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blue morpho sequence

An Artist Masterfully Illustrates The Golden Ratio, By Hand


A collection of virtuous drawings remind us of nature’s perfection expressed in this golden number.

Magical numbers have fascinated men since time immemorial. One of the most powerful, perhaps, is the golden ratio, which has inspired monumental works of art and astonished scientists for thousands of years. The mysterious figure has also provided inspiration for Venezuelan architect and artist, Rafael Araujo, who from a very young age devoted himself to observing the patterns of nature and their portentous geometry. He later reproduced them, by hand, with amazing results and always with a timeless beauty.

The golden ratio has a long history. One of earliest theorists of the mean was Euclid in the third century BCE. Ever since then, the proportions born of this irrational number have inspired science and art – from music (for its powerful sound) to architecture, painting, and cinema – showing the vital importance of mathematics to art.

Spirals, butterflies, and sea shells, born (paradoxically) to the exact algebraic calculations visible in the drawings of Araujo, might remind us of a Renaissance diagram. They’re made entirely by hand using only a pencil, compass, ruler and protractor, in an act of impressive virtuosity that impressively unites both science and art.

spiny shell

Clearly influenced by the work of M. C. Escher, for his geometric precision, Rafaela Araujo’s work seems to have been made by a machine. Each of his drawings takes about 100 hours to complete, and any mistake would be ruinous. Yet the seeming mathematical coldness of his creations doesn’t detract from their delicate sensibility. The work of the artist, whose architectural background is evident, ends up being a classic expression (in the term’s most rigorous sense) of the beauty and power existing in the universe of numbers.

The mystical importance of the golden ratio, evident in the Venezuelan artist’s work, endows his artistic work with a special power, and not only because it’s a mathematical representation of the universe’s perfection (through an act that unexpectedly even imitates the divine act of creation). But to look for geometries that, in their precision, seem magical; the bearers of sacred information and using but these two languages which have accompanied humankind through all of our attempts at deciphering the universe, mathematics, and art.

4 blue morpho sequence




phoebis triple helix


golden ratio spiral


fibonaccis four leaves clover


golden ratios 3 branches


log spiral


butterfly loop






*Images: Rafael Araujo ©

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