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The golden ratio's negative −φ and reciprocal φ−1 are the two roots of the quadratic polynomial x2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial.
In perceptual psychology, the phi phenomenon is the apparent motion caused by the successive viewing of stationary objects, such as the frames of a motion picture. In linguistics, φ-features denote features such as case, number and gender in which adjectives and pronouns agree with nouns. In lexical-functional grammar, the function that maps ...
It is claimed that the upper level of 21 rows and the lower level of 34 rows of the Ancient Theatre of Epidaurus form an approximation of the Golden number since 21 and 34 are successive Fibonacci numbers with their ratio at / and a careful examination of the theatre's center reveals two back-to-back triangles balanced by the Golden number.
Fibonacci sequence. For the chamber ensemble, see Fibonacci Sequence (ensemble). In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although ...
For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x 2 − 2 = 0. The golden ratio (denoted or ) is another irrational number that is not transcendental, as it is a root of the polynomial equation x 2 − x − 1 = 0.
Golden number (time) Month of January from Calendarium Parisiense (fourth quarter of the 14th c.). The golden numbers, in the leftmost column, indicate the date of the new moon for each year in the 19-year cycle. A golden number (sometimes capitalized) is a number assigned to each year in sequence which is used to indicate the dates of all the ...
Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number 1 + √ 5 / 2 ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes referred to as base-φ , golden mean base , phi-base , or, colloquially, phinary .
Golden number (time), a number assigned to a calendar year denoting its place in a Metonic cycle. Golden ratio, an irrational mathematical constant with special properties in arts and mathematics. Fibonacci number, a sequence of numbers which converges on the golden ratio. Category: Disambiguation pages.