design · Geometric Drawings · geometry and paper

What to do about Color Combinations

 

Steal them.

Since I started decorating my own papers with geometric designs (as well as decorating geometric designs) I’ve been flummoxed about color combinations. Some of the decisions I’ve made have been truly horrible. Sometimes they’ve not been so awful, but, even then, it takes way too long to come up with color combinations that look good to me.

I suppose I could take an on-line class about color theory, but somehow I’m just not drawn to do that just now. Abode has a palette-sharing site, but it’s not supported in the version I use. Recently, having spent way too much time having way too little success, it finally occurred to me to try out dipping directly into the palettes of painters who use color in a way that sing to me.

Geometry and Georgia O'Keefe
Geometry and Georgia O’Keefe

I probably wouldn’t write about this if  I could do this only in Adobe Illustrator, since this info would be totally useless to most people. I noticed, though, that more and more people in my circle are using Inkscape, which is a free graphics program, and it turns out that dipping into the palettes my favorite painters is even easier to do in Inkscape than Illustrator.

Fra Angelico
Fra Angelico

Here’s what to do in Inkscape. Find a painting you’d like to dip into. Save it to your computer. Drag and drop it into Inkscape. Select the shape or area that  you want to color. Press F7 or choose the eyedropper tool (second to the last tool from the bottom on the left side) and click on the color on the painting that you want to use. That’s it.

Vectorizing the Image in Adobe Illustrator
Vectorizing the Image in Adobe Illustrator

To do this in Adobe Illustrator, it’s bit more complicated. Place the image into the Illustrator file, then vectorize it  in Image Trace. I generally use the high fidelity photo setting in image trace. This separates the painting into regions, which if you zoom in really closely looks abstract and totally cool (in Inkscape, getting this close just looks blurry).

Up-close O'Keefe
Up-close O’Keefe

Just like in Inkscape, to harvest the color use the eyedropper tool, which has the key shortcut “I”. I’ve been using the live paintbucket tool (k) to fill in the areas that I want to color, but, like Inkscape, choosing the shape then the eyedropper works too.

Even more O'Keefe
Even more O’Keefe

Now, I just want to mention that even though this is the best method I’ve used to choose colors digitally, there’s still a bunch of trial and error. But instead of me doing trail and error with millions of colors, I’m using this more limited palette. Works for me. Am having lots of fun with this.

Addendum:

Harry O’Malley just pointed me towards http://www.colourlovers.com/, which looks like the internet’s free version of Adobe’s Kuler. Yay! Another color resource! (I can use all the help I can get.)

 

 

 

 

folding · geometry and paper · geometry and paperfolding

A Square of Your Own

Squares, scaled
Squares, scaled

Making a plain old square exactly the size that you want can be such a chore. Too much can go wrong.

Squares can become so many different things (think ALL origami) that it’s worth knowing how to make a square just the size you want without getting stressed out.

Here’s how to do it, via the photo essay, followed by the video tutorial.

plain piece of copy paper
plain piece of copy paper

Here’s a regular piece of copy paper. The first steps look like I’m heading towards folding a square whose side is already predetermined by the short edge of the paper, but no. Be patient. This is going to be a surprise. Trust me.

First Step
First Step

Fold that short edge to meet the long edge, making sure that your fold ends (or starts) exactly at that corner. What you are doing here is bisecting that corner angle. If you cut away that rectangular flap on the edge, and unfold the triangle you’d have a square, but this isn’t what we are doing now. (Doing that was a different post, )

Marking the size of the new square
Marking the size of the new square

Unfold the fold then make a mark to indicate size of the square you want to make.

continuing...
continuing…

What I’m going to write next sounds horribly complicated but it’s easy to see and do.

Curl over that corner that has the fold going through it, lining up that corner point with the fold line it is leaning towards, and also lining up the upper edge of the paper with that mark you made. Press the fold.

Here’s a closer to look:

Closer Look
Closer Look

Now draw a line that traces around that folded down corner.

Time to cut out the square
Time to cut out the square

There’s your square!

Confused? Here’s a video to watch:

Got it?

Origami Pockets
Origami Pockets

Now make cool stuff.

Addendum: here’s a post that shows what I showed, plus another great way of making a square. https://mikesmathpage.wordpress.com/2018/01/23/a-fun-folding-exercise-for-kids-from-paula-beardell-krieg/

geometry and paper

Last Minute Wrapping Paper 2017

PaulaKrieg
Paula Krieg
Triangles

Last year, on December 24, I posted a page of decorative papers I had created to do some last minute wrapping. To make the papers I lifted images from pages and posts made by people whose work I love, so, naturally, I loved the papers. It was such a pleasure to do that I’m doing it again.

See the PDF at the bottom of the post to get the best copies.

