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:
“The glory of the farmer is that, in the division of labors, it is his part to create. All trade rests at last on his primitive activity.”
—Ralph Waldo Emerson (1803–1882)
“For a small child there is no division between playing and learning; between the things he or she does “just for fun” and things that are “educational.” The child learns while living and any part of living that is enjoyable is also play.”
—Penelope Leach (20th century)
“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)