Fundamental Recurrence Formulas - A Simple Example

A Simple Example

Consider the regular continued fraction in canonical form that represents the golden ratio φ:

Applying the fundamental recurrence formulas we find that the successive numerators An are {1, 2, 3, 5, 8, 13, ...} and the successive denominators Bn are {1, 1, 2, 3, 5, 8, ...}, the Fibonacci numbers. Since all the partial numerators in this example are equal to one, the determinant formula assures us that the absolute value of the difference between successive convergents approaches zero quite rapidly.

Read more about this topic:  Fundamental Recurrence Formulas

Famous quotes containing the word simple:

    “The thought of our past years in me doth breed
    Perpetual benediction: not indeed
    For that which is most worthy to be blest—
    Delight and liberty, the simple creed
    Of Childhood, whether busy or at rest,
    With new-fledged hope still fluttering in his breast:—”
    —William Wordsworth (1770–1850)