Golden Ratio Base - Division

Division

No non-integer rational number can be represented as a finite base-φ number. In other words, all finitely representable base-φ numbers are either integers or (more likely) an irrational in the field Q. Due to long division having only a finite number of possible remainders, a division of two integers (or other numbers with finite base-φ representation) will have a recurring expansion, as demonstrated above.

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Famous quotes containing the word division:

    O, if you raise this house against this house
    It will the woefullest division prove
    That ever fell upon this cursed earth.
    William Shakespeare (1564–1616)

    Don’t order any black things. Rejoice in his memory; and be radiant: leave grief to the children. Wear violet and purple.... Be patient with the poor people who will snivel: they don’t know; and they think they will live for ever, which makes death a division instead of a bond.
    George Bernard Shaw (1856–1950)

    That crazed girl improvising her music,
    Her poetry, dancing upon the shore,
    Her soul in division from itself
    Climbing, falling she knew not where,
    Hiding amid the cargo of a steamship
    Her knee-cap broken.
    William Butler Yeats (1865–1939)