Marc Chamberland, Math Fonts, and Congruent Triangles

Welcome to this week’s Math Munch!

Marc Chamberland

Up first, a follow up to our post about the World Cup a while back. We received an email from Marc Chamberland linking us to a nice little video (below) about World Cup Balls and their various properties. You may remember seeing Marc’s mathematical art in this post. Below you can see another nice piece that was included in the mathematical art exhibit at the 2013 Joint Mathematics Meetings. Click for a nice description of the math puzzle it solves. (in short: What’s the area of the red square?)

“Inner Square” by Marc Chamberland

Marc is a math professor at Grinnell College. In March of 2014 (3-14?) he began working on Tipping Point Math, a youtube channel full of videos showing “math as you never imagined.” I encourage you to find something nice there. For now, here’s that video about World Cup Balls I promised you.

A font based on glass bending

Up next are some nifty, fun fonts based on mathematics. Erik Demaine is no stranger to Math Munch readers, and it’s no wonder why. His stuff is clever and downright intriguing. He and his father Martin published a very interesting paper last April about a series of mathematical typefaces they’ve created over the course of their last decade of research and play.

A conveyor belt typeface by Erik and Martin Demaine

Their paper was published to the arXiv (pronounced “archive”) where it is publicly available. You can read it here. Or, if you like something slightly more plain-language, here’s a nice review over on medium.com.

The 4051 Tektronix Graphics Terminal

Finally, I want to share a sleepy little video called “Congruent Triangles.” I like to think of it as a slice of mathematical cultural history. This film was made in 1977 on an early computer called a Tektronix 4051 Graphics Terminal. It was made by Bruce and Katherine Cornwell as part of a series of mathematical videos. The way the shapes move and deform to present the ideas and connect the pieces together is so very cool. I also love the choice of music. It tells you something about what math was like for people then. I’d say sort of “groovy.”

There’s more to the story and many more cool videos to enjoy. You can look forward to seeing more from the Cornwells, but for now, enjoy this one video and do some hunting on your own if you’re interested. That’s called “research.”

I had NO idea that there was so much math in creating a soccer ball. I was really surprised that there’s also a math to designing the outside, too. When I think of a soccer ball, I think of the black and white one. I wonder how many different soccer balls have been created. I also wonder how the design affects the flight of the ball.

A soccer ball is really basic but when you explain it like that it makes me realize that even the simplist things can have a lot of math and difficulty. The next time i see a soccer ball i’ll try to find what shapes it has. Lastly i wonder how the different soccer balls feel when you kick them and if you can feel the texture

A soccer ball could seem really basic, when you show us the mathematics, it really is difficult to design. Like the difficulty of the math designing the outside AND inside of the ball. Next time I notice a soccer ball, I’ll be sure to check out the texture, and the type of shape. I really wonder with all the styles of the soccer ball, which one really has the best flight based on the designs, and or math.

I’m not sure if there’s any way to predict what the next designers will come up with, but maybe something based on the truncated dodecahedron. That would be cool.

Hey David, that’s a really awesome design. I was wondering, what software did you use to create your design?

Seeing how some of our favorite activities are connected with mathematics, proves that math is everywhere! It’s pretty awesome to look at things through the eyes of a mathematician and I really enjoyed getting to see the different soccer balls. The concept kind of reminded me of tessellations 🙂

wow!! This is amazing how math can be everywhere. the video was so interesthing because i certainly didnt know balls where created it by using math.now theres just this question thats on my head right now how is the part that its inside of the soccer ball made out of

I never really noticed that the soccer balls had so much math on them. Before I watched the video I just thought that they looked cool. Who knew they had different names? It’s funny how every where you look there is math.

Before watching this video, I thought a soccer ball wasn’t that complicated and wondered how it was related to math. After watching the video, I realized that designing a soccer ball is very mathematical and complex. I like how they used cubes to compare the soccer balls to. I also wonder if the design of the soccer ball efects the way of the soccer balls traveling. This video was very understandable and didn’t leave me hanging with questions. I was fascinated when I learned this information.

this video is cool, showing how there are even ways to make a ball out of a square, and all that you have to do for a design is cut off the 4 corners. is it competitive to come up with a design form the world cup, or is there just a company who already has dibs on making it each year?

this video is very interesting if you want to know more about soccer. I learned very much, like addais make all the fifa world cup and i know there names now. I also learned how math ties into making a soccer ball . also i relized that making a soccer ball is very complex and hard to make.

I never really thought of how they even make and design the soccer balls.I thought they could make any patters they wanted to and not use squares and triangle as there base. My favorite pattern was the newest one it looked really cool I bet it got great reviews!

