Rabatment of the rectangle

Last updated
The dotted line represents one of two possible rabatments of the rectangle Rabatment rectangle.png
The dotted line represents one of two possible rabatments of the rectangle

Rabatment of the rectangle is a compositional technique used as an aid for the placement of objects or the division of space within a rectangular frame, or as an aid for the study of art.

Contents

Every rectangle contains two implied squares, each consisting of a short side of the rectangle, an equal length along each longer side, and an imaginary fourth line parallel to the short side. The process of mentally rotating the short sides onto the long ones is called "rabatment", and often the imaginary fourth line is called "the rabatment".

Also known as rebatement and rabattement, rabatment means the rotation of a plane into another plane about their line of intersection, as in closing an open hinge. [1] In two dimensions, it means to rotate a line about a point until the line coincides with another sharing the same point. The term is used in geometry, art and architecture. [2]

Theory

There is no absolute explanation of the mechanism of this method, but there are various theories. [3] One argument is that squares are such a simple, primal geometric shape that the brain automatically looks for them, mentally completing this rabatment whether it is made explicit or not. When a composition uses elements of the scene to match, the square feels complete in itself, producing a feeling of harmony. [3]

Practice

Animation of a rabatment line within a rectangle Rabatment animation.gif
Animation of a rabatment line within a rectangle

Renaissance artists used rabatment as a foundation to art and architectural works, [4] [5] but the rabatment can be observed in art taken from almost any period. [6]

As one of many composition techniques, rabatment of the rectangle can be used to inform the positioning of elements within the rectangle. There is no hard and fast rule regarding such positioning; a composition can have a sense of dynamic unrest or a sense of equilibrium relative to important lines such as ones taken from rabatment or from the rule of thirds, or from nodal points such as the "eyes of a rectangle"—the four intersections derived from the rule of thirds. [7] Primary image elements can be positioned within one of the two rabatment squares to define the center of interest, and secondary image elements can be placed outside of a rabatment square. [8]

The concept of rabatment can be applied to rectangles of any proportion. [9] For rectangles with a 3:2 ratio (as in 35mm film in still photography), it happens that the rabatment lines are exactly matched to the rule of thirds lines. [10]

In a horizontally-aligned rectangle, there is one implied square for the left side and one for the right; for a vertically-aligned rectangle, there are upper and lower squares. [3] If the long sides of the rectangle are exactly twice the length of the short, this line is right in the middle. With longer-proportioned rectangles, the squares don't overlap, but with shorter-proportioned ones, they do. In Western cultures that read left to right, attention is often focused inside the left-hand rabatment, or on the line it forms at the right-hand side of the image. [11]

When rabatment is used with one side of a golden rectangle, and then iteratively applied to the left-over rectangle, the resulting "whirling rectangles" describe the golden spiral. [12]

Examples

Gimpressionist 22 fishing0070a 3 nevit rabatment study.jpg
This computer art image has the fisherman positioned facing into the left-hand rabatment square.
Monet - Mohnblumenfeld rabatment study.jpg
Claude Monet's painting of a poppyfield includes one tall tree at the rightmost border of the left-hand rabatment square.
Rembrandt The Artist in his studio rabatment study.jpg
Rembrandt's self-portrait places the lit part of his studio within the left-hand rabatment square. The artist himself stands at the border of the other square facing inward.
Gustave Caillebotte Boater Pulling on His Perissoire rabatment study.jpg
Gustave Caillebotte's painting shows the boat outside the right-hand rabatment square and the man at the rightmost border of the left-hand square, leaning and reaching across the empty central expanse. Both the upper and the lower river banks intersect the rabatment lines at the painting's border.

Related Research Articles

Euclidean geometry Mathematical model of the physical space

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.

Golden ratio Ratio between two quantities whose sum is at the same ratio to the larger one

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with

Rectangle Quadrilateral with four right angles

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal ; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as  ABCD.

Right angle 90° angle (π/2 radians): an angle that bisects the angle formed by two halves of a straight line

In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin angulus rectus; here rectus means "upright", referring to the vertical perpendicular to a horizontal base line.

Parallelogram Quadrilateral with two pairs of parallel sides

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.

Shape Form of an object or its external boundary

A shape or figure is the graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type. A plane shape or plane figure is constrained to lie on a plane, in contrast to solid 3D shapes. A two-dimensional shape or two-dimensional figure may lie on a more general curved surface.

Golden rectangle

In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, , which is , where is approximately 1.618.

Apollonius of Perga Ancient Greek geometer and astronomer noted for his writings on conic sections

Apollonius of Perga was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. Gottfried Wilhelm Leibniz stated “He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.”

Perspective (graphical) Form of graphical projection where the projection lines converge to one or more points

Linear or point-projection perspective is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. The most characteristic features of linear perspective are that objects appear smaller as their distance from the observer increases, and that they are subject to foreshortening, meaning that an object's dimensions along the line of sight appear shorter than its dimensions across the line of sight. All objects will recede to points in the distance, usually along the horizon line, but also above and below the horizon line depending on the view used.

