The golden ratio (symbol is the Greek letter phi shown at left) is a special number approximately equal to 1.618 ... It appears many times in geometry, art, architecture and other

There is a special relationship between the Golden Ratio and Fibonacci Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc, each number is the sum of the two numbers before it).

We get the Golden Ratio when a line is split into two parts so the ratio of the whole to the larger part is the same as the ratio of the larger to the smaller part.

It takes longer to get good values, but it shows that not just the Fibonacci Sequence can do this! Using The Golden Ratio to Calculate Fibonacci Numbers And even more surprising is that we can calculate any Fibonacci Number using the Golden Ratio: x n = φn − (1−φ)n √5

Ratios The regular pentagram has a special number hidden inside called the Golden Ratio, which equals approximately 1.618 a/b = 1.618... b/c = 1.618... c/d = 1.618... When I drew this, I measured the 4 lengths and I got a=216, b=133, c=82, d=51. So let's check to see what the ratios are: 216/133 = 1.624... 133/82 = 1.622... 82/51 = 1.608...

Illustrated definition of Golden Mean: Another name for Golden Ratio: the number approximately equal to 1.618033989...

Can you make a ratio of 5:2? How about 1:4? Using Ratios The key to working with ratios is to always multiply or divide both numbers by the same value. This keeps the relationship …

A ratio shows the relative sizes of two or more values. Ratios can be shown in different ways: • using the ":" to separate example values • using the "/" to separate one value from the total • as a decimal, after dividing one value by the total • as a percentage, after dividing one …

Golden Ratio It appears many times in geometry art architecture and other areas. We find the golden ratio when we divide a line into two parts so that: Have a try yourself (use the slider): /numbers/golden-ratio.html

The Golden Ratio is an irrational number. The first few digits look like this: 1.61803398874989484820... (and more ...)