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The mathematics lover's companion : masterpieces for everyone / Edward Scheinerman.
- Format:
- Book
- Author/Creator:
- Scheinerman, Edward R., author.
- Language:
- English
- Subjects (All):
- Mathematics--Problems, exercises, etc.
- Mathematics.
- Mathematics--Popular works.
- MATHEMATICS / History & Philosophy.
- MATHEMATICS / Applied.
- Local Subjects:
- MATHEMATICS / History & Philosophy.
- MATHEMATICS / Applied.
- Genre:
- Problems and exercises.
- Popular works.
- Physical Description:
- xx, 274 pages : illustrations ; 25 cm
- Place of Publication:
- New Haven : Yale University Press, [2017]
- Summary:
- In bite-sized chapters that require only high school algebra, [Edward Scheinerman] invites recreational mathematicians and neophytes alike to try their hands at solving mathematical puzzles and provides an engaging and friendly tour of numbers, shapes, and uncertainty. The result is an unforgettable introduction to the fundamentals and pleasures of thinking mathematically. -- From book jacket.
- Contents:
- Machine generated contents note: The last words
- pt. I NUMBER
- 1. Pn'rae Numbers
- The integers
- Factoring
- Hozu many?
- A constructive approach
- A different proof
- Two infamous problems
- Application to cryptography
- 2. Binary
- When in Rome
- Unary
- A middle ground
- Calculation
- Extensions
- 3. 0.999999999999...
- The meaning of decimals
- Decimal numbers with infinitely many digits
- Let's be reckless
- 4. [√]2
- Rational numbers
- The diagonal of a square
- Beyond the rational
- Constructible numbers
- Playing in tune
- 5. i
- Another square-root conundrum
- Imaginary numbers
- Complex numbers
- The Fundamental Theorem of Algebra
- 6. π
- What is π?
- Transcendence*
- Relatively prime
- 7. e
- Leonhard Euler
- An "interesting" number
- The deranged hat check clerk
- The average gap between primes
- A miraculous equation
- 8. [∞]
- Sets
- Infinite sets of unequal size
- Transfinite numbers
- Weirdness in setland
- 9. Fibonacci Numbers
- Squares and dominoes
- The Fibonacci numbers
- Sums of Fibonacci numbers
- Proof fry induction
- Combinatorial proof
- Ratios of Fibonacci numbers and the golden mean
- 10. Factorial!
- Books on the shelf
- Is there a formula?
- A puzzle
- What is 0!?
- 11. Benford's Law
- Wild measurements
- Multiplication tables
- Catching crooks cooking books
- Refining the problem with scientific notation
- Yards or feet?
- What's logs got to do with it?
- Collecting the loose ends
- 12. Algorithm
- Sorting
- Greatest common divisor
- Least common multiple
- pt. II SHAPE
- 13. Triangles
- It all adds up to 180
- Area
- Centers
- Lurking equilateral triangles
- 14. Pythagoras and Fertnat
- The Pythagorean Theorem
- Absolute value of complex numbers
- Pythagorean triples
- Fermat's Last Theorem
- 15. Circles
- A precise definition
- An equation
- Triangles right inside
- Ptolemy's Theorem
- Packing
- Kissing circles
- Pascal's Hexagon Theorem
- 16. The Platonic Solids
- Polyhedra
- Euler's polyhedral formula
- Is that all There is?
- Archimedian solids
- 17. Fractals
- Sierpinski's triangle
- Between dimensions
- Boa: counting
- The dimension of Sierpinski's triangle
- Pascal and Sierpinski
- Tne Kocn snowflake
- 18. Hyperbolic Geometry
- Euclid's Postulates
- What is a line?
- An entire plane inside a disk
- Implications
- pt. III UNCERTAINTY
- 19. Nontransitive Dice
- A game of two dice
- A challenger
- Triumph of the underdog
- Further examples
- 20. Medical Probability
- Conditional probability*
- 21. Chaos
- Functions
- Iterating the logistic map
- From order to chaos
- The Collatz 3x + 1 problem
- 22. Social Choice and Arrow's Theorem
- Two-party elections
- Elections with more than two candidates
- The independence of irrelevant alternatives
- 23. Newcomb's Paradox
- Newcomb's game
- Don't leave money on the table!
- Greed doesn't pay
- Conflict and resolution
- Computer as the Chooser.
- The last words
- pt. I Number
- 1. Prime Numbers
- How many
- 3. 0.999999999999 ...
- What is π
- Proof by induction
- Is there a formula
- What is 0!
- Yards or feet
- What's logs got to do with it
- pt. II Shape
- 14. Pythagoras and Fermat
- Is that all there is
- Box counting
- The Koch snowflake
- What is a line
- pt. III Uncertainty
- Notes:
- Includes bibliographical references (pages 269-270) and index.
- Local Notes:
- Acquired for the Penn Libraries with assistance from the Edward Potts Cheyney Memorial Fund.
- ISBN:
- 9780300223002
- 0300223005
- OCLC:
- 959033299
- Publisher Number:
- 99985548531
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