Sharing Kelsey Houston-Edwards’s singularity video with kids

We’ve been enjoying going through Kelsey Houstin-Edwards’s new video series. This week’s was a bit more advanced than some of the prior ones, but I gave it a shot with the kids anyway. I tried to focus on connecting the ideas about singularities in the video with some of the 3D printed shapes we’ve been studying from Henry Segerman’s new book.

Also, I’m just getting over a few days with the norovirus, so sorry if this one (including the write up) has a bit less energy than usual.

Here’s the latest PBS Infinite Series video:

Here’s what the boys took away from the video:

Next we looked at a couple of the shapes that Henry Segerman has made to study with shadows. We were able to see (eventually) that the shadow of the north pole would be a point at infinity – or a singularity.

At the end of this video we started looking at a torus, and the conversation took a very interesting topological turn.

So, we landed on a question of what different shapes might be a torus. It took a bit of time to straighten out this idea, but after a few minutes we came to an agreement on what a torus was.

After that we saw that we didn’t have the same singularity problem trying to create a map that we had on the sphere.

After talking about the torus we spent the rest of this video talking about the pseudosphere which has more than one singularity.

So, another great video from Kelsey Houston-Edwards. It was fun connecting her ideas with some of the 3d prints we’ve been studying lately.

Things to print and do in the 4th dimension

Today our math and 3d printing project combined ideas from two great books.Β  First Matt Parker’s book Things to Make and Do in the Fourth Dimension and Henry Segerman’s book Visualizing Mathematics with 3D Printing

books

We started out the project today by watching Parker’s fun video about 4 dimensional platonic solids:

Next we look at some of the 3d prints we have of projections of the four dimensional platonic solids from Segerman’s book. Here’s what the boys had to say:

Then we went through some of the shapes in more detail. Here’s the 5-cell

Here’s what the boys thought about the two different versions of the hypercube that we have.

I’d add that our Zome version of Bathsheba Grossman’s “Hypercube B” blew me away, too:

Finally, we talked about the 24-cell and the 120-cell. Sorry this part went a little long, but the shapes are really cool!

I’m loving 3d printing more and more every day. The opportunities to take ideas from books and videos and put them directly into the hands of kids is just amazing. Thanks to Parker and Segerman for doing the heavy lifting for me on this project!

More projects from Henry Segerman’s math and 3d printing book

We are continuing to explore the different ways for kids to see math with 3d printing. Henry Segerman’s new book has been an incredible resource for us in this long-term project:

segerman

Yesterday I asked the kids to pick more shapes from his book to print. My older son picked “Topology Joke” and my younger son picked a shape that we’d already printed, but unfortunately the prior pick didn’t survive an unexpected encounter with a book πŸ™‚ Here are the shapes and what the kids see in those shapes.

“Topology Joke”

My favorite quote – “A torus somehow equals a coffee cup”

Here’s my younger son looking at the trefoil knot on a torus. The interesting thing to me about his discussion of the shape is that he thought the torus was just as interesting as the knot:

At this point we have close to 50 3d printing projects for kids on the blog. Henry Segerman’s work and Laura Taalman’s work have been incredible inspirational for me. I can’t wait to explore more with how 3d printing can help kids see math in a way that was far more difficult to see previously.

Our Facets have arrived

About two years ago we supported the Kickstarter campaign for Facets. The program had quite a few road blocks thrown in its way, but Ron Worley stuck with it and has nearly completed the project. Good for him.

Our package arrived last night and we did a quick project. Here’s the “unboxing”:

After opening the box I had each of the kids build a shape. Here’s what they had to say – younger son first:

Older son next:

I’m excited to do some more projects with the Facets – it was really cool to see how quickly the boys could create interesting shapes from 3d geometry. The Facets look like they’ll be a really fun tool to use to explore geometry with the boys.

Gil Kalai’s Median game

Saw this neat tweet from Jordan Ellenberg yesterday:

The game itself is really simple enough for kids to understand, so I thought it would be fun to explain it to the boys and play. Here’s the explanation and a little bit of discussion about some math-related ideas that the boys had about the game:

Next we played the game with the boys writing down their numbers on the board and me selecting my number with an 8-sided die. We didn’t know the tie breaker rules so we just made up something at the end. It was fun watching them find a little bit of strategy on the fly:

Finally we wrapped up by talking about some strategy ideas they learned playing the game:

Definitely a fun game. It would be fun to play this in a room full of kids (of any age!) and see what creative strategies they would come up with.

Sharing Kelsey Houston-Edwards’s Markov Chain video with kids

The latest video from Kelsey Houston-Edwards is incredible:

I love the problem she’s presenting – it seems completely impossible to someone hearing it for the first time, but after her video kids can solve similar problems immediately!

