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Literary notes about Denominator (AI summary)

The term “denominator” appears in literature both as a literal mathematical concept and as a metaphorical tool to draw parallels between numerical relationships and broader human or social contexts. In mathematically inclined texts, such as those by Thomas Jefferson and Henry Ernest Dudeney, the denominator is used in straightforward calculations—reducing several fractions to a common denominator to compare values [1, 2, 3, 4, 5]—underscoring its critical role in quantifying and comparing parts of a whole. Conversely, in works of philosophy and social commentary, authors adopt the term metaphorically; for instance, Santayana likens language to money whose value can only be understood once reduced to a common denominator [6], and Rousseau sees the citizen as the numerator whose value is defined by the community, the denominator [7]. This dual usage reflects a broader literary fascination with how the same concept can articulate both concrete mathematical truths and abstract societal relationships.
  1. Reduction of several fractions to the same denominator.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  2. Any two fractions will do if the denominator equals the sum of the two numerators.
    — from Amusements in Mathematics by Henry Ernest Dudeney
  3. Then ab + c 2 =denominator, and a 2 - c 2 , b 2 - c 2 , and a 2 - b 2 will be the three numerators.
    — from Amusements in Mathematics by Henry Ernest Dudeney
  4. = 1 / 9 The sum of the numerator digits and the denominator digits will, of course, always be 45, and the "digital root" is 9.
    — from Amusements in Mathematics by Henry Ernest Dudeney
  5. The denominator must always be a prime number of the form 6 n +1, or composed of such primes.
    — from Amusements in Mathematics by Henry Ernest Dudeney
  6. Language is like money, without which specific relative values may well exist and be felt, but cannot be reduced to a common denominator.
    — from The Life of Reason: The Phases of Human Progress by George Santayana
  7. The citizen is but the numerator of a fraction, whose value depends on its denominator; his value depends upon the whole, that is, on the community.
    — from Emile by Jean-Jacques Rousseau

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