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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. Category:Rational numbers - Wikipedia

   en.wikipedia.org/wiki/Category:Rational_numbers

   This category represents all rational numbers, that is, those real numbers which can be represented in the form: ...where and are integers and is ...

4. Number theory - Wikipedia

   en.wikipedia.org/wiki/Number_theory

   Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."

5. 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 ...

6. Egyptian fraction - Wikipedia

   en.wikipedia.org/wiki/Egyptian_fraction

   Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including 2 3 {\displaystyle {\tfrac {2}{3}}} and 3 4 {\displaystyle {\tfrac {3}{4}}} as summands , were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations ...

7. Numeral system - Wikipedia

   en.wikipedia.org/wiki/Numeral_system

   A number has a terminating or repeating expansion if and only if it is rational; this does not depend on the base. A number that terminates in one base may repeat in another (thus 0.3 10 = 0.0100110011001... 2). An irrational number stays aperiodic (with an infinite number of non-repeating digits) in all integral bases.