Quadratic surd : An algebraic number that is the root of a quadratic equation.
2.
These are a subset of the algebraic numbers, and include the quadratic surds.
3.
Galois proved that the regular continued fraction which represents a quadratic surd ? is purely periodic if and only if ? is a reduced surd.
4.
More recently, sharper arguments based on the divisor function have shown that " L " ( " D " ), the length of the repeating block for a quadratic surd of discriminant " D ", is given by
5.
He also proved that if ? is a reduced quadratic surd and ? is its conjugate, then the continued fractions for ? and for ( & minus; 1 / ? ) are both purely periodic, and the repeating block in one of those continued fractions is the mirror image of the repeating block in the other.
मोबाइल