Paula Beardell Krieg

Just for the record, I agree with David on everything.

It’s one of the few books that I reread multiple times. felt like it illuminated so much that was interesting to know. A hidden history that explained so much.

Ooo! I can get this book through my library system!

Did you read his book Infinitesimal? I liked that book very much, love the deep historical perspective. I don’t know anyone else who read it. It didn’t get good reviews…. Either I have bad taste, or the negative reviews were just because it’s a book about math?

The constraints of the typewriter.

Can’t resist aharing today’s wordle
Wordle 1,714 2/6*

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Paper cubes which have been truncated, pierced and altered in various ways. Some of the negative spaces have been reconstructed.

Towers, or totems, of altered cubes

Am teaching a class right now in which we construct cubes then alter them... Reminds me of the math concept of parents functions which are altered. We then combine the truncated and pierced cubes in fun ways. #mathart #paperengineering

Happy Valentines Day.
Made this in 2018, and still love it.
Loving Triangles.

So super cool!!

I image that your students are thrilled with their work. i predict that they will always joyfully remember this week ?

Folding a polyhedron

Using paper pedestal for an octahedron

Wooden sculpture on paper. PO edestal

Artist @hakoyamaho post models and their nets on Instagram. This one of golden ratio proportioned prisms caught my eye. Makes a cool pedestal for my Minnesota themed octahedron and for a small wooden sculpture by my husband.

I've been hearing from blog readers, in comments and DMs, who have lived in Minnesota, but who are not there now, It's touching how much they appreciate having something to make that honors their connection to the state.

Heartbroken over the events of the past few days. For my Minnesota friends, here is an Octahedron decorated with the color of your flag and your North Star motif. PDF on my blog post bookzoompa.wordpress.com/2026/01/26/s...

It looks like it's easiest to break up just one of the numbers, but not both. It's helpful that you show common mistakes.

I'm thinking that they believe that they've rounded up 300% to 400% of the illegals, and that it is looking like they have detained something 1000% of the worst of the worst. Waiting for verification.

Octagons ornaments with heart decorations, sending out some love in the world. From me to you

Octagon ornaments hanging in my favorite coffee shop.

If the events of the day feel unbearable, I offer a bit of geometry to help you feel grounded. Here's a PDF to make some octagons. drive.google.com/file/d/1bOJ5... Print on card weight paper if you can, glue neighboring tabs together, add string before closing up. #mathart #octahedron #Healing

Good to know that they can wield knives well....? :)

Ahh! I've never feasted on a mobius bagel!! Can't wait.

Summer Projects with Teens It’s not really possible to express how excited I was to be working with teenagers this summer. I saw a group of 6 thirteen-year olds and along with two 18 year- old assistants, who did most …

You probably have it all planned out. Even so, you might enjoy this post of mine from the past bookzoompa.wordpress.com/2019/08/28/s...

7 days, 5 hours each day is a lot of time, for you and for them too! Hope you can balance some quieter explorations with the more dynamic stuff. Are you doing anything with Mobius strips?

Oh! So glad you are doing this!

Note the negative area between the cube and the cuboctahedron to imagine the firm of the differences between the shapes

Just because I like surprises, this cuboctahedron has a hidden compartment which stores the pieces that are the difference between the cube and cuboctahedron.

Here's the cuboctahedron with its irregular tetrahedron corners reattached, reverting the cuboctahedron to its original cubic state. PS I am so glad the Bluesky automatically writes out the word"cuboctahedron" after I write the first four letters of the word! TY

...seeing the space between the octahedron and the cube defines the piece of the cube that has been removed. But why stop there? My cuboctahedron has a secret compartment that stores the liberated edges, which can be examined and reattached.

The Archimedean Solid cuboctahedron. Although its Parent Platonic solid can be either a cube or an octahedron, I'm looking just at the cube derivation.

The cube around the cuboctahedron splays open for maximum exposure

What bothers me about Archimedean Solids is that I can't visualize the part that was removed from the Platonic parent shape. Here's a solution for the cuboctahedron: build the Platonic Solid parent cube around it and notice the shape of the negative space+

So glad you like it David. Love the idea of sharing a smile with you.

Top view of cube,/ octahedron duality

The octahedron in this little packet can jump right out and see the world outside of its nest.

Opening the cube to reveal the octahedron in position to touch the middle of each face of the cube nicely illustrates how the octahedron is the dual of the cube.

Bonus: the octahedron can be removed.

Cube, waiting to be opened

Cube, nicely splayed to reveal an octahedron whose vertices are the mid points of the faces of the cube.

I super like making models that illustrate simple concepts that are hard to grasp with words or in pictures, but which are easily grasped when seen in 3D.

I've been pondering how to make a good model that show dual polyhedra, starting with the cube and octahedron. finally got it.

This is so awesome!

Watching.

Always call. Never just wait.

Both fractals and planar tilings use symmetry actions, just different kinds. Fractals introduce scaling to the iterations.