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  2. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...

  3. Niven's theorem - Wikipedia

    en.wikipedia.org/wiki/Niven's_theorem

    In radians, one would require that 0° ≤ x ≤ π/2, that x/π be rational, and that sin(x) be rational. The conclusion is then that the only such values are sin(0) = 0, sin(π/6) = 1/2, and sin(π/2) = 1. The theorem appears as Corollary 3.12 in Niven's book on irrational numbers. [2] The theorem extends to the other trigonometric functions ...

  4. Algebraic number field - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number_field

    The study of algebraic number fields, that is, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory. This study reveals hidden structures behind the rational numbers, by using algebraic methods.

  5. Quadratic field - Wikipedia

    en.wikipedia.org/wiki/Quadratic_field

    In algebraic number theory, a quadratic field is an algebraic number field of degree two over , the rational numbers. Every such quadratic field is some Q ( d ) {\displaystyle \mathbf {Q} ({\sqrt {d}})} where d {\displaystyle d} is a (uniquely defined) square-free integer different from 0 {\displaystyle 0} and 1 {\displaystyle 1} .

  6. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Number theory began with the manipulation of numbers, that is, natural numbers (), and later expanded to integers and rational numbers (). Number theory was once called arithmetic, but nowadays this term is mostly used for numerical calculations. [15]

  7. 22 arrested in Pennsylvania in connection to alleged human ...

    www.aol.com/22-arrested-pennsylvania-connection...

    Pennsylvania officials announced 22 arrests in connection to an alleged human trafficking operation at two massage parlors.

  8. Florida dad keeps 200 exotic snakes in converted garage - AOL

    www.aol.com/florida-dad-keeps-200-exotic...

    The proud father described his daughter and son Maximus, 5, as seasoned snake handlers — Ariana even keeps 30 of her own scaley pets in her bedroom.

  9. Class number problem - Wikipedia

    en.wikipedia.org/wiki/Class_number_problem

    For given low class number (such as 1, 2, and 3), Gauss gives lists of imaginary quadratic fields with the given class number and believes them to be complete. Infinitely many real quadratic fields with class number one Gauss conjectures that there are infinitely many real quadratic fields with class number one.