10 More math ideas from mathematicans to share with kids

About a year and a half ago I wrote this blog post about using math from mathematicians to share with kids:

Amazing math from mathematicans to share with kids

Since then I’ve been lucky to encounter even more ideas and wanted to put them together:

(1) Jim Propp is doing an fantastic job sharing interesting math on his blog

His most recent post (September 2017) was about counting in base 3/2:

Bases

Our projects using this base 3/2 essay are here:

Sharing Jim Propp’s base 3/2 essay with kids part 3

and the full list of projects we done base on math he’s shared is here:

Our projects inspired by Jim Propp

(I particularly recommend the 2xN rectangle tiling project if you are looking to share a really fun math surprise with kids)

(2) Elchanan Mossel’s probability problem

I learned of an incredible probably problem from Elchanan Mossel from this Lior Pachter tweet:

Exploring Elchanan Mossell’s fantastic probability pboelm with kids

It is always fun to learn about a problem that is accessible to kids that generates interest from math professors!

(3) Here’s a fun one about higher dimensional spheres that I originally learned from Bjorn Poonen

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A strange problem I overheard Bjorn Poonen Discussing

It turns out that a version of the problem can be found in an old Martin Gardner book, too (and just to avoid any misunderstanding, Poonen was clear that the problem was not his invention, though I’ve not seen the 3rd part of his problem discussed anywhere else).

A collection of our projects relating to this problem is here. For more advanced students who have seen Stirling’s approximation for n!, the “fun surprise” post might be interesting after they’ve played with the problem.

A problem discussed by Martin Gardner, Grant Sanderson, Bjorn Poonen, and the AMC 10

(4) Laura DeMarco and Kathryn Lindsey’s 3d folded fractals

Quanta Magazine published an amazing article about new research from Laura DeMarco and Kathryn Lindsey:

3-D Fractals Offer Clues to Complex Systems

The research itself isn’t accessible to kids (obviously!) but some of the ideas in the article are fun to play with. Trying to make the folded shape coming from this diagram, in particular:

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We made the shape out of cloth, for example:

Our projects inspired by the Quanta Magazine article about DeMarco and Lindsey’s work are here:

Our projects inspired by DeMarco and Lindsey’s work

(5) Kelsey Houston-Edwards’s PBS Infinite Series videos are amazing

This video is one of my favorites math videos ever made:

Our project with that video is here:

Kelsey Houston-Edwards’s Proof video is incredible

but she’s inspired dozens of other projects, too:

All of our projects inspired by Kelsey Houston-Edwards

(6) Sharing John Baez’s “juggling roots” post

This incredible tweet from John Baez inspired two really fun projects:

and also some really great 3d prints:

The collection of projects is here – and it was incredibly fun to watch the boys explore some of the math ideas involved with these pictures and prints:

Sharing John Baez’s “juggling roots” post with kids

and here:

My week with “juggling roots”

(7) Stephen Wolfram’s public lecture at MoMath

This public lecture is fascinating to watch. He starts and asks the audience for ideas and off they go. Wolfram has no idea ahead of time what paths they’ll walk down or what ideas they will stumble on. It turns out they found some fascinating ideas to play with. Having Mathematica obviously helps if you want to play with those ideas, but even just watching the lecture is an amazing mathematical experience.

Here are our two projects with Wolfram’s ideas:

Sharing Stephen Wolfram’s MoMath talk with kids

Revisiting Stephen Wolfram’s MoMath talk

(8) Sharing a paper cutting projects from James Tanton’s “Solve This”

James Tanton’s “Solve This” is hard to find, but if you find it – just wow!

One of the projects I stumbled on in the book was a paper cutting project that completely took my breath away. Below is a peek at one of the ideas. The shape we are cutting is made from putting a one half twist into one of the strips left over after cutting an ellipse out of the cylinder (the description makes the set up sound more complicated than it is – the picture is worth 1000 words here).

The full project is here:

An absolutely mind blowing project from James Tanton

And all of our projects from “Solve This” are here:

Our projects from “Solve This”

(9) Sharing projects from Dave Richeson’s “Euler’s Gem”

Finding Dave Richeson’s “Euler’s Gem” book was a real treat:

We did several fun projects – even our cat loved them 🙂

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All of our projects we did from the book are here:

Looking at Dave Richeson’s “Euler’s Gem” with kids

(10) Evelyn Lamb’s pentagons

Evelyn Lamb has been sharing amazing math ideas for as long as I can remember. One of her more recent hobbies is sharing neat pictures of math ideas she runs across on walks. A picture she shared of an octagon divided into two pentagons led to one of the most fun math explorations that we’ve ever done:

LambPentagon

Evelyn Lamb’s pentagons are everything

I love that she noticed these amazing pentagons and how the version of the pentagons she found helped me understand the tiling pentagon ideas much better than I ever had before. Sharing all of the pentagon tiling ideas with boys over the last few years has been incredibly fun.