Mathematicians celebrate Valentine’s Day with more unbridled abandon than any group I’ve ever seen. Kindergartners get the silver, for liking the day of hearts, but, hands down, mathematicians take the gold.
I’m gathering just a fraction of the posts I saw coming out of the math community this past February 14. Images started popping up early in the week in anticipation of the big day. Luke Walsh and and Iva Salley were the early birds. Iva with her heart shaped number puzzle…
I still have some holiday cards hanging around, giving me pleasure each time I see them. For instance, there’s this one from Judith. Looks like she got it at the Museum for Modern Art. It’s shiny and sparkly, many layered and changes with the light.
This one is from Ed, It’s like a little box, though it collapses flat. There’s two layers inside, This one also changes quite a bit with the light, which I love. I particularly like the little dog in the corner, and the way she’s bonding with the snowman. Or the bird? This card was designed, then cut and assembled by Ed’s own hands.
Another homemade card, from my friends Joan and Hank. Joan delights me every year with her drawings. She printed this on her home copy machine, then added embellishments by hand. Notice how my little bird statue it hoping to bond with the trumpet.
There’s nothing handmade about this card with the deer and snowman, but I like the expression and the gesture of the snowman so much that this card from my sister-in-law has stayed on display.
In December Susan Joy Share and I took a ride together from NYC to New Haven and visited the studio of the pop-up card company Up With Paper. We were mesmerized by just about everything about our time with them. They gifted us some cards, including this multilayered unicorn card which becomes even more magical when the spot that says PRESS is pressed: lights flicker on behind the unicorn. This is quite lovely. It sits on sort of dark shelf in my house, so the full effect of the lights is always a possibility. (Thank you, Monica!)
This cluster of gingerbread houses is also from Up With Paper. The pop-up in the middle is surprising to me, as I don’t generally think about making a house from center-aligned criss-cross. This criss-cross structure has tabs on it that extend to become the flanking gingerbread houses. Very beautiful, very elegant, very clever. I actually got a box of eight of these. I gave away a few. The first one I gave away was to Fabio, who ended up being our taxi driver for each of our stops during Susan’s and my day in New Haven. If you go to New Haven you must contact Ada’s Taxi service and ask for Fabio. You must.
The day after Susan and I were in New Haven, we spent the day in NYC, mostly at the Cooper Hewitt Museum. I bought this snowflake card in the museum shop. I love how the slits in the snowflake allow the snowflakes to rotate.
This strange-looking rectangle arrived in the mail. It’s all cut paper and tabs and slits. I don’t think there’s a drop of glue in this. It moves! When it moves, those odd little shapes line up!
I don’t really think it’s time to put this one away. Maybe I will put it away when we achieve world peace.
Then there’s this lovely image to maybe put away.
Us girls colored this Christmas Eve and Christmas Day. It sits in a corner near our couch.
This gives me such pleasure every time I see it that I don’t think I will be putting it away yet.
I got to spend some time with a group of kids and moms this past Sunday. They had asked me to plan a math/art project for them. Last time we did this we played with shapes scaled according to the golden ratio. This time I wanted to help them make images that are made by rotating a graphic around a circle. We used a circle that was divided into twelve equal sections, and we got to talk about how rich the number 12 is, in that it comes up often in measurement of time (hours, months), quantities (dozen), distance (Inches) and so much more.
Images were made in two ways. One was to connect the dots around the circle according to a rule, such as connect the first dot to the fifth, connect the fifth dot to the tenth, connect the tenth dot to the dot that is plus+5 further around the circle, then continue until you are back where you started from. A star emerges!
We started the afternoon by sitting in a circle of eight people, and doing the skip-counting activities that I described above. This was actually a thrill to me, as it’s something I’ve wanted to try out for a long time. As the star shape grew within the circle of people, who were the “points”, everyone was thrilled. They had no idea a star would emerged. I knew, but I was thrilled too.
I had PDF printout of circles and shapes.People cut out shapes that they wanted to rotate around the center, then colored them in if they wanted to.
The moms seemed to like this activity at least as much as the kids.
I never know how these projects will go. A couple of the boys didn’t want to be coloring any more after a while. One boy in particular really liked cutting paper, so I got him started with another kind of rotational symmetry: making snowflakes!
I hadn’t thought about snowflakes beforehand, but liked the way I was able to link to something that was already familiar to this group.
After awhile one of the girls was finished with coloring, I showed her how to make an origami pockets that were sized for the drawings to slip into.
