The** golden ratio** is based on a measure or number also called golden, and represented by the Greek letter φ (fi) (lowercase) o Φ (fi) (capitalize). It is a ratio of roughly: 2 + 1,6 . This means that une mesure **a=2** plus another mesure ** b=1,618**…. will be together a mesure of **c= 3,618**…. Although this is the way that I have invented to quickly understand this ratio and to detect, in a composition, that the golden ratio exists between the measures** a, b y c** in a image. And, therefore, they have the magical balance where a measurement contains the other plus a little.

**The golden ratio mesures:**

They say that the golden ratio is an irrational number, which does not fit the exact measurements. And indeed, because the measure ** b ** is like a small infinity, because it never ends, and it becames more smaller.

**Golden ratio conjugate:**

### Visual patterns with rectangular golden ratio:

### How do you draw the golden ratio?

**Easy step by step to draw this “divine proportion” that appears in many natural forms:**

- We draw a square with a measure
**a**. - From the lower base and center of this square, we create a circle that must have the radius just until the corners of the square we are.
- The new circle is bigger that the mesure of
**a**. It give us the point of the new mesure**b**, by continuing the bottom line of the square just to the point. We have the fragment**a + b.** - The vertical rectangle is drawn next to our square.The union of both is the
**first golden rectangle**. - Inside the rectangle, and from the upper right corner can create a square, whose mesures are the section
**b**. And from this second square**we start again all the steps**, because now we can find the golden section of the new square.

The spiral we build is called **golden or Fibonacci Spiral**.

Drawing system drawing of a rectangular golden ratio. SVG, scalable vector format.

### Visual patterns with triangular golden ratio:

Also called the** Aristotle triangle or logarithmic**, contains the two measures of **a** and** b**.

To create the triangle we use the two measures **a and b**. Inside, we can draw the Fibonacci spiral like in the square we did.

Golden ratio within a triangle. SVG, scalable vector format.

**Other geometric shapes:**

The decagon containing 10 golden triangles. SVG, scalable vector format.

As I’m not a mathematician and I get really bad, if someone wants to provide information about the golden ratio it´s ok, because I still have my share difficulties to see quickly their proportions.

This theme continues in **Golden spirals on flowers and plants**

More information on applications including: **http://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html**

And on the Wikipedia.