How the golden ratio and the Fibonacci sequence are connected

Recall that the golden ratio is a special irrational number that is approximately equal to 1.618.  It appears frequently in geometry, art, and architecture. Also recall that the Fibonacci sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 … Each number is found by adding up the two numbers before it.  For example 5 is found by adding 3 and 2. German Astronomer Johannes Kepler once wrote that “as 5 is to 8, so 8 is to 13, approximately, and as 8 is to 13, so 13 is to 21, approximately”.  What Kepler…

Phi, the number that helps us make beautiful art

The Golden Ratio (phi) There are several well known “irrational numbers”, which are numbers that cannot be expressed as a ratio between two numbers and it cannot be written as a simple fraction because there is not a finite number of numbers when written as a decimal.  When irrational numbers are written as decimals the decimal would go on forever without repeating.  An irrational number you are probably very familiar with is pi or Π which is equal to 3.14159265359 …. it is the irrational number that helps us understand everything that is circular.   Another irrational number you may have…