Looking for small/inexpensive items to put inside a piece of festive footwear (or, to keep for yourself)? Here’s a selection of things we’ve seen lately that you might want to buy! All the items we’re showing are under £20, and range from slightly mathematical to very mathematical.

Jewellery

Friends of the site Maths Gear have their usual selection of excellent gifts, including a new range of Maths Icons earrings (£14.99) including the Mandelbrot set, and a set of nested polygons. They also have a range of other jewellery and cufflinks which includes the wonderful mug/donut earrings (£17.89) and π cufflinks (£6.91).

There’s also some great Impossible Shape jewellery (from £3) – including Borromean Rings and Necker cubes – available from Earth Symbols, and there’s of course the classic Cofactor Pythagorean theorem earrings ($15 in 3D printed nylon).

Dice

Maths Gear also have a wide collection of different types of dice, as do scholastic suppliers Tarquin (including class sets and some individual items). We particularly like Maths Gear’s set of polyhedral dice in shapes they don’t usually come in (£10.97), and Tarquin’s set of blank rewriteable dice (£5.99), for when you want to make your own rules.

More generally, Tabletop Supply are a good go-to for many different types of dice, as well as replacement (or upgrade!) pieces for existing games, or games you’ve invented yourself.

Games and toys

Plenty of mathematically interesting board games come in travel versions which can fit into a small space – some of our favourites include number-based favourites Red 7, 6 Nimmt! and The Game, and if shapes is more your think we can also recommend travel Blokus and travel Qwirkle.

Oink Games also do some visually stunning and simple games with a mathsy vibe, and our favourites include Troika, Deep Sea Adventure and The Pyramid’s Deadline. We also love OK Play which is very compact.

Simple classic board games with a mathematical twist include Shut The Box, and you can’t go wrong with a deck of cards (this Math Stack variant (£10.49) from Maths Gear is pretty, but any will do!)

Site editor Christian recommends what he calls a Nobbly Wobbly, but tends to be sold under the name ‘woven bouncy ball’ or ‘rainbow spaghetti ball‘ (£5.95 for 5) depending on who you ask. The underlying geometry of the shape makes it mathematically interesting, but dogs and small children alike will have fun with it.

Puzzles

Happy Puzzle Co have IQ Minis which fit in your hand, and a range of other pocket puzzles. We also love Edmund Harriss’ Curvahedra (£11.93), which are available from Maths Gear. Paper-folding puzzle Manifold was a big hit with us a few years ago, and it looks like Manifold 2 is now available.

There’s also Rush Hour (£16.49), and we’ve had a recommendation for the STAX games from Huch’s range of puzzles, which comes in Cat, Dog and Sea versions. Don’t forget about the Rubik’s cube and other twisty puzzles too!

Maths Paraphernalia

For a more refined mathematical palate, you can pick up some elegant vintage maths gifts from Present and Correct, including a 1970s desk abacus (£19.50), gorgeous metal protractors (£4), this ruler sticker tape (£3) and a classic geometry puzzle (£12). Or why not pick up a Golden Mean Compass (£14.99) from Grand Illusions?

If you have any suggestions of your own, feel free to include them in the comments below!