A polyhedron is Rupert if you can cut a hole in it that’s large enough for an identical polyhedron to fit through. I’ve already talked about the Rupert tetrahedron and the Rupert cube. Now it’s the turn of the octahedron.

Continue reading Rupert Polyhedra: Octahedron# Rupert Polyhedra: Cube

Last week, I wrote about Rupert polyhedra, and how a tetrahedron has the Rupert property. The idea dates back to the 1600s, when Prince Rupert of the Rhine won a bet that it was possible to make a hole in a cube that was large enough for an identical cube to pass through, so let’s look at how the Rupert property works for a cube.

Continue reading Rupert Polyhedra: Cube# Rupert Polyhedra: Tetrahedron

For a polyhedron to be classed as Rupert, it must be possible to cut a hole in it that is large enough for an identical polyhedron to pass through. It sounds impossible, but many polyhedra have this property, including the tetrahedron.

Continue reading Rupert Polyhedra: Tetrahedron# The Multiples of Me

Continue reading The Multiples of MeI’m a prime

You know what that means

I have no factors

Okay, there’s one, and me

But they’re not proper factors

Real factors

Tangible factors

They don’t count, you see

# I Like Brussels Sprouts

At the choir I sing with, we sang a Christmas-themed warm-up song to the tune of Jelly on a Plate. It’s a simple song with just one repeated sentence: ‘I like Brussels sprouts’. The catch is that you don’t break the sentence, even when it doesn’t fit with the phrasing of the song. The syllable counts for each verse are 5, 5, 4, 4, 5, so the first verse goes

Continue reading I Like Brussels SproutsI like Brussels sprouts

I like Brussels sprouts

I like Brussels

sprouts I like Bruss

els sprouts I like Bruss

# (Not) Squaring the Circle: Explained – Part 2

For MathsJam 2019 I wrote a poem, (Not) Squaring the Circle, which features the construction of squares with the same area as given polygons. To make the poem work I had to omit some of the details of the constructions, and a few people have asked for more information about how they work. There is an explanation of the first part of the poem here. This post explains the second part of the poem, including how to construct squares with the same area as given triangles, pentagons and other polygons.

Continue reading (Not) Squaring the Circle: Explained – Part 2# (Not) Squaring the Circle: Explained – Part 1

For MathsJam 2019 I wrote a poem, (Not) Squaring the Circle, which features the construction of squares with the same area as given polygons. To make the poem work I had to omit some of the details of the constructions, and a few people have asked for more information about how they work. So here is an explanation of the first part of the poem, including some background on the problem and details of how to construct a square with the same area as a given rectangle.

Continue reading (Not) Squaring the Circle: Explained – Part 1# Fold-and-Cut Christmas Tree

This time last year, The Aperiodical featured the fold-and-cut Christmas tree I designed in their Aperiodvent calendar. I designed it to use as a Christmas card. Print out the PDF, write a message on the tree, or decorate it if you like, then fold it following the dashed lines. When the recipient cuts along the solid black line, they will open out a beautiful Christmas tree.

Continue reading Fold-and-Cut Christmas Tree# (Not) Squaring the Circle

Continue reading (Not) Squaring the CircleSo I had this circle, but I wanted a square

Don’t ask why, that’s my affair

The crucial aspect of this little game

Is that the area should stay the same

Ruler and compass are the tools to use

It’s been proven impossible, but that’s no excuse

Many have tried it, but hey, I’m me

I’m bound to find something that they couldn’t see

# Ruler Compass Animations

It’s well known that you can’t use a ruler and compass to construct a square with the same area as a given circle. But did you know that you can use a ruler and compass to construct a square with the same area as a given rectangle? Or triangle? Or other polygon?

Continue reading Ruler Compass Animations