Also, an excellent book by Eli Maor, subtitled "A Cultural History of the infinite". It covers pretty much the full breadth of topics about infinity, broken into four parts :
- Mathematical Infinity - limits, primes, infinite series, ...
- Geometric Infinity - asymptotes, tiling the plane, shapes with finite volume and infinite surface area, ...
- Aesthetic Infinity - The Mobius Strip, mirrors, lots of M.C. Escher, ...
- Cosmological Infinity - ancient astronomy, the expanding universe, the infinitesimal, ...
I found out about this book because I sat in on a math class given by Tom Lehrer (yes, The Tom Lehrer) in Santa Cruz, where he used it as a textbook for a class on infinity for non math majors.
Eli Maor claims that he got the idea for the title from the manual for his telescope which read
"The range of focus of your telescope is from 15 feet to infinity and beyond."
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