Wow!!! I really didn’t think something as simple as a soccer ball involved so much math. I guess soccer balls aren’t that simple. I think my favorite was the 2014 version. I think its really cool how u turn a square into a sphere and even more complicated shapes. This is really cool!!

my name is willie i thought pancake art was really cool because before i watched this video people wer saying look i drew pabcake art and i was clueless but i know know and its fasinating

The amount of geometry that is used to make a soccer ball is absolutely astounding to me. I never thought of soccer balls of being something that would use geometric shapes and points to create them. I’m really interested in the multitude of shapes that can be used, instead of the original pentagon/hexagon.

I had already known there was a whole science to the soccer ball. However, i had never really thought about it. After watching this fascinating video my mind kind of delved into it. I got curious and found this website: /2014/06/12/the-chemistry-of-the-world-cup-football/

No problem! I love to see how math is incorporated into our everyday life. Math is everywhere! This isnt really relevant to this video but it goes to show how math is EVERYWHERE! 🙂 sa.org/events/audio-and-past-events/2011/supercooperators-the-mathematics-of-evolution,-altruism-and-human-behaviour

I’ve never thought of soccer to have math in it. When the video was showing how you can make a simple cube into a soccer ball by doing some simple tricks, I was amazed! Math CAN really be everywhere!

It is amazing how much soccer balls have evolved and how easily math can be applied to this sport. It’s fascinating how you can take multiple 3 dimensional shapes, add some numbers and lines and make decades worth of soccer ball designs!!! Like Whoa.

I have never thought to think that soccer balls were based on shapes. Really complicated shapes. It’s cool to think that sports like soccer was based on math. Like the soccer ball. The original soccer ball has octagons on it all over. Octagons are a mathematical shape. it just shows that math can be everywhere!!!

Out of all the soccer balls, I think the latest Brazilian one is my favorite. I was wondering, do they get more difficult to make with less panels or do less panels make the process quicker. Also, did the soccer ball making companies originally base it off those shapes or was that discovered after the fact. Of all of them, which one is the “best”. Wait, let me rephrase that: Which is the most reliable in going where you aim it and doing what it is supposed to do as a soccer ball?

What? Soccer balls actually have different shapes? Who knew that they inspired by cubes and pyramids. All that math was very cool. Find the corner, divide it into thirds and wallah! The traditional soccer ball shaped with black pentagons and white hexagons, the telstar. It’s my favorite kind of ball. That’s not all there is though, there’s Brazilian, teamgeist, and many more with their special shape patterns. I’m curious whether they’ll make a new pattern. I bet it will be stunning to use. How many combinations are there? Soccer is such an interesting sport!

this video i do not realy get and almost all the soccer balls has pentigons on it and the facts i never knew about them and mostly we play soccer with my family i will see the square and the triangles

First of all, i had no idea that a soccer ball could have any math to it. This is actually very interesting to me because i watch the world cup. I heard there were like these special things to the soccer balls and i guess that the math of it is one of them.

I didn’t know there was so much math u can put in a ball. I think the 2014 ball is the best because it is the most resent and i felt like there was a lot of math into that one ball out of all of them. it amazed me that i found out that its more then making just a simple round ball. Do all balls for sports require math?

I liked the video Congruent Triangles. It was really interesting learning how congruent triangles are made, and what you need to have a congruent triangle. What program was used to make the video? Was it coding? Or was it some sort of animation? What are the different types of Math coding programs out there? Example: Mathlab

I never knew that a soccer ball had so much math put into it! I wonder if any other sports require math. I am currently doing a project on basketball, and I just wondered, do they do the same thing to make basketballs? My favorite is the 2014 Brazuca because it looks quite simple, considering that 6 panels is the fewest. Also because it is related to a cube and I never imagined a round ball coming from a cube! It is cool to think about!

Wow! I had no idea that soccer balls were made starting from geometric shapes. I was more surprised to learn that math was used to make soccer balls. I wonder if all sport balls were created by math. My favorite ball is the 2014 Brazuca just because it looks pretty cool.

I did not know that so much thinking went into making soccer balls. It’s amazing how humans thought is such a creative way to create this for soccer. I didn’t even know that geometric shapes are used to make a soccer ball. My favorite is the one from Brazil, the latest one.

I had no idea that the Telstar was not just hexagon pattern trough the entire ball. I also thought that the balls were still stitched, not thermally bonded.

The way the soccer balls were made and the designs on them were very cool. I think the way math was used to designs these was very cool. Now i know how the designs on score balls are made.

