Number City

What is Number City?

Number City is a giant interactive cityscape, made from stacks of cardboard boxes, and designed to allow people to explore the hidden structures within numbers.

Every number can be broken down into its prime factors - 4 is 2 × 2, 12 is 2 × 2 × 3 and 110 is 2 × 5 × 11. This can be calculated uniquely for every number, and in Number City each prime factor is represented by a cardboard box.

We're laying out the city on a giant grid - the number being represented is marked along one edge of the grid, and the prime factors each have their own row. For a number like 12, it'd have two 2 boxes in the 2 row, and one 3 in its own row.

An illustration of children's building blocks stacked as described in the text

A CGI rendering of Number City made from grey boxes

A 3D rendering of Number City. Explore this model using our interactive Geogebra applet.

The Team

The Number City team includes maths communicators Matt Parker, Katie Steckles, Ayliean MacDonald and Ben Sparks, as well as science artist Hana Ayoob, who’s managing the project. The idea for Number City was originally developed by Paul Stephenson as the Number Landscape Project, and Paul will be there to speak to participants. We'll be joined by a team of volunteers including Ben Ashforth, Paul Taylor, and Eve Armstrong.

Building the City

Diagram of a children's building block with the number 2 on it'

Visitors will be able to create and personalise a box to represent a particular factor - for example, you might create a 'two' box which has pictures of pairs of things, or different representations of the number 2 on it - then place it in the city to form part of the installation.

Number City has been made possible through the MEGA Grant, a scheme for large-scale activities bringing mathematics to public view. It is funded by Stand-up Maths, and coordinated by Talking Maths in Public, the UK’s network for maths communicators. We're also grateful to Robertson Facilities Management, who've provided us with bricks and sourced cardboard boxes, and to Qwirkshop for assistance with laser cutting and vinyl cutting for our stall activities and vinyl numbers to mark the pitch.

Get Involved

We'll be building Number City all day (10am-4pm) on Saturday 7th September 2024, at the Pickaquoy Centre in Kirkwall, Orkney. You'll find us on the all-weather pitch (head through the centre and follow the signs out the back of the building). Anyone who drops by during the day can help by creating a box (or more than one!) to add to the city, and we'll also have a range of related activities to explore the mathematics behind Number City - both at the pitch, and on a stall inside the Centre. Admission is free, and everyone is welcome!

If you'd like to get involved as a volunteer to help run the activity, contact project manager Hana Ayoob to find out how you can help.

Activities

Here are some more ways to explore the mathematics behind number city - we'll be running a selection of these at our stall as part of the Family Day. There are also some activities for schools linked on Paul Stephenson's Magic Mathworks website, under 'Number City' and 'The Number Landscape project'.

Watch some numbers animate their prime factorisations in the Factor Conga
Test your prime-spotting prowess using the Is This Prime? Game
Play our Where in Number City? game
Use our storytelling prompts (PDF) to write a story set in Number City
Build your own mini-City using multilink cubes or building blocks (see examples below)

Photo of a mini-Number City built on a large sheet of paper on the floor using Multilink cubes

Multi-link cubes, laid out like Number City - Hana Ayoob

Photo of a number line arranged along a wall using different coloured Duplo blocks to represent different primes

Building blocks, using colours to represent factors - Charlotte Morris

Frequently Asked Questions

The activity will be running from 10am - 4pm on Saturday 7th September, and we're hoping that with enough members of the public joining us to create boxes, we'll make all the numbers up to 128 in that time.

To create all the numbers up to 128, we will need 315 boxes, which will be arranged in 224 stacks. Each box will measure 50cm on each side, and the whole city will measure 64m by 64m - with the tallest stack we build being 3.5m tall! We'll mark out the pitch using 2,334m of adhesive tape, and the numbers along the sides of the grid will be made from 632 individual digits cut from vinyl.

We'll be weighing down each box with bricks (kindly supplied by Robertson Facilities Management) to keep them from blowing away in the event of windy weather. We're hoping the weather will be nice enough to stay outside for the whole day, but in the event of heavy rain we will need to hide inside the Pickaquoy Centre!

If you have any further questions about Number City, contact hello@hanaayoob.co.uk. Website design by Tooplate.