Exploring an amazing tweet from John Carlos Baez with my younger son

I saw an incredible tweet from John Carlos Baez last week:

Here’s the picture in case the tweet isn’t embedding all that well for you:

Baez

I thought exploring some of these shapes would make a great project for kids, so I began by asking my son (in 7th grade) for his thoughts on the shapes he was seeing:

Next we built a few of the cubes from our Zometool set and talked about some of the shapes. First, though, I asked my son to give his definition of what an n-dimensional cube was:

Finally, we played around by a different version of a 4-dimensional cube – “Hypercube B” by Bathsheba Grossman. This amazing version of the hypercube makes amazing shadows and my son was able to find a projection that was a little closer to the projection of the 4d cube in Baez’s tweet:

Also, here’s a video I made a while back showing some other (almost freaky) 2d projections from our Zometool model of Hypercube B:

Definitely a fun project – thanks to John Carlos Baez for sharing some of his ideas about higher dimensional cubes on twitter!

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Finding the volume of a rhombic dodecahedron with our zometool set

Yesterday we did a neat project inspired by a tweet from Alex Kontorovich:

Sharing a 3d geometry idea from Alex Kontorovich with kids via zometool

At the end of that project a question about finding the volume of a rhombic dodecahedron came up. Since I was going to be out this morning (and my older son was working on a calculus project) I asked my younger son to play around with the Zometool set and see if he could actually find the volume.

Fortunately he was able to – here’s how he described his work:

Sharing a 3d geometry idea from Alex Kontorovich with kids via Zometool

I saw an interesting tweet from Alex Kontorovich earlier this week:

We’ve looked at but the Cuboctahedron and the Rhombic dodecahedron before, but I thought it would be fun to revisit the shapes. I also hoped that we’d be able to recreate the shape in the picture with our Zometool set.

So, first we built a cuboctahedron and the boys talked about what they saw in the shape:

At the end of the last video the boys thought that the dual of the cuboctahedron would possibly also be another cuboctahedron. Off camera we built the dual, and happily were able to recreate the shape from Kontorovich’s shape!

They were a little worried that we didn’t have the “true” dual, but I think they came around to believing that these two shapes were indeed duals:

Definitely a fun project – it is always fun to see what you can make with a Zometool set. Maybe tomorrow we’ll revisit an old project of finding the volume of a rhombic dodecahedron. That’s another project which Zometool really brings a lot to the table.

A fun creation with our facets

My older son is working on a different math project this morning, so once again my younger son was working along. While cleaning up a little bit yesterday we found our old collection of “facets” – so I asked my son to build something for the Family Math project today.

He built a really neat shape:

We have done two previous projects with the facets (including making a big circle 🙂

Our Facets have arrived!

Our second facets project!

They are definitely fun to play around with!

Playing with Archimedean solids

For today’s math project we are doing a 2nd project from George Hart and Henri Picciotto’s Zome Geometry:

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I asked the boys to pick three shapes from the section on Archimedean solids. Here’s what they picked:

Shape 1: A Truncated Icosahedron

You start with a triple length icosahedron:

They you truncate it:

Shape 2: A truncated dodecahedron

Start with a dodecahedron with sides made from two short blue struts and 1 medium blue strut:

Now truncate it:

Shape 3:

Truncated Octahedron;

Start with an octahedron with side lengths equal to 3 long green struts.

Now truncate:

Two projects from Zome Geometry

For today’s math project I asked the boys to pick a project from George Hart and Henri Picciotto’s Zome Geometry:

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My younger son picked a project about “Rhombic Zonohedra” which led to a terrific discussion about quadrilaterals and 3d geometry:

Ny older son picked a project on stellations of a dodecahedron. He was a little confused by the directions, but sorting out the confusion led to a great discussion.

I wish every kid everywhere could have the chance to play around with a zometool set.

Revisiting folding a dodecahedron into a cube

Folding a dodecahedron into a cube has been one of my favorite projects to do with the boys. Our first few projects about a “dodecahedron folding into a cube” are here:

dodecahedron fold

A neat post from Simon Gregg showing that a dodecahedron can fold into a cube

Can you believe that a dodecahderon folds into a cube?

(see the link above for the source of the amazing GIF on the right of the screen!)

Some 3D Geometry for Pamela Rawson

Today I had the boys work through the whole project on their own – just stopping every now and then to check in and hear about the progress.

Here are their initial thoughts after building the dodecahedron:

In the second part of the project the boys constructed one of the cubes that can be inscribed in a dodecahedron:

For the 3rd part of the project they “folded” the dodecahedron into a cube

Finally, the boys connected up the zome balls inside the cube and found an icosahedron.

Folding up the dodecahedron into a cube is one of my all time favorite math projects.  It is such a surprise that the two shapes can be connected in this way, and it is really fun to explore this connection with our zometool set!