read like 20% of it but probably won't finish it cause I don't feel like I'm actually learning anything. There's too many random mathematical facts just strung together without an explanation of what they mean and when he digs into the maths a bit it's very confusing and the explanations are very short. partially it's just that I'm dumb and haven't done maths for a while but I really don't think most of this would appeal to your average person - and if they know maths well enough to understand the explanations/wider meaning idk why they'd read the book in the first place

As an example: he talks about parities of permutations. He then says these show that the 15 puzzle is unsolvable, because the starting grid is an odd permutation of the required final grid but you can only make even permutations. But he doesn't show or explain how this is true. It's just a random fact that you learn and move on and can't actually apply.

Think of a number, any number...

Multiply it by 2

Add 10

Then divide by 2

Subtract your original number

And I will tell you your answer later on.

Stewart has a knack of making complicated and difficult mathematical concepts easy to comprehend and understand. In this book he introduces us to the numbers that we come across day in and day out. Some will be familiar, zero, one and Pi for example. Other are less familiar, from logs (not trees) to that strange areas of mathematics that encompass imaginary numbers and the vastness of infinity.

In this journey we venture through the primes, peers back into the history of mathematicians, informs us what is a rational number, traverses the circular numbers, plumbs the depths of fractals and explains the birthday paradox. There is a brief sojourn to the really small, before seeing the really really large numbers stretching away in the distance, and reaching the restaurant at the end of the universe with a reservation at table 42.

Occasionally complex, most of this is written with the layman in mind. Stewart writes with clarity on a subject that he knows and loves, and what really comes across is his enthusiasm to get other to love, or at the very least like maths once again.

Oh, and the answer is 5. ( )

Indeholder "Preface", "Numbers", "Small Numbers", " 1. The Indivisible Unit", " 2. Odd and Even", " 3. Cubic Equation", " 4. Square", " 5. Pythagorean Hypotenuse", " 6. Kissing Number", " 7. Fourth Prime", " 8. Fibonacci Cube", " 9. Magic Square", " 10. Decimal System", "Zero and Negative Numbers", " 0. Is Nothing a Number?", " -1. Less Than Nothing", "Complex Numbers", " i. Imaginary Number", "Rational Numbers", " 1/2. Dividing the Indivisible", " 22/7. Approximation to π", " 466/885. Tower of Hanoi", "Irrational Numbers", " sqrt(2) ~ 1.414213. First Known Irrational", " π ~ 3.141592. Circle Measurement", " φ ~ 1.618034. Golden Number", " e ~ 2.718281. Natural Logarithms", " log 2 / log 3 ~ 1.584962. Fractals", " π/sqrt(18) ~ 0.740480. Sphere Packing", " 2^(1/12) ~ 1.059463. Musical Scale", " ζ(3) ~ 1.202056. Apéry's Constant", " γ ~ 0.577215. Euler's Constant", "Special Small Numbers", " 11 String Theory", " 12 Pentominoes", " 17 Polygons and Patterns", " 23 Birthday Paradox", " 26 Secret Codes", " 56 Sausage Conjecture", " 168 Finite Geometry", "Special Big Numbers", " 26! = 403291461126605635584000000. Factorials", " 43252003274489856000. Rubik Cube", " 6670903752021072936960. Sudoku", " 2^57885161 - 1. (Total of 17425170 digits)", " Largest Known Prime", "Infinite Numbers", " א0. Smallest Infinity", " C. Cardinal of Continuum", "Life, the Universe, and ...", " 42. Not Boring at All", "Further Reading", "Figure Acknowledgements".

"Preface" handler om ???
"Numbers" handler om ???
"Small Numbers" handler om ???
" 1. The Indivisible Unit" handler om ???
" 2. Odd and Even" handler om ???
" 3. Cubic Equation" handler om ???
" 4. Square" handler om ???
" 5. Pythagorean Hypotenuse" handler om ???
" 6. Kissing Number" handler om ???
" 7. Fourth Prime" handler om ???
" 8. Fibonacci Cube" handler om ???
" 9. Magic Square" handler om ???
" 10. Decimal System" handler om ???
"Zero and Negative Numbers" handler om ???
" 0. Is Nothing a Number?" handler om ???
" -1. Less Than Nothing" handler om ???
"Complex Numbers" handler om ???
" i. Imaginary Number" handler om ???
"Rational Numbers" handler om ???
" 1/2. Dividing the Indivisible" handler om ???
" 22/7. Approximation to π" handler om ???
" 466/885. Tower of Hanoi" handler om ???
"Irrational Numbers" handler om ???
" sqrt(2) ~ 1.414213. First Known Irrational" handler om ???
" π ~ 3.141592. Circle Measurement" handler om ???
" φ ~ 1.618034. Golden Number" handler om ???
" e ~ 2.718281. Natural Logarithms" handler om ???
" log 2 / log 3 ~ 1.584962. Fractals" handler om ???
" π/sqrt(18) ~ 0.740480. Sphere Packing" handler om ???
" 2^(1/12) ~ 1.059463. Musical Scale" handler om ???
" ζ(3) ~ 1.202056. Apéry's Constant" handler om ???
" γ ~ 0.577215. Euler's Constant" handler om ???
"Special Small Numbers" handler om ???
" 11 String Theory" handler om ???
" 12 Pentominoes" handler om ???
" 17 Polygons and Patterns" handler om ???
" 23 Birthday Paradox" handler om ???
" 26 Secret Codes" handler om ???
" 56 Sausage Conjecture" handler om ???
" 168 Finite Geometry" handler om ???
"Special Big Numbers" handler om ???
" 26! = 403291461126605635584000000. Factorials" handler om ???
" 43252003274489856000. Rubik Cube" handler om ???
" 6670903752021072936960. Sudoku" handler om ???
" 2^57885161 - 1. (Total of 17425170 digits)" handler om ???
" Largest Known Prime" handler om ???
"Infinite Numbers" handler om ???
" א0. Smallest Infinity" handler om ???
" C. Cardinal of Continuum" handler om ???
"Life, the Universe, and ..." handler om ???
" 42. Not Boring at All" handler om ???
"Further Reading" handler om forslag til yderligere læsning.
"Figure Acknowledgements" handler om hvor de forskellige illustrationer kommer fra.

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Here the prolific math popularizer uses the different kinds of numbers (integers, reals, rationals, complex numbers, irrationals, transfinite cardinals) as hooks on which to hang a lot of little forays into various areas of mathematics. Some of the forays follow well-worn paths, and proofs are noticeably lacking. Good reading though.