Quoted By:
you got a special rectangle. you make a ratio of the two sides of the rectangle. it will equal the golden ratio only if the longer side divided by the shorter side equals the two sides added together divided by the longer side. a/b = (a+b)/a
You get the same figure if you divide the length of a diagonal of a regular pentagon by the length of a side. (a diagonal is a line segment joining two corners that aren't next to each other, a regular pentagon is a 5-sided shape whose sides and angles are all the same)
If you make Fibonacci sequence 1, 1, 2, 3, 5, 8, 13 and so on so that the next term is always the sum of the two earlier terms, then if you make a sequence of dividing pairs of these terms like this 1/1, 2/1, 3/2, 5/3, 8/5, 13/8, and so on, the ratios get closer and closer to the golden ratio as you continue.