Sharing a Lévy Flight random walk program from Dirk Brockmann with kids

Last month I learned about a terrific online random walk program to share with kids:

Here’s our project with that program:

Sharing a great random walk program with kids

Last week Dirk Brockmann shared a new program:

Today I showed the boys Brockmann’s original random walk program followed by the new “Anomalous Itinerary” program to see what the boys would think about them.

My older son played with the programs first. Here are his thoughts looking at the original program – he thought the this random walk would be a good description of a particle moving through air:

And here are his thoughts on the new program. One thing that I found really interesting is that he found it difficult to describe the difference between what he was seeing here vs the prior random walk program:

Next up was my younger son. Here are his thoughts on the original program – he thought this random walk would be a good description of how a chipmunk moves.

Here are his thoughts on the new program. He initially thought this was the same as the Gaussian random walk program, but was eventually able to describe the difference:

These programs are definitely fun to share with kids. The “Lévy Flight” paths are definitely not intuitive and very different from the Gaussian random walks. It is really interesting to hear kids trying to find the words to describe what they are seeing.

10 fun geometry ideas to share with kids – inspired by a Jordan Ellenberg tweet

I saw an interesting tweet from Jordan Ellenberg earlier this week – here’s writing a new book on geometry and was asking for suggestions for neat geometry ideas people have seen:

Having spent close to 10 years now searching for fun math ideas to share with kids, the tweet from Ellenberg was a good motivation to catalog some of them.

The first thing I did was ask my kids what their favorite geometric project was – my younger son answer was about tiling pentagons and my older son mentioned Platonic solids.

So, with those ideas to start things off, below a list of some of the neat ideas related to geometry that we’ve played with in the last few years.

(1) Tiling (and non-tiling!) Pentagons

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After some new results about tiling pentagons came out a few years back, math professor and 3d printing super grand master Laura Taalman made some 3d printed models available and we had an enormous about of fun playing with them. Several projects are below, and even more information is in Patrick Honner’s article about tiling pentagons in Quanta Magazine

Using Laura Taalman’s 3D Printed Pentagons to talk math with kids

Tiling Pentaon Cookies

Evelyn Lamb’s Pentagons are Everything

Sharing Annie Perkins’s Cairo Pentagons with Kids

Sharing a Craig Kaplan post on “non-tiling” Pentagons with kids

(2) Platonic Solids

dodecahedron fold

I was really happy to hear my older son bring up the idea of Platonic solids. We’ve done more than 100 projects with our Zometool set – one of the most amazing was putting all of the Platonic solids together in one shape. Other projects were inspired by the GIF above and a Matt Parker video:

Nesting Platonic Solids from our Zometool set

Can you believe that a dodecahedron folds into a cube?

Using Matt Parker’s Platonic Solid video with kids

(3) Folding / Cutting

The idea of approaching geometry through folding hadn’t really ever been on my radar. This video featuring Katie Steckles opened a new world to me (also see the Patty Paper Geometry book below):

Our One Cut Project

Fold and Punch

Math for Nine Year Olds -> Joel David Hamkins’s take on Fold and Punch

A fun folding exercise for kids from Paula Beardell Krieg

(4) Geometry and Art

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The image above was inspired by a tweet I saw from the artist Ann-Marie Ison. It shows an incredible connection between geometry and number theory and you can play more with that connection with this Martin Holtham Desmos program:

Our project inspired by Ison’s work and a few other art-related projects are below.

Extending our project with Ann-Marie Ison’s Art

Using Joel David Hamkins’s Perspective Drawing posts with kids

Paula Beardell Krieg’s Puff Boxes

An Amazing Visual math project for kids I learned from Jessica Rosenkrantz

(5) Fun geometry ideas I’ve learned from math teachers

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I’ve learned about so many fun projects from ideas that teachers have shared on twitter – a few of the geometry-related projects are below:

Playing with Varignon’s Theorem thanks to Patrick Honner

Fawn Nguyen’s incredible Euclidean Algorithm project

Geometric Tilings inspired by Annie Perkins

Using Martin Holtham’s Inversion program (inspired by Dan Anderson) with kids

(6) Books

I’ve come across several amazing – and I’d say fairly non-standard – books related to geometry in the last few years. Pics of those books plus a sample project from each of them are below:


Sharing an idea from Experiencing Geometry with kids


Learning from Zome Geometry


Playing with Patty Paper Geometry

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Using Ernest Irving Freese’s “Geometric Transformations” with kids

(7) Number Theory

Revisiting Martin Weissman’s An Illustrated Theory of Numbers to talk about Gaussian Integers with kids

Using Mathologer’s Triangular Squares Video with kids

Writing an Integer as a Sum of Squares

Connecting Arithmetic and Geometry

A really neat problem that Gauss solved

(8) Topology

The connections between geometry and topology have been some of the most eye-opening projects that we’ve done. The James Tanton project at the bottom of the list below is one of the most amazing math projects that I’ve seen.

