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:
“Sometimes in our relationship to another human being the proper balance of friendship is restored when we put a few grains of impropriety onto our own side of the scale.”
—Friedrich Nietzsche (1844–1900)
“The relationship between mother and professional has not been a partnership in which both work together on behalf of the child, in which the expert helps the mother achieve her own goals for her child. Instead, professionals often behave as if they alone are advocates for the child; as if they are the guardians of the child’s needs; as if the mother left to her own devices will surely damage the child and only the professional can rescue him.”
—Elaine Heffner (20th century)
“I had but three chairs in my house; one for solitude, two for friendship; three for society. When visitors came in larger and unexpected numbers there was but the third chair for them all, but they generally economized the room by standing up.”
—Henry David Thoreau (1817–1862)