Dan-Anderson's wrap
Dan Annderson
https://twitter.com/dandersod/status/939290160570789889

Here’s an exquisite doodle by Dan Anderson. Of this, he indicated that he didn’t really know what was going on with the creation of this graphic….which is how I usually feel about everything I do.

https://seekecho.blogspot.fr/2017/12/nicomachuss-theorem.html
Simon Gregg’s wrap
https://seekecho.blogspot.fr/2017/12/nicomachuss-theorem.html
https://twitter.com/mathhombre/status/940263419957178369

The page above is based off a graphic by Simon Gregg. A big part of the reason I picked this image is that it is part of a post that I really loved reading, https://seekecho.blogspot.fr/2017/12/nicomachuss-theorem.html

https://www.desmos.com/calculator/1vhiosg7gs
Suzanne von Oy
https://www.desmos.com/calculator/1vhiosg7gs

Suzanne Von Oy created a Desmos graph, which showed cows in a tornado. It was so silly that I, of course, had to play around with  it. That middle, green swirl in the picture above, is suppose to be kind of like a Christmas Tree with cow ornaments. (don’t judge me)

https://mikesmathpage.wordpress.com/2017/05/09/sharing-john-baezs-juggling-roots-post-with-kids-part-2/
Mike Lawler https://mikesmathpage.wordpress.com/2017/05/09/sharing-john-baezs-juggling-roots-post-with-kids-part-2/

Here’s another image that I chose based on how much I liked the post that it is part of. There were all sorts of wild shapes associated with this Lawler family post, but I like how rotating just one of the images made this fun pattern.

Malke Rosenfeld
https://mathinunexpectedspaces.wordpress.com/2017/12/10/star-o-rama-and-how-to-make-them/

When I saw this image stars-in-circles posted by Malke Rosenfeld, it just knocked my socks off.  Note the link in the caption, it says Star-o-Rama and how to make them!

https://twitter.com/GHSMaths/status/934026448767258624
Martin Holtham
https://twitter.com/GHSMaths/status/934026448767258624

It was unusually hard to figure out which of Martin Holthman mathart images to play with, as, lately, he has been having way too much fun making cool stuff. .Finally picked out this,  because it was not only awesome, but also seasonally snowflakish.

https://www.geogebra.org/m/xdHeBmYq
John Golden
https://www.geogebra.org/m/xdHeBmYq

I discovered the graphing program Desmos shortly after it came on-line. I’m not fluent enough in math to make amazing graphics with it (yet?).  Geogebra has been around for, well, I don’t know how long. I haven’t spent much time with it, but John Golden has spent a great deal of time with it. I really couldn’t decide which of his images to use, so I chose two. I considered chosing three, but I’ll save that third one for another project. I think that wrapping a small package with these undulating black and white lines will look really great. I’m especially looking forward to using this one.

https://www.geogebra.org/m/BqtGmER7
John Golden
https://www.geogebra.org/m/BqtGmER7

What’s the point of making mathy wrapping paper without some rhombic tori? No point at all. So here you have them, thanks to Mr. Golden.

If you want to print any or all of these papers,  I thin that the best way to do it is from a PDF.

Here’ the PDF Wrapping Paper 2017 . All nine images are here, but you can choose to print just the ones you need today using the dialog box on your printer.

Happy wrapping.

geometry and paper · geometry and paperfolding

Alison and her Milk Cartons

The Star that Nancy picked out to keep
The Star that my friend Nancy picked out to keep

The morning that I started this post I saw a series of photos tweeted out by Alison Martin. She’s been making some wondrous constructions using milk cartons. Here are two of the five tweets that caught my attention:

My attention was riveted on the fact that she had thought of this very accessible way to make slices of squares which she could then skew to make a veritable symphony of constructions. (Yes, am mixing metaphors. Will welcome edits…)

Sadly, our milk comes in glass bottles.

Also, since I do projects with students in schools, I have this thing about wanting to make everything from regular copy paper.

Paper Starbursts made from regular copy paper
Paper Starbursts made from regular copy paper

As I worked out how to create these starbursts I thought about the methods I use of working with paper that are not obvious. I made a video, in which I’m talking the whole way through, pointing out details of working with paper.

 

 

Here are some photos which repeat bits of what I’m showing in the video.

Not exactly a milk carton
Not exactly a milk carton, but it has a square end. Cuboid? Rectangular Prism?

Start with folding a tab. Next, ignoring the tab, fold a piece of regular copy paper into fourths, and then glue to the tab to make a shape with a square end.

Slice and glue
Slice and glue

Slice off a strip. Now, it’s not obvious how to continue, so don’t start slicing lots of strips. Just STOP after one slice.

Spread glue on one section of the tube (the part in the photo that has pencil lines on it)  then glue down that one slice of the paper at the edge of the tube. See photo below.

First Ray
First Ray, glued

Cut away another slice from the glued section, the same width as the slice that’s been glued on to it. Repeat and repeat…

A series of Rays
A series of Rays

…until you have 5 or 6 or 7 or 8 or however many rays you want or have materials for. I usually make 7 rays. Then glue the parts together that make them stay fully rotated.

The inside stars are a bit different to do. Make that shape with the square end again, but the width of the of this paper with should be about a third thinner than the paper you started with. (My first paper was 8 1/2″ wide, this second part was done with 5 1/2″ wide paper)

I’m going to let you figure out where the glue will go: this is pretty obvious.

What’s not so obvious is how to get the ray nicely placed.

What you do it this:

Placing an inner ray
Placing an inner ray

Splay open the big ray, slide in the small ray, then….(this is important, not obvious!)…

mvimg_20171220_171238~33729147328732120578..jpg
Sandwiching squeeze

...squeeze the neighboring rays together, which makes all layers align just right.

After making this inner layer of rays, if you want to make an even more inner layer of rays, don’t bother with making a closed shape with a tab, just fold paper into fourths.

mvimg_20171220_180530~22052134737897814684..jpg

See, like this.

mvimg_20171220_180947~33464398805300240078..jpg

Now here’s something I wasn’t expecting: they stand up by themselves.

And they stack.

(Watch the video. To the end. It’s much better than this post.)