A Rational Approach to the Irrationals
More and more numbers are getting their special books...e, π, and φ...even Euler's special constant. Luckily for prospective authors, the number of real numbers is uncountable!
A recent addition to number lore is Julian Havil's book πhe Irratiφnals: The Story of the Numbers You Can't Count On (2012). Clever title...so rational!
Havil provides a lot of interesting content:
So, if you like numbers, the book is a winner. And if you like history, special numbers, and interesting tangents, then this book not only needs to be on your shelf but also read....
- Historical background for the irrationals as a class of numbers, as well as the special numbers e, π, φ, etc.
- Discussions of key proofs, such as why e, π, or φ are irrational...or transcendental
- The associated idea of randomness (i.e. non-repeating decimals)
- Approximation of the irrationals by rationals
- Neat ideas such as continued fractions, the Spiral of Theodorus, and Roger Apery's proof that the special number Seta(3) is irrational
- Plus a ton of other interesting tidbits so characteristic of Havil's books on mathematical topics