
The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress and also when it did not, because science was being stifled by militarism or religious fanaticism. The mathematical level of this book is flexible, and there is plenty for readers of all ages and interests.
A History of Pi - Petr Beckmann
Journey through Genius: The Great Theorems of Mathematics - William Dunham
How to Bake Pi - Eugenia Chang
These are all sort of 'pop-math' books -- that is, they're more intended to spark a joy & love for math than teach rigorous mathematics. Great Theorems and A History of Pi include a lot of history (edit to add: in addition to covering the math involved!) -- did you know some mathematicians in history would duel over their theorems? That theorems were a carefully guarded secret instead of something you shared?
Introduction to Graph Theory is specifically intended as an introduction to mathematics for 'the mathematically traumatized'.
In my opinion, after reading these, if you've sparked a joy for the puzzles and fun of mathematics, then I would then suggest branching out into more formal presentations of them relevant to your interests... it's much easier to slog through a book on abstract mathematics when you receive from enjoyment from the puzzles presented.
Zero: The Biography of a Dangerous Idea - Charles Seife
Measurement - Paul Lockhart
Prelude to Mathematics - W. W. Sawyer
Proofs from The Book - Aigner and Ziegler
The Joy of x - Steven Strogatz
Things to Make and Do in the Fourth Dimension - Matt Parker
What is Mathematics? - Courant and Robbins
A History of PI - Petr Beckmann
An Imaginary Tale - Paul Nahin
e: The Story of a Number - Eli Maor
Imagining Numbers - Barry Mazur
Journey Through Genius - William Dunham
Prime Obsession - John Derbyshire
Note that Archimedes used a 96-sided polygon to estimate bounds on the value of pi (http://en.wikipedia.org/wiki/Pi)! This was quite a feat since arithmetic calculations and algebraic was one area that ancient Greeks were weak at.
My theory is that pi is the first interesting mathematical number that people often encounter in grade school (even before sqrt(2)), so it holds a special place in their fascination.
"His account was largely sourced from a 1797 work by Johann Beckmann titled A History of Inventions, Discoveries, and Origins.[11] In fact, Beckmann's account, and thus Mackay's by derivation, was primarily sourced to three anonymous pamphlets published in 1637 with an anti-speculative agenda.[36] Mackay's vivid book was popular among generations of economists and stock market participants. His popular but flawed description of tulip mania as a speculative bubble remains prominent, even though since the 1980s economists have debunked many aspects of his account."
Also see the "Modern views" section. Basically, as far as anyone can tell Mackay's account of tulip mania is mostly bullshit.