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Twelve Sides of Sticky Note Pentagons

Present from Angela

My daughter gave me an dodecahedron. Each of its 12  faces holds 25 sheets of sticky note papers. I’ve been doodling on them.

Doodling on a Dodecahedron
Doodling on a Dodecahedron

With my family around this week this is the perfect thing for me to be playing around with. As I drew on the sides it was nice to know that when I finished all 12 sides that I could peel off the pentagonal sides and start all over again.

But what should I do with the first set?

Pentagons on Black Dodecahedron undone
Pentagons on Black/
Dodecahedron undone

What I’ve been doing is sticking them on black paper. Then I filled the sides of the shape again. And again. And again.

Lots of Pentagons
Lots of Pentagons

So far I’ve filled up the sides four times.

This is a perfect project for right now. While we are sitting around together talking, having coffee, or just being in each others’ presence, I can be using my colors.

Vacation week shapes
Vacation week shapes

I don’t intend to fill all 300 pentagons from my 12-sided shape, but I think I’ll do a good bit more.

a growing shape from shapes
a growing shape from shapes

Am satisfied to be finishing off this year with this construction

Happy New Years to all. May your New Year be filled with curiosity, exploration, and color.

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.)

 

simple book binding

Little Books to Give Away

Three Inch Square books

An artist friend of mine makes something each year for the children who come to the food bank in her community. Last weekend she came over and we worked out how to make a box that would contain items for the kids. After she left I started thinking about making little books to donate towards her efforts. It took awhile for me to come up with what kind of book I could make that was just the right balance of being not incredibly work intensive, while still being something that I am proud to offer.

3" x 11" paper strips
3″ x 11″ paper strips

These books began with some medium weight papers strips, cut 3″ x 11″. I used something kind of fancy because I have it around, but any kind of colored copy paper would have been fine to use.

Book Block paper 3" x 6"
Book Block paper 3″ x 6″

I’m using regular copy paper for the book block. This shows the paper separated into grouping of 12 papers, so the books will have 48 pages.

These papers for the inside of the book are cut to be 3″ x 6″. (Question for the grammar police: does the period go inside the inch symbol?)

I have a little guillotine cutter in my house that cuts piles of paper nicely. I paid $800 for it at a time when I barely had two nickels to rub together. It was so worth it. I see similar ones on the market now for $99.00.

Next, each cover got folded in half, then I lined the center up with the number 7 on my little paper-cutter.

A little wide of the 10 inch and 4 inche marks
A little wide of the 10 inch and 4 inch marks

These covers need to be just a bit longer than 6 inches so I made the folds at about 3 1/8″ away from the center, using the markings on my paper-cutter to show me where to fold.

 

Modified Pamphlet Stitch
Modified Pamphlet Stitch

I decided to use a needle with a  modified pamphlet stitch to for the binding so that I’d have to make only one hole in the spine (with my very sharp bookbinders awl). (I love my tools)

All done!
All done!

Here they are, all ready to go.

This was such a satisfying little project.