Chapter 1

Toy: Number base converter

Are you totally addicted to base? Type a number into any box and see it magically appear in other number-base systems. Add extra rows to view as many bases simultaneously as you can handle without overdosing. (Full version)

Chapter 2

Download: Equally Spaced Dots

This is page of equally spaced dots. I’m not sure how much more I can say about it. Use them to practise drawing overly elaborate stars. Or in any other situation when you require dots equally spaced around a circle.
Equally spaced dots (PDF)

Chapter 3

Link: Grafting Numbers

Rob Tanniru saw my Numberphile video about Grafting Numbers and then went and wrote a whole mathematics paper about them. What a legend. Go read his paper now.
Grafting numbers (website)

Link: Euclid’s Elements

Euclid’s original Elements was amazing but it had a terrible refresh-rate. Thank goodness it is now all available online and in interactive form.

Or if you are feeling a bit retro: ‘The first six books of the Elements of Euclid in which coloured diagrams and symbols are used instead of letters, by Oliver Byrne; 1847’ is also available online for free.
Euclid’s Elements (website)
Byrne’s Euclid (website)

Link: NASA’s random digits

Here’s the story about digits of irrational numbers on the NASA website, told by the NASA folks themselves.
Digits of Irrational Numbers

Toy: Polygonal Number Calculator

Play with this online toy which allows you to visualise polygonal numbers of different types. Watch as the numbers you choose dance  before you as you change between different geometric representations. Or just choose one and stare at it intently. It’s up to you.
Polygonal number calculator