She really liked making the pockets, and made them for everyone. This also let me segue into showing her how to make a square from a sheet of paper.
In the end, we had made lots of images, pockets, snowflakes and our work area was delightfully messy. Everyone helped with the cleanup, especially with the tiny pieces of paper on the floor.
At the end we put our tiles out on display.
A couple of hours later one of the mom’s texted me saying that, on the way home, her kids were asking to do more of these. YAY!
I’m continuing to work on coming up with designs to use with some of my paper folding projects. This time around curvy lines are what I’m interested in. Valentine’s day is around the corner so of course I’m thinking about curvy lines.
After seeing some images I posted on twitter ,my friend Kathy H @kathyhen_asked me to blog about how I make these so her students might have some fun with curves. My initial reaction to her inquiry was negative, as I rely heavily on Adobe Illustrator, which isn’t very accessible. It took me a day or two to realize there are other options available for a student/person-with-computer, so here goes.
I start out in a free on-line graphing program called Desmos. To plot curvy lines we need to direct the graphing calculator to plot something that is cyclical. Think of a pulsing wave that goes up and down. The easiest way to tell the graphing calculator to make a wave is to reference a sine function. This is as easy as typing in a few letters. Here, take a look! https://www.desmos.com/calculator/welqj0gbm2 Be sure to play around with changing the numbers on this graph, so you can see how simply changing the numbers changes the curve.
The next thing I do is try to make the curves more interesting. One the ways I do this is to direct the graphing calculator to multiply two cyclical functions together. To see what this looks like, go here https://www.desmos.com/calculator/deea2nnuzb. BTW one of the advantages of going to these graphing links is that you can use and modify these if that is more comfortable for you. The only thing to keep in mind is that if you want to save your own changes you have to make your own account, Which I recommend.
Last thing I play around with is making curves which relate to the curves that I have, but are different. These secondary curves are derived from the first curves, but follow different rules, Look at this link https://www.desmos.com/calculator/iedzflkoot Be sure to read the notes.
Here’s the graph that I made, after much playing around, to use on the box in the photo above:
What I need to do next is to make the graph into a an image that I can color. For me, that means taking it into Adobe Illustrator and trace it using the pen tool, then color it in with the Live Paint Bucket tool. There are other options.
The simplest option would be to hit the print button in Desmos, then simply trace the pattern you’ve made and color it in. Make copies of this if you have access to a printer. Doing these by hand has a charm that no computer can match.
Another option is to use a different graphing tool called Geogebra that can output a file that can be opened in a free online vector program called Inkscape. https://inkscape.org/ What you have to do is, from the dropdown menu on the upper left hand corner of Geogebra, is choose Download As, then choose SVG. Then, open this file in Inkscape.
Personally, I can’t do everything I want in Geogebra simply because I am not familiar enough with Geogebra. Today I wanted to use the workflow I’m describing here, but I couldn’t figure out how to tell the graphing program what I wanted to do. What I did next was ask for help. Jen Silverman @jensilvermath came to my rescue and inputted my curves. https://www.geogebra.org/m/vtstwgwx Asking for help is a completely reasonable workflow. These programs are so user friendly that, after not-too-long, we won’t need to ask for help. But ask for help for as long as it takes to learn how to do this on your own.
Used Inkscape for the first time today. I didn’t know how to do anything. Googling questions about Inkscape was easy. Again, this is a program that is designed to be user friendly.
This is a post that makes sense to me, but am not sure if I’ve been clear enough.
Having access to this technology that creates these magnificent curves can be so enjoyable. Be patient, though as it takes a good bit of playing around to get a really satisfying image. Then don’t forget to hit the save button! Happy almost-Valentines day.
Addendum, later today. Read all about it!
This may make for an easier workflow.
My friend John Golden got me to try out coloring a Desmos file in Paint, which, I think, is standard program on most computers? Well, as least my computers always seemed to come with Paint, so it must be easy to get. It’s a raster program, so images won’t be super smooth, but, for classroom work, it’s looks great.
The workflow would be to save the Desmos file as a PNG by clicking the Share icon that’s in the upper right corner, then choose export. But before you do this, go into the settings by clicking the wrench icon on the near the top right and make sure everything is UNCHECKED! Your png will look like this:
Next open the image in Paint then use the paint bucket to fill in the blanks.
It’s true that the edges won’t be perfect. Raster images don’t do curves well.
Even though, close up, the edges are rough, still, this prints up quite nicely. This is definitely a way of getting the job done!