Numbers in General

  • John Stillwell
Part of the Undergraduate Texts in Mathematics book series (UTM)


The rational numbers are beautifully suited to arithmetic, being closed under +, −, x, ÷, but they are inadequate for geometry. Their inadequacy is exposed by the Pythagorean theorem, according to which the diagonal x of the unit square (Figure 3.1.1) satisfies x2 = 12 + 12 = 2. We can see that no rational number x satisfies this equation as follows.


Fundamental Theorem Algebraic Number Irrational Number Pythagorean Theorem Rational Length 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

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