There is a danger, when your book comes plastered in praise from people like Art Benjamin and Ron Graham, that reviewers will hold it to a higher standard than a book that doesn't. That would be unfair, and I'll try to avoid that.
This is a book with plenty to recommend, after all: for instance, it's beautifully laid out. What would normally be footnotes are given alongside the text, Tufte-style, which means you can read them without having to hunt around in the text. If I ever write a book that needs footnotes, that's how I'll do it. It also means there's plenty of space on the page – it's both uncluttered, and leaves plenty of room for notes, if you're inclined to take them.
It's hard to fault the topic choice, either – the paths to $\pi$ and $\phi$ and similar are well-worn in popular maths books, but only because they're interesting.
Stylistically, though, this book falls short for me. There are a few creditable humoristic asides, but in large part it reads like lecture notes, full of We defines and let us considers – and that's problematic. If you're new to the topics, you're almost certainly not used to reading acadamese at this level. Conversely, if you read this style of writing at a decent level, you've almost certainly come across almost all of the topics covered.
Overall, I think I liked it, even though I'm not sure it passed the 'teach Colin something new' test. I can’t tell for sure who would benefit greatly from it. (Perhaps it's a nice introduction to an academic writing style for someone about to start a maths degree?) On the plus side, it's a pleasant enough read and visually very appealing. In most cases, though, I think I'd recommend Matt Parker's Things To Make And Do… or Ian Stewart's 17 Equations… some way ahead of this.