Using the Infinite Galaxy Puzzle from Nervous System to talk Topology with kids

Dave Richeson’s Knotted Bubbles Project

Fun with Mobius Strips

A Zipper Mobius Strip from Mathjams

An Absolutely Mind Blowing Project from James Tanton

(9) A few real world applications


The exercises for K-12 students from Moon Duchin’s Geometry and Gerrymandering conference are an absolutely terrific example to go through with kids. I’ve also used some ideas from Katherine Johnson’s NASA technical papers and a computer program about black holes to share interesting applications of geometry with kids:

Sharing some ideas about math and gerrymandering with kids

Using an idea from one of Katherine Johnson’s NASA Technical Papers to introduce polar coordinates

Having kids play with the Binary Black Hole Explorer made by Vijay Vara, Leo Stein, and Davide Gerosa

(10) A few miscellaneous topics of interest to math professors that made for really fun geometri-realted projects for kids.

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I didn’t really know how to classify these projects, so consider this last section “other”. The Larry Guth “no rectangles” project below is a super fun activity to do with a group of kids (of any age!). When I played around with the problem with a group of 3rd graders, I actually couldn’t end the session when the parents came to pick up the kids – the kids wouldn’t stop working on the problem!

The Arctic Circle Theorem

Has the Perfect Cuboid Problem been solved?

Larry Guth’s “No Rectangles” problem

A strange problem I overheard Bjorn Poonen discusing

Having kids play with Swarmalators

Exploring machine learning with a 7th grader using Tensorflow’s Playground

Yesterday we did a project exploring machine learning using the site

Using to let kids explore machine learning

My younger son was interested in doing another project on machine learning today, so we revisited an old idea and went to the Tensorflow Playground:

Tensorflow’s machine learning “Playground”

We started the project today with a short explanation of classification problems and then saw how the algorithm on the Tensorflow website solved a relatively simple classification problem:

Next we studied a slightly simpler classification problem that is the second example on the Tensorflow site:

The third example on the site looks very easy, but it got pretty interesting when we added some noise:

Finally, we looked at the most difficult classification problem on the Tensorflow Playground site -> the spiral. Even the most complicated program we could build still struggled with the classification problem here:

This is either our 3rd or 4th project using the Tensorflow Playground site. I think it is a great way to help kids see some of the basic concepts and ideas in machine learning.

Using to let kids explore machine learning

Last week attended a lecture by Gil Strang. He had selected a few topics from his new book about machine learning and linear algebra and the lecture was absolutely terrific.

At the end of the lecture he showed two websites that allow anyone to explore machine learning. One – the Tensorflow Plaground – site we’ve played with before:

Sharing basic machine learning ideas with kids

The other site was new to me, though ->

If I understood correctly from the lecture, the website was actually a student project from the linear algebra and machine learning course that Strang taught last year. It is a really great site for exploring some basic ideas in machine learning.

For today’s project I explained the site to each of my sons individually, and then had them play a bit.

Here’s how I introduced the site to my younger son:

Here are his thoughts after playing with the program:

Here’s how I introduced the program to my older son:

Here are his thoughts after playing with the program for a bit:

Sharing a fun calculus example from John Carlos Baez with my son

Saw a neat tweet from John Carlos Baez last week:

It was an nicely timed tweet for me because my son is beginning a long review of calculus ideas this year. Tonight I finally got around to sharing the idea with him.

We began by talking about some basic properties of the function:

Next we talked about how you could approach integrating the function and then used Mathematica to help with the polynomial division:

Finally, we went to the whiteboard to work through the integral and talk about the nice surprise:

I really like this integral. It is both a neat “fun fact” and a great example to share with kids learning calculus.

Sharing Jez Swanson’s amazing Fourier transformation program with kids

I saw an incredible tweet from Jez Swanson yesterday:

The program makes the ideas behind Fourier transformations accessible to kids and I decided to share the program with the boys this morning. So, I had each of them play around with it on their own for about 10 to 15 min. Here’s what they thought was interesting. (sorry for all of the sniffing – I’ve got a cold that’s been kicking my butt for the last few days):

(1) My older son who is in 9th grade:

(2) My younger son who is in 7th grade – it is really fun to hear how a younger kid describes advanced mathematical ideas:

I think Swanson’s program is a great program to share with kids – feels like at minimum it would be fantastic to share with kids learning trig.

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.

Sharing Cédric Villani’s amazing talk about John Nash’s work with my younger son

Yesterday I saw an absolutely incredible talk by Cédric Villani on youtube:

Although the talk is a public lecture and fairly accessible to anyone interested in math, it really isn’t aimed at kids. That said, Villani gives a beautiful description of the flat torus starting around 28:00 that I thought my younger son would find interesting. So, I had him watch that part of the video, then play a few rounds of Pac Man, and then we talked about the ideas. As always, it is really fun to hear a kid thinking through and describing ideas from advanced math: