Relationship To Fibonacci Numbers
The Lucas numbers are related to the Fibonacci numbers by the identities
- , and thus as approaches +∞, the ratio approaches
Their closed formula is given as:
where is the Golden ratio. Alternatively, as for the magnitude of the term is less than 1/2, is the closest integer to or, equivalently, the integer part of, also written as .
Conversely, .
Read more about this topic: Lucas Number
Famous quotes containing the words relationship to, relationship and/or numbers:
“Artists have a double relationship towards nature: they are her master and her slave at the same time. They are her slave in so far as they must work with means of this world so as to be understood; her master in so far as they subject these means to their higher goals and make them subservient to them.”
—Johann Wolfgang Von Goethe (1749–1832)
“The proper aim of education is to promote significant learning. Significant learning entails development. Development means successively asking broader and deeper questions of the relationship between oneself and the world. This is as true for first graders as graduate students, for fledging artists as graying accountants.”
—Laurent A. Daloz (20th century)
“Out of the darkness where Philomela sat,
Her fairy numbers issued. What then ailed me?
My ears are called capacious but they failed me,
Her classics registered a little flat!
I rose, and venomously spat.”
—John Crowe Ransom (1888–1974)