Paula Beardell Krieg

Paula Beardell Krieg

@paulakrieg.bsky.social

Happy to share art and math play

184 Followers 106 Following 173 Posts Joined Nov 2024
4 days ago
Preview
Make Art — Joshua W. Cotter

#makeart www.joshuawcotter.com/words/make-art

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4 days ago

Yes.

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4 days ago

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

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5 days ago

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.

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5 days ago

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

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5 days ago

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?

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1 week ago

The constraints of the typewriter.

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2 weeks ago

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

⬜🟩🟩🟩⬜
🟩🟩🟩🟩🟩

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2 weeks ago
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

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1 month ago
Video thumbnail

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

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1 month ago

So super cool!!

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1 month ago

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

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1 month ago
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.

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1 month ago

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.

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1 month ago
Post image Post image

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...

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1 month ago

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.

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1 month ago

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.

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1 month ago
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

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1 month ago

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

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1 month ago

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

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1 month ago
Preview
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...

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1 month ago

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?

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1 month ago

Oh! So glad you are doing this!

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1 month ago
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.

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1 month ago
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+

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1 month ago

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

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1 month ago
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.

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1 month ago
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.

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1 month ago

This is so awesome!

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1 month ago

Watching.

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