Phi for "Neo-Phi-tes:" Phi ( Φ = 1.618033988749895... ), most often pronounced fi like "fly," is simply an irrational number like pi ( p = 3.14159265358979... ), but one with many unusual mathematical properties. Unlike pi, which is a transcendental number, phi is the solution to a quadratic equation. Phi is the basis for the Golden Ratio, Section or Mean The ratio, or … [Read more...]
These articles provide a basic overview of number 1.618 known as Phi (and also as the Golden Ratio, Golden Mean, Golden Section and Divine Proportion) and its mathematical cousin, the Fibonacci sequence. Learn about what it is, its appearance in nature, the history of the mankind's application of the golden ratio and other interesting topics.
What is the Fibonacci Sequence (aka Fibonacci Series)?
Leonardo Fibonacci discovered the sequence which converges on phi. In the 1202 AD, Leonardo Fibonacci wrote in his book "Liber Abaci" of a simple numerical sequence that is the foundation for an incredible mathematical relationship behind phi. This sequence was known as early as the 6th century AD by Indian mathematicians, but it was Fibonacci who introduced it to the west … [Read more...]
The Golden Section / Golden Ratio
GoldenNumber.Net explores the appearance of Phi, 1.618 (also known as the Golden Ratio, Golden Mean, Golden Section or Divine Proportion, in mathematics, geometry, life and the universe and shows you how to apply it, and its applications are limitless: Art Architecture Design of any kind – Graphics, logos, products, fashion, web sites and more Photo composition, photo … [Read more...]
Quotes related to Phi
"Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel. --Johannes Kepler "The most beautiful thing we can experience is the mysterious. It is the source of all true art and science." --Einstein, Albert … [Read more...]
Phi to 20,000 Places and a Million Places
Just can't get enough of Phi? Here's a couple of ways to get as much as most anyone would ever need. There are millions of places to find phi, but here's some help in finding phi to a million places. You can download the PhiCalculator, a program provided free of charge by Alireza Shafaei. It will compute phi to the number of decimal places you specify, to 1 million and … [Read more...]
Phi Phonetics
A little riddle: When does Φ + V = 5? Φ, the Greek symbol for phi, represents the number 1.61803398874989..., which is intrinsically related through math and geometry to the number 5. V is the Roman symbol which represents the number 5. So when does Φ + V = 5? All you mathematicians are probably rushing to your calculators, knowing that the answer must be when V = 5 - Φ, … [Read more...]
Pronouncing Phi
Phee, Phi, Pho, Phum™ ... or how do you say Φ? The generally accepted pronunciation of phi is fi, like fly. Most people know phi as "fi," to rhyme with fly, as its pronounced in "Phi Beta Kappa." In Dan Brown's best selling book "The Da Vinci Code," however, phi is said to be pronounced fe, like fee. The following is offered in response to the questions received on phi's … [Read more...]
The Phi Symbol
Φ vs. Ø: Will the real Phi please stand up! In the texts of ancient Greece, the letter phi looked like this: Φ When you see the Greek letter Phi on a fraternity or sorority house, it usually looks like this: Φ When you see Phi on a web site, it often looks like this: Ø What's the slant on this? Is Phi no longer the upright character it once was? Has Phi become an … [Read more...]
History of the Golden Ratio
While the proportion known as the Golden Mean has always existed in mathematics and in the physical universe, it is unknown exactly when it was first discovered and applied by mankind. It is reasonable to assume that it has perhaps been discovered and rediscovered throughout history, which explains why it goes under several names. Uses in architecture potentially date to the … [Read more...]
