Art and Math · Arts in Education

Designing Outside My Envelope

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! Be sure to play around with changing the numbers on this graph, so you can see how simply changing the numbers changes the curve.

Decorated Boxes
Decorated Origami Boxes

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 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.

Origami Masu box
Origami Masu box

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 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:

Design to apply to origami box
Design to apply to origami box

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. 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. 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.

Heart, with help from Jen
Heart, with help from Jen

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:

Polar Rose, Desmos
Polar Rose, Desmos

Next open the image in Paint then use the paint bucket to fill in the blanks.

polar rose raster
polar rose raster

It’s true that the edges won’t be perfect. Raster images don’t do curves well.

polar rose raster detail
polar rose raster detail

Even though, close up, the edges are rough, still, this prints up quite nicely.  This is definitely a way of getting the job done!

Here’s what John just did, using this workflow

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