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)
“Harvey: Oh, you kids these days, I’m telling you. You think the only relationship a man and a woman can have is a romantic one.
Gil: That sure is what we think. You got something better?
Harvey: Oh, romance is very nice. A good thing for youngsters like you, but Helene and I have found something we think is more appropriate to our stage of life—companionship.
Gil: Companionship? I’ve got a flea-bitten old hound at home who’ll give me that.”
—Tom Waldman (d. 1985)
“Think of the earth as a living organism that is being attacked by billions of bacteria whose numbers double every forty years. Either the host dies, or the virus dies, or both die.”
—Gore Vidal (b. 1925)