The Fibonacci sequence has a pattern that repeats every 24 numbers. Numeric reduction is a technique used in analysis of numbers in which all the digits of a number are added together until only one digit remains. As an example, the numeric reduction of 256 is 4 because 2+5+6=13 and 1+3=4. Applying numeric reduction to the Fibonacci series produces an infinite series of 24 … [Read more...]
89, 109 and the Fibonacci Sequence
The reciprocal of 89, a Fibonacci number, is based on the Fibonacci series. This is a little curiousity involving the number 89, one of the Fibonacci series numbers. 1/89 is a repeating decimal fraction with 44 characters: .01123595505617977528089887640449438202247191 You can see the beginning of the Fibonacci sequence in the first 6 digits of the decimal equivalent of … [Read more...]
Number Five (5) and Phi
The number 5 is intrinsically related to Phi and the Fibonacci series. Phi can be derived from several formulas based on the number 5. The most traditional, based on the geometric construction of phi is this: This formula for phi can also be expressed all in fives as: Φ = 5 ^ .5 * .5 + .5 Another formula for phi based entirely on 5's, an original insight … [Read more...]
Geometric and Golden Means
What do we mean by "mean?" Math isn't tough, but it can be mean. The term "mean" in mathematics simply reflects a specific relationship of one number as the middle point of two extremes. Arithmetic means The arithmetic mean of 2 and 6 is 4, as 4 is equally distant between the two in addition: 2 + 2 = 4 and 4 + 2 = 6 For the arithmetic mean (b) of two numbers (a) and … [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...]
