first one. I liked this puzzle a lot because it was confusing, interesting,and hard.

I thought that this video was really interesting because the cutting of these geometrical shapes are amazing, it’s hard to tell if it was either drawn or cut. It’s also amazing how something so simple can turn into something so complex. The shapes that were cut were really mind boggling.

T hat is amazing how you can make that flip book!!! How long does it take to make those. If it was me making that it would take me hours. What would be the area of those.

Two things:
1) this was quite interesting, but only slightly related to math based on watching the video alone.
2) Both my friend and my dad agree, that is the most annoying noise in the world

I read Martin Gardner’s long interview. It is interesting to know that his hobby in magic, his love for math and his writing for children’s and scientific magazines led him to creating mathematical games and puzzles. My two questions are: What are your first steps to creating a new puzzle or game? What age group do you like to make games for (children, teenagers or adults)? Thank you.

Hey Sophia. Thanks for your questions. Were they for me (author of this blog post) or Martin Gardner? Unfortunately, Martin Gardner died in 2010, so he won’t be able to answer your question.

I think the key to creating new puzzles and games is trying to clever, imaginative, and tricky. I don’t think that’s very clear, but a lot of it is just playing around and seeing what works.

I think a really good puzzle is good for any age group! Here’s a link to a page of puzzles I wrote that I think are good for a lot of different age ranges. My goal was to write a puzzle that used tipping scales. I had to figure out what would make a good question and how I could design them to sneakily reveal information.

http://bit.ly/imbalanceproblems

Well first of all I though the interview was intresting because I found out that the way he decided to create mathamatical games. Also I would like to ask if he did all those games and puzzles to make the viewer get intrested to all the those games and puzzles? If you get to answer my question I will be happy and Thank You.

Also if there will be more fantastic games and I have also enjoyed playing and solving all those games and puzzles.

You know, I can’t really speak for Martin Gardner, but I think his major motivation was curiosity and enjoyment. He liked the puzzles and games that he worked on. I also imagine he took pleasure in sharing math with other people, but again, I can’t really speak for him.

Just when I thought I’ve seen everything about the mobius strip this little gem comes along. How have I never seen this before? I’m getting out my scissors and tape now…GTG

Here’s another Möbius thing you might enjoy. (It might be featured in a future “munch.”)

http://xkcd.com/381/

I looked into Martin Gardner’s dollar bill geometric vanish and found it quite unique. Instead of relying on a trick of the eyes to distract the audience from the cuts, the edges get closer in. If you make a big show of measuring the borders people will be less likely to see the edges shrink. Keep up the great work!

Am I right that it kind of flips the bill inside out, so that the new corners come from interior points of the first bill?

That video of geometrical spaces is one of the most incredible things that I’ve seen in a while. It’s interesting to think that someone can be so accurate with cutting that they can create the masterpieces shown. Although I know that I could never compete with such magnificent work, it does inspire me to pick up some paper and an x-acto knife and just start experimenting with making shapes. At first glance, I thought that in the second video it was a three dimensional paper ball-like figure, but once I watched it several more times, I realized that it was, instead, a stop motion video of many different paper made cutouts. It really makes me wonder how long it would take to make all of those various configurations. Through and through it was an excellent display that really made me think about all of the different everyday items that could be used for a plethora of uses.

So glad you liked it, Matthew! I bet you’d really like this “Worm eaten sphere” piece in the middle of this page.

http://gallery.bridgesmathart.org/exhibitions/2013-bridges-conference/friedhelm-kurpig

If you create anything of your own, let us know for our Readers Gallery.

I read the geometrical spaces video by Elena Mir. It was very interesting looking at the paper cut outs. The cot outs were very detailed and had looked like it was a flat surface in front of me.

I like the video because the pattern that Matt Shilian was doing aswome

I thought that the geometric figures was really cool. It inspired me into trying to do that myself. You cannot wonder how many pieces of paper it takes to make ONE of those. Is there a certain template you use to make that or do you just freestyle it? Elena Mir is very talented in make wonderful projects. I can’t wait to see more of her work!

