App review: Incredible Numbers, by Ian Stewart

Mathematician and author Professor Ian Stewart, helped by Touch Press and his publisher Profile Books, has recently released a new app for iOS (suitable for use on an iPad) called Incredible Numbers. We saw this tweet:

I highly recommend Incredible Numbers, iPad app by Ian Stewart. New gold standard for interactive maths. For all. https://t.co/bI9YfUpViP

— Alex Bellos (@alexbellos) March 31, 2014

and how could we resist? We borrowed a nearby iPad, downloaded the app and had a play.

What struck us first was that the app is very much like reading a good popular maths book, except with interactive diagrams that you can fiddle about with and lots of pretty pictures. It’s all beautiful and well executed, and while the app gives you a path to follow whilst explaining things, and instructions on what to do, it doesn’t mind too much if you mess about a bit.

Incredible Numbers is divided into eight main areas, each of which covers a different topic in maths – mostly numbers, although some shapes do creep in, and infinity isn’t a number – and each has around three short articles, containing interactive sliders to punctuate the text, accompanied by one main interactive demonstration gadget, depending on the topic.

The app makes good use of the iPad control system, with lots of sliders and pinch-zoomable images, although some are a little difficult to control precisely – disappointingly, some zoomable diagrams which could have been generated on-the-fly and go on for much longer stop after a certain amount, which made us a bit sad, but they do go pretty far – there’s a million digits of π, which you can search for your birthday in: mine was in the 84,851st decimal place.

Our personal highlights included: a simplified enigma machine you can use to encode/decode text; a beautiful sunflower seed arranger allowing you to specify the angle, which shows off the Golden Ratio nicely; and an XKCD-esque noughts and crosses grid, explaining and demonstrating the 9! ways to order 9 things. The app also includes a selection of maths puzzles which kept us going for a while.

We did succeed in crashing the app while playing with the Hilbert’s Hotel animation; although admittedly we had countably infinitely many countably infinite sets to fit in, and I’m not sure how much RAM an iPad has. We did get it working again shortly afterwards, and then spent ages playing with the interactive ‘approximations to π’ sliders, to see whose approximation is the best (go Chudnovsky!).

There wasn’t much to see that hasn’t been done before elsewhere – I noticed a version of the Factor Conga, among other things – but everything that’s there is interesting, and the maths is well explained. This would make a great gift for someone you’d buy one of Ian Stewart’s books for, and would be great for inquisitive youngsters (actual age or mental age) who want to discover things for themselves, but whose attention spans are too short for the printed word.

One of the reviews on the app store complains that the explanations are pitched too high for a complete non-mathematician – which might be a fair accusation, as they do assume a little knowledge – but if you’ve got no maths background whatsoever, it’d be great working through it with someone who could explain things to you.

[youtube url=https://www.youtube.com/watch?v=FCz3dJaSgHg]