These can be stated as quadratic equations, the only positive solution of which is: Phi is an irrational number, a number which cannot be expressed as a ratio of two integer numbers. Phi is also the only number whose reciprocal is less than itself by one, expressed as 1/ Φ = Φ - 1 = 0.618. Phi is the only number whose square is greater than itself by one, expressed mathematically as Φ² = Φ + 1 = 2.618.
Part of the uniqueness of Phi is that it can be derived in many other ways than segmenting a line. Its appeal thus ranges from mathematicians to doctors to naturalists to artists to investors to mystics. It’s found in the proportions of many other animals, in plants, in the solar system and even in the price and timing movements of stock markets and foreign currency exchange. What makes this so much more than an interesting exercise in mathematics is that this proportion appears throughout creation and extensively in the human face and body. There is one unique point, however, at which the ratio of the large piece to the smaller piece is exactly the same as the ratio of the whole string to the larger piece, and at this point this Golden Ratio of both is 1.618 to 1, or Phi. There’s any number of places that you could cut it, and each place would result in different ratios for the length of the small piece to the large piece, and of the large piece to the entire string. To illustrate, suppose you were asked to take a string and cut it. Where Pi or p (3.14…) is the ratio of the circumference of a circle to its diameter, Phi or Φ (1.618 …) is the Golden Ratio that results when a line is divided in one very special and unique way. Both Pi and Phi are irrational numbers with an infinite number of digits after the decimal point, as indicated by “…”, the ellipsis.
Most everyone learned about the number Pi in school, but relatively few curriculums included Phi, perhaps for the very reason that grasping all its manifestations often takes one beyond the academic into the realm of the spiritual just by the simple fact that Phi unveils a unusually frequent constant of design that applies to so many aspects of life. The “mathematically challenged” may be more interested in the appearances of Phi in nature, its application to art, architecture and design, and its potential for insights into the spiritual realm, but let’s begin with the purest of facts about Phi, which are found in mathematics. This Golden Ratio truly is unique in its mathematical properties and pervasive in its appearance throughout nature. This site studies this golden number Phi, and its mathematical cousin, the Fibonacci sequence, both of which have roles in the plot of this murder mystery, and distinguishes between the myth and the math. The allure of “The Da Vinci Code” was that it creatively integrated fiction with both fact and myth from art, history,theology and mathematics, leaving the reader never really knowing what was truth and what was not.
Golden ratio numbers movie#
It was written about by Euclid in “Elements” around 300 B.C., by Luca Pacioli, a contemporary of Leonardo Da Vinci, in “De Divina Proportione” in 1509, by Johannes Kepler around 1600 and by Dan Brown in 2003 in his best selling novel, “The Da Vinci Code.” With the movie release of the “The Da Vinci Code”, the quest to know Phi was brought even more into the mainstream of pop culture.
What makes a single number so interesting that ancient Greeks, Renaissance artists, a 17th century astronomer and a 21st century novelist all would write about it? It’s a number that goes by many names. This “golden” number, 1.61803399, represented by the Greek letter Phi, is known as the Golden Ratio, Golden Number, Golden Proportion, Golden Mean, Golden Section, Divine Proportion and Divine Section.
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