Descriptive geometry

Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. The theoretical basis for descriptive geometry is provided by planar geometric projections. The earliest known publication on the technique was "Underweysung der Messung mit dem Zirckel und Richtscheyt", published in Linien, Nuremberg: 1525, by Albrecht Dürer. Italian architect Guarino Guarini was also a pioneer of projective and descriptive geometry, as is clear from his Placita Philosophica (1665), Euclides Adauctus (1671) and Architettura Civile, anticipating the work of Gaspard Monge (1746–1818), who is usually credited with the invention of descriptive geometry. Gaspard Monge is usually considered the "father of descriptive geometry" due to his developments in geometric problem solving. His first discoveries were in 1765 while he was working as a draftsman for military fortifications, although his findings were published later on.

Semicircle Geometric shape

In mathematics, a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180°. It has only one line of symmetry. In non-technical usage, the term "semicircle" is sometimes used to refer to a half-disk, which is a two-dimensional geometric shape that also includes the diameter segment from one end of the arc to the other as well as all the interior points.

Cylinder Three-dimensional solid

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. Geometrically, it can be considered as a prism with a circle as its base.

Rule of thirds Composition technique

The rule of thirds is a "rule of thumb" for composing visual images such as designs, films, paintings, and photographs. The guideline proposes that an image should be imagined as divided into nine equal parts by two equally spaced horizontal lines and two equally spaced vertical lines, and that important compositional elements should be placed along these lines or their intersections. Proponents of the technique claim that aligning a subject with these points creates more tension, energy and interest in the composition than simply centering the subject.

Composition (visual arts) Placement or arrangement of visual elements or ingredients in a work of art

The term composition means "putting together". It can be thought of as the organization of the elements of art according to the principles of art. Composition can apply to any work of art, from music through writing and into photography, that is arranged using conscious thought.

Jay Hambidge Canadian-American painter

Jay Hambidge (1867–1924) was a Canadian-born American artist who formulated the theory of "dynamic symmetry", a system defining compositional rules, which was adopted by several notable American and Canadian artists in the early 20th century.

British flag theorem On distances from opposite corners to a point inside a rectangle

In Euclidean geometry, the British flag theorem says that if a point P is chosen inside rectangle ABCD then the sum of the squares of the Euclidean distances from P to two opposite corners of the rectangle equals the sum to the other two opposite corners. As an equation:

A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry which, in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books. These dynamic rectangles begin with a square, which is extended to form the desired figure, which can be the golden rectangle, the 2:3 rectangle, the double square (1:2), or a root rectangle.

Mathematics and art Relationship between mathematics and art

Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.

Pythagorean theorem Relation between sides of a right triangle

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:

References

  1. ↑ Oxford English Dictionary (2 ed.). Oxford University Press. 2003.
  2. ↑ Paynter, J.E. (1921). Practical geometry for builders and architects. London: Chapman & Hall.
  3. 1 2 3 Mize, Dianne (27 January 2009). "How to Use Rabatment in Your Compositions". Empty Easel. Retrieved 26 February 2011.
  4. ↑ Sriraman, Bharath; Freiman, Viktor; Lirette-Pitre, Nicole (2009). Interdisciplinarity, creativity, and learning: mathematics with literature, paradoxes, history, technology, and modeling. IAP. p. 122. ISBN   978-1-60752-101-3.
  5. ↑ Fett, Birch (2006). "An In-depth Investigation of the Divine Ratio" (PDF). The Montana Mathematics Enthusiast. The Montana Council of Teachers of Mathematics. 3 (2): 157–175. ISSN   1551-3440.
  6. ↑ Bouleau, Charles (1963). The painter's secret geometry: a study of composition in art. New York: Harcourt, Brace. pp. 43–46.
  7. ↑ Feltus, Alan. "Painting and Composition". Umbria, Italy: International School of Painting, Drawing, and Sculpture. Retrieved 26 February 2011.
  8. ↑ Mize, Dianne (16 July 2008). "Placing Our Images: Rabatment". Compose. Retrieved 27 February 2011.
  9. ↑ Dunstan, Bernard (1979). Composing your paintings. Start To Paint. Taplinger Publishing. pp. 22, 26. ISBN   0-8008-1803-2.
  10. ↑ Brown, Scott (2009). "Glossary". Watercolorists of Whatcom. Retrieved 27 February 2011.
  11. ↑ Nelson, Connie (2010). "Composition in art: Rabatment". Explore-Drawing-and-Painting.com. Retrieved 1 March 2011.
  12. ↑ Fairbanks, Avard T.; Fairbanks, Eugene F. (2005). Human Proportions for Artists. Fairbanks Art and Books. p.  210. ISBN   0-9725841-1-0.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.