We started the project today right after we watched the video. The first thing I did was ask the kids about what they just saw:

Next we tried to solve the rook problem that Houston-Edwards posed at the end of the video. The kids were able to solve it pretty quickly πŸ™‚

To wrap up, we took a crack at solving the same problem with a bishop. This took a little longer, but was a great lesson. Hopefully this slightly more challenging problem allowed some of the ideas from Houston-Edwards’s video sink in:

I’ve been loving this new series of math video since it started, but this one was extra impressive for me. It is really cool to see someone explain such a challenging problem in essentially a public lecture setting. Can’t wait to see where this series goes in 2017!

Exploring 3 intersecting cylinders with 3d printing

Calculating the volume of 3 intersecting cylinders is a classic calculus problem.Β  The 3 cylinder problem caught my attention a few years ago when Patrick Honner shared this video about the 3d printing lab at his high school:

I wrote about my reaction to the video here:

Learning from 3D Printing

Today we used our 3d printer and the F3 program to explore the intersection of three cylinders. Here’s what they boys had to say when they saw the setup on the F3 program – my older son went first:

Here’s what my younger son had to say:

After the shape finished printing I had the boys talk about their thoughts when they had the shape in front of them. Here’s my older son’s thoughts:

And next my younger son:

Even though this is probably a better Calculus example, I loved being able to share the shape with the boys. It is fun to hear kids talk and wonder about fun shapes like this one.

My plan for the 2017 Grades 2-3 Family Math night

I’ve been running the “Family Math” nights at my younger son’s elementary school for the last two years.

For the grade 2 and 3 kids last year we had a really fun program. The details are here:

2016 Family Math night for grades 2 and 3

The main program was:

(i) Doing some mathematical coloring,
(ii) Exploring the fold and cut theorem, and
(iii) Larry Guth’s “No Rectangles” program

The kids love the “no rectangles” problem so much that I basically couldn’t get them out the door after the hour was up!

The event will be similar this year – a 30 min introduction with fun little math activities spread throughout the room followed by a 60 min session with 3 longer activities. The activities for the main session this year will be:

(1) Playing with “Over / Under” by Gamewright (10 min)

over-under

I learned about this game over the year-end break. We did a short project with it last week, and I think some of the questions will make for a really fun ice breaker in a room full of kids and parents. Here’s theΒ  project we did with the game last week:

A review of “Over / Under” by Gamewright

(2) “Fold, Punch and Cut for Symmetry” by Joel David Hamkins (20 min)

Last year while planning for the Family Math nights I found this fun activity:

Joel David Hamkins turned the picture into an incredible activity for kids and I’ve been waiting to use it ever since πŸ™‚

Math for Nine year olds by Joel David Hamkins

I’ve printed out the full activity for the kids to play with. We won’t be able to go all the way through it in 20 min, but I hope the kids (and parents!) will enjoy completing the activity together when they go home.

(3) Jim Propp’s 2xN rectangle exercise (20 min)

Last March Jim Propp suggested that I try out a neat counting exercise with my kids.Β  His suggestion came after seeing our project on the Aztec Diamond:

Screen Shot 2016-03-02 at 7.07.20 PM

I’ll use the Aztec Diamond to motivate the project which is counting the number of ways you can create a 2xN rectangle with 2×1 dominoes. My hope is that the enthusiasm from the “no rectangles” problem from last year will carry over to the “lots of rectangles” problem this year! I also hope the kids and parents will enjoy the surprising appearance of the Fibonacci numbers. Here’s what it looked like when I went through the project with the boys last Spring:

A fun counting exercise for kids suggested by Jim Propp

The event with the 2nd graders is next Tuesday. Can’t wait to see how this all goes πŸ™‚

Using 3d printing to talk symmetry with kids

We’ve done a lot of projects relating to platonic solids and dodecahedrons in particular. A really neat fact about dodecahedrons is that you can use the verticies to put 5 cubes inside!

It isn’t just a mathematical “fun fact” either – the symmetry groups involved play roles in important mathematical theorems.

For today’s project I wanted to explore one cube in a dodecahedron and look at the relationship between the rotations of the cube and the rotations of the dodecahedron.

We started by looking at the dodecahedron by itself:

Next we moved to looking at the cube in the dodecahedron and studied what rotating the dodecahedron did to the cube:

Finally we looked at some 3d printed models that we made to see if these models helped us explore the rotations a bit more:

I was a little disappointed that I made the 3d printed models a bit too small, but I still like how this project went. I’m going to try again with some slightly larger models with my older son.

A fun project on the Arecibo Message inspired by a Holly Krieger Tweet

Saw this neat Tweet from Holly Krieger earlier today:

After reading the post I was super excited to go through it with the boys when they got home from school.

So, we read the post after dinner and then made a code out of snap cubes. Here’s what the boys thought of the post:

and here’s our secret message!

We had a lot of fun with this project. It looks like something that could be pretty fun with a group, too, so I’m thinking about using it for 4th and 5th grade Family Math night at my younger son’s school next month.