Journal for Geometry and Graphics 26 (2022), No. 1, 115--124
Copyright Heldermann Verlag 2022
A Graphical Analysis of “The Geographer”
Tokyo University of the Arts, Tokyo, Japan
and: Joshibi University of Art and Design, Kanagawa, Japan
This research conducts a graphical analysis of The Geographer, a seventeenth-century painting by Dutch artist Johannes Vermeer. Produced in 1669, it creates a contrast between light and shadow by depicting a close-up view in dark tones with a long-distance view on a bright floor. This contrast creates a sense of depth in the painting’s virtual space. A rectangle like the seat of a backless chair at the bottom right of the screen creates a difference in height with respect to the floor in the back, and functions as a motif to give a sense of depth to the picture. This sense of depth would be lost without the bright flooring. Vermeer painted the flooring when The Milk Maid was created, which would indicate that the flooring configuration was done in the early stages of his career. However, The Geographer belongs to the latter period. Furthermore, checkered tiles were brilliantly placed on the floor of the interior paintings produced before and after 1669. Nevertheless, the flooring in this work does not constitute tiles. Therefore, this study analyzes whether the backless chair depicted in the foreground of this work was a part of the tiled floor that Vermeer intended to depict. As a result, the seat of this backless chair was equivalent to two square tiles. And if we assume that the construction method for those tiles that cover the floor of this painting was the first step, it suggests that a trigonometric ratio may have been used there. From this analysis, a hypothesis is formulated about Vermeer constructing floors of checkered tiles.
Keywords: Geometric aspects of technical art, seventheenth-century painting, perspective technique, golden ratio, drawing tiles.
MSC: 51N05; 00A66.
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