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searching for Quadratic irrational number 7 found (10 total)

alternate case: quadratic irrational number

Apotome (mathematics) (227 words) [view diff] exact match in snippet view article

modern algebraic language, an apotome can be interpreted as a quadratic irrational number formed by subtracting one square root of a rational number from

Solving quadratic equations with continued fractions (1,700 words) [view diff] exact match in snippet view article find links to article

the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated as a decimal

Periodic continued fraction (2,989 words) [view diff] exact match in snippet view article find links to article

group S L ( 2 , Z ) . {\displaystyle SL(2,\mathbb {Z} ).} A quadratic irrational number is an irrational real root of the quadratic equation a x 2 +

Hermite's problem (1,064 words) [view diff] exact match in snippet view article find links to article

since ?(x) is rational if and only if x is either rational or a quadratic irrational number, and moreover x is rational if and only if ?(x) is a dyadic rational

Restricted partial quotients (819 words) [view diff] exact match in snippet view article find links to article

{\overline {a_{k+1},a_{k+2},\dots ,a_{k+m}}}],\,} then ζ is a quadratic irrational number, and its representation as a regular continued fraction is periodic

Irrational number (5,253 words) [view diff] exact match in snippet view article find links to article

number proved irrational. The golden ratio is another famous quadratic irrational number. The square roots of all natural numbers that are not perfect

J-invariant (5,813 words) [view diff] exact match in snippet view article find links to article

Theodor Schneider proved the aforementioned result that if τ is a quadratic irrational number in the upper half plane then j(τ) is an algebraic integer. In