Hi Shelby-

It actually says in the video how many sheets each one uses. “Hojas” is Spanish for “sheets.” You’ll see things that say “30 hojas.”

I know Matt Shlian has these things planned out and uses a computer to do the patterns. You could definitely do it “freestyle” though. I hope you give it a try.

OK I will try to make on of my own! Thank you! I was wondering what hojas meant and I take Spanish class!

Great! If you make something, definitely let us know. Send us a picture and we’ll put it in our “readers gallery.” 🙂

I liked playing Martin Gardner’s puzzle games on http://www.puzzles.com/puzzleplayground/Authors/MartinGardner.htm

His puzzles are really fun and interesting! I like his logic puzzles the best! What are your favorite puzzles?

A set of five different letters can be arranged in such a way that to produce the name of an animal. What familiar animal should it be?

A C E L W

I also liked finding out that even Martin Gardner had problems with Calculus! Even if math is hard he still had fun with it!

Those Geometric shapes are amazing. Do you know how to make them?

That Dollar Bill Geometric Vanish forms 4 trapezoids.

I love these little flip books! They looks like it would be pretty simple to make a tiny one but these big ones would take a ton of time and skill. I am so doing a few!

I was wrong they are way harder then they seem to be. It might have been the exacto blade i was using or something but i had a ton of trouble.

I made one of my own cutoust but I turned it in to my teacher so I can’t take a picture of it though :-<

I like the video because it is cool how the diamond moved around and around

I really liked the video about the the flip book. I watched it a few times and it really does look like a three dimensional figure. I think that its amazing that someone cut all of those papers. How long did this take? These seem like they take so long to only have a few seconds. Another question is how many papers were in the book?

I really liked the video about the flip book. I watched this a few times and it doesn’t look like paper it looks like a three dimensional figure. I love flip books. These take so long and you only get a few seconds. How long did it take? Also how many pieces of paper were in this?

I really like the Geometrical Spaces video. I love the music that went with it and I love how the its a shape in the spaces. In one of them, I thought it looked like a diamond. It was really cool. I got really fascinated by it. I was enjoying it, a lot actually. 🙂 🙂

This was very interesting, I thought it was a drawn figure, but i now think it’s actual paper i’m still not sure, but it was really interesting, i believe my favorite figure was #12, i wonder what other notebook figures he could make.

this is awesooome. do you have anymore puzzles from him that you can show. Also, what year was he born?

this was a really cool video. I thought it was a drawing but it was a figure cut out to a shape. i had to watch it again because i couldn’t believe that it was a cut out figure made out of paper. i cant wait to see another video of this.

i love how has wrote over a hundred books. And what i thibk is carzy is that we have the same birthday October 21. i checked out one his puzzels. its really cool. what i was always wonderig is hwo does he make up his remarkable and fun puzzels. and the videos of the paper making those patterns brilliant.

even though the video was very short it was amazing on how the diamond was a 3D shape I’ve tried to make a 3D shape but the shape never came out the way as planed :[

this video was short and this shape looks challenging to do I love doing these shapes because they are challenging and fun to do.

I did the puzzle The Two Spirals and at first it was hard, but then with my eyes i trieed to trace the figures and i got the answer. It was the first one. I liked this puzzle a lot because it was confusing, interesting,and hard.

I thought that this video was really interesting because the cutting of these geometrical shapes are amazing, it’s hard to tell if it was either drawn or cut. It’s also amazing how something so simple can turn into something so complex. The shapes that were cut were really mind boggling.

How much time did it take for those patterns. Are they difficult to do ?

These videos are really interesting. The second video’s was kind of confusing too. Was it also a paper cutout?

Awesome! I learned, in this video, that by reduces the size of the next shape cutout, can make this awesome 3D effect.

T hat is amazing how you can make that flip book!!! How long does it take to make those. If it was me making that it would take me hours. What would be the area of those.

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Two things:

1) this was quite interesting, but only slightly related to math based on watching the video alone.

2) Both my friend and my dad agree, that is the most annoying noise in the world

Disclaimer: I am only starting geometry, so I may have missed something

😶