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.
Read more about this topic: Golden Ratio Base
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)
“The division between the useful arts and the fine arts must not be understood in too absolute a manner. In the humblest work of the craftsmen, if art is there, there is a concern for beauty, through a kind of indirect repercussion that the requirements of the creativity of the spirit exercise upon the production of an object to serve human needs.”
—Jacques Maritain (1882–1973)
“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)