I think the brazuca ball is the best. I have one, and have played soccer with some of the Adidas balls. They aren’t as good. The brazuca is also the most simple, maybe because it only has 6 panels.

I did not know that there was that much math you could do with soccer balls. I also did not know there was so much math in making a soccer ball.

I had NO idea that there was so much math in creating a soccer ball. I was really surprised that there’s also a math to designing the outside, too. When I think of a soccer ball, I think of the black and white one. I wonder how many different soccer balls have been created. I also wonder how the design affects the flight of the ball.

It’s amazing how everyday objects can have so much math involved in it. For instance a soccer ball, now that i know.

A soccer ball is really basic but when you explain it like that it makes me realize that even the simplist things can have a lot of math and difficulty. The next time i see a soccer ball i’ll try to find what shapes it has. Lastly i wonder how the different soccer balls feel when you kick them and if you can feel the texture

I think the 2014 is the best world cup soccer ball because it was the most recent. and that is a lot of math for one soccer ball.

A soccer ball could seem really basic, when you show us the mathematics, it really is difficult to design. Like the difficulty of the math designing the outside AND inside of the ball. Next time I notice a soccer ball, I’ll be sure to check out the texture, and the type of shape. I really wonder with all the styles of the soccer ball, which one really has the best flight based on the designs, and or math.

would you be able to predict the next soccer ball and what if the soccer ball had circles as its design

I’m not sure if there’s any way to predict what the next designers will come up with, but maybe something based on the truncated dodecahedron. That would be cool.

I like your circles idea.

Jacob, it’s fun to predict (or just design) your own soccerball panel designs. Last month I made a “prediction” that uses 4 panels.

Hey David, that’s a really awesome design. I was wondering, what software did you use to create your design?

Seeing how some of our favorite activities are connected with mathematics, proves that math is everywhere! It’s pretty awesome to look at things through the eyes of a mathematician and I really enjoyed getting to see the different soccer balls. The concept kind of reminded me of tessellations 🙂

wow!! This is amazing how math can be everywhere. the video was so interesthing because i certainly didnt know balls where created it by using math.now theres just this question thats on my head right now how is the part that its inside of the soccer ball made out of

I never really noticed that the soccer balls had so much math on them. Before I watched the video I just thought that they looked cool. Who knew they had different names? It’s funny how every where you look there is math.

Before watching this video, I thought a soccer ball wasn’t that complicated and wondered how it was related to math. After watching the video, I realized that designing a soccer ball is very mathematical and complex. I like how they used cubes to compare the soccer balls to. I also wonder if the design of the soccer ball efects the way of the soccer balls traveling. This video was very understandable and didn’t leave me hanging with questions. I was fascinated when I learned this information.

I never knew that soccer balls had to be done with so munch math. I think the 2014 ball was the best and nice video so interesting.

this video is cool, showing how there are even ways to make a ball out of a square, and all that you have to do for a design is cut off the 4 corners. is it competitive to come up with a design form the world cup, or is there just a company who already has dibs on making it each year?

this video is very interesting if you want to know more about soccer. I learned very much, like addais make all the fifa world cup and i know there names now. I also learned how math ties into making a soccer ball . also i relized that making a soccer ball is very complex and hard to make.

I never really thought of how they even make and design the soccer balls.I thought they could make any patters they wanted to and not use squares and triangle as there base. My favorite pattern was the newest one it looked really cool I bet it got great reviews!

Wow!!! I really didn’t think something as simple as a soccer ball involved so much math. I guess soccer balls aren’t that simple. I think my favorite was the 2014 version. I think its really cool how u turn a square into a sphere and even more complicated shapes. This is really cool!!

my name is willie i thought pancake art was really cool because before i watched this video people wer saying look i drew pabcake art and i was clueless but i know know and its fasinating

The amount of geometry that is used to make a soccer ball is absolutely astounding to me. I never thought of soccer balls of being something that would use geometric shapes and points to create them. I’m really interested in the multitude of shapes that can be used, instead of the original pentagon/hexagon.

What if there were square designs on the soccerball

I had already known there was a whole science to the soccer ball. However, i had never really thought about it. After watching this fascinating video my mind kind of delved into it. I got curious and found this website: /2014/06/12/the-chemistry-of-the-world-cup-football/

Thanks for sharing that link, Diego!!

No problem! I love to see how math is incorporated into our everyday life. Math is everywhere! This isnt really relevant to this video but it goes to show how math is EVERYWHERE! 🙂 sa.org/events/audio-and-past-events/2011/supercooperators-the-mathematics-of-evolution,-altruism-and-human-behaviour

Thanks again!

