# The Artist Who Fell in Love with the Golden Ratio

For 40 years, Venezuelan architect and illustrator Rafael Araujo has been perfecting his amazing drawings of nature with nothing more than pencil, compass, ruler and protractor. Every one of his drawing is painstakingly detailed; some take up to 100 hours to complete. All the drawings depict a unity of shapes explained by the Golden Ratio, a special number commonly annotated with the Greek symbol $\phi$ and whose value is 1.618.

The golden ratio appears in some patterns in nature, such as the spiral arrangement of sea shells (famously, the nautilus shell), crystals, butterfly wings, leaves, petals and other plant parts. As if by magic, $\phi$ is in turn connected to the famous Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … By dividing each of these numbers by the previous, we have a sequence of ratios that tend to the golden ratio. That is, we have 1/1 = 1, 2/1 = 2, 3/2 = 1.5, and so on up to 144/89 = 1.6179.

Araujo’s golden ratio illustrations are a beautiful fusion of art with science, a joyful celebration of the brilliance of a natural world that is governed by mysterious numbers. He has compiled his art into an adult coloring book (Golden Ratio Coloring Book, 2016) that aims to reconnect humans more closely with nature.

Selected Drawings of Rafael Araujo

The following picture gallery showcases Araujo’s “butterfly drawings”, where he creates complex fields of three dimensional space in which butterflies take flight and the logarithmic spirals of shells swirl into existence. He calls the series of work Calculation. Many of his drawings recalls the look and feel of the drawings found in Leonardo Da Vinci’s sketchbooks. In an age when 3D programs can render a digital version of something like this in just minutes, it makes you appreciate Araujo’s remarkable skill.