GoGeometry Portrait of Joseph Roulin by Vincent van Gogh and Golden Rectangles

Successive Golden Rectangles dividing a Golden Rectangle into squares (Portrait of Joseph Roulin by Vincent van Gogh, Museum of Modern Art).

Portrait of Joseph Roulin by Vincent van Gogh and Golden Rectangles

Portrait of Joseph Roulin by Vincent van Gogh, 1889
The Museum of Modern Art, New York acquired from Thomas Ammann Fine Art through exchange and sale of seven works of art. It was sold in 1989 for a price estimated at $58 million plus exchange of works (adjusted price $108 millions).

The 1889 painting is believed to be van Gogh`s last and most modern of at least four portraits of Roulin, the postmaster of Arles, who is shown as a man with a commanding face, intense green-blue eyes, and flowing mustache and beard.

Vincent van Gogh
Vincent van Gogh (Dutch: (1853 – 1890) was a Dutch post-Impressionist painter whose work, notable for its rough beauty, emotional honesty and bold color, had a far-reaching influence on 20th-century art.

Golden rectangle
A golden rectangle is a rectangle whose side lengths are in the golden ratio, one-to-phi, that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden or Fibonacci spiral.

Droste Effect
The Droste effect is a specific kind of recursive picture, one that in heraldry is termed mise en abyme. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. This smaller version then depicts an even smaller version of itself in the same place, and so on. Only in theory could this go on forever; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration geometrically reduces the picture's size. It is a visual example of a strange loop, a self-referential system of instancing which is the cornerstone of fractal geometry. Source: Wikipedia, Droste Effect.
 

Portrait of Joseph Roulin by Vincent van Gogh and Golden Rectangles

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