And one last thing,Its a huge “mathmatical breakthrough”: http://www.answers.com/Q/Why_is_42_the_answer_to_life_the_universe_and_everything

I’ve never thought of soccer to have math in it. When the video was showing how you can make a simple cube into a soccer ball by doing some simple tricks, I was amazed! Math CAN really be everywhere!

It is amazing how much soccer balls have evolved and how easily math can be applied to this sport. It’s fascinating how you can take multiple 3 dimensional shapes, add some numbers and lines and make decades worth of soccer ball designs!!! Like Whoa.

It amazed me that there are so many different ways soccer balls can be made/formed.

I have never thought to think that soccer balls were based on shapes. Really complicated shapes. It’s cool to think that sports like soccer was based on math. Like the soccer ball. The original soccer ball has octagons on it all over. Octagons are a mathematical shape. it just shows that math can be everywhere!!!

Out of all the soccer balls, I think the latest Brazilian one is my favorite. I was wondering, do they get more difficult to make with less panels or do less panels make the process quicker. Also, did the soccer ball making companies originally base it off those shapes or was that discovered after the fact. Of all of them, which one is the “best”. Wait, let me rephrase that: Which is the most reliable in going where you aim it and doing what it is supposed to do as a soccer ball?

What? Soccer balls actually have different shapes? Who knew that they inspired by cubes and pyramids. All that math was very cool. Find the corner, divide it into thirds and wallah! The traditional soccer ball shaped with black pentagons and white hexagons, the telstar. It’s my favorite kind of ball. That’s not all there is though, there’s Brazilian, teamgeist, and many more with their special shape patterns. I’m curious whether they’ll make a new pattern. I bet it will be stunning to use. How many combinations are there? Soccer is such an interesting sport!

the video is very intresting and i never knew that much stuff at about the soccer balls in the world cup. Soccer is my favorite sport

Your video was complicated.I did not know that soccer balls had shapes like that in them.I have to say that was a cool video.

this video helped me learn two more shapes. This was a very clever choice to make everything out of triangles and square.

I like the way how you describe a soccer ball with math in it ! I like soccer but did not relies this.

this video i do not realy get and almost all the soccer balls has pentigons on it and the facts i never knew about them and mostly we play soccer with my family i will see the square and the triangles

First of all, i had no idea that a soccer ball could have any math to it. This is actually very interesting to me because i watch the world cup. I heard there were like these special things to the soccer balls and i guess that the math of it is one of them.

I didn’t know there was so much math u can put in a ball. I think the 2014 ball is the best because it is the most resent and i felt like there was a lot of math into that one ball out of all of them. it amazed me that i found out that its more then making just a simple round ball. Do all balls for sports require math?

I like this video because it talks about soccer and soccer is my live # 20 and its easy to get

I liked the video Congruent Triangles. It was really interesting learning how congruent triangles are made, and what you need to have a congruent triangle. What program was used to make the video? Was it coding? Or was it some sort of animation? What are the different types of Math coding programs out there? Example: Mathlab

I never knew that a soccer ball had so much math put into it! I wonder if any other sports require math. I am currently doing a project on basketball, and I just wondered, do they do the same thing to make basketballs? My favorite is the 2014 Brazuca because it looks quite simple, considering that 6 panels is the fewest. Also because it is related to a cube and I never imagined a round ball coming from a cube! It is cool to think about!

It is so cool how there is so much math in making a soccer ball. I learned that a soccer ball is make in several equal parts.

I had no idea that soccer balls even had solid shape faces in them (also my favorite ball is the African one)

Wow! I had no idea that soccer balls were made starting from geometric shapes. I was more surprised to learn that math was used to make soccer balls. I wonder if all sport balls were created by math. My favorite ball is the 2014 Brazuca just because it looks pretty cool.

I love the idea of this video, but its very confusing if you have not been tought the subject yet

I find it interesting how each design a soccer ball has started out from geometric shapes and so munch math was conducted to make a soccer ball

the “Congruent Triangles” video wos cool because all triangles were they could fold from one small triangle to a huge shape.

I did not know that so much thinking went into making soccer balls. It’s amazing how humans thought is such a creative way to create this for soccer. I didn’t even know that geometric shapes are used to make a soccer ball. My favorite is the one from Brazil, the latest one.

I had no idea that the Telstar was not just hexagon pattern trough the entire ball. I also thought that the balls were still stitched, not thermally bonded.

The way the soccer balls were made and the designs on them were very cool. I think the way math was used to designs these was very cool. Now i know how the designs on score balls are made.

I think the brazuca ball is the best. I have one, and have played soccer with some of the Adidas balls. They aren’t as good. The brazuca is also the most simple, maybe because it only has 6 panels.