mathematics

Rabatment of the rectangle

Rabatment of the rectangle is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Rabatment of the rectangle rather than just read about it. In short: 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. 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.

Key takeaways

Rabatment of the rectangle belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Rabatment of the rectangle to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Rabatment of the rectangle from memory before moving on to harder problems.

Reference excerpt

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. 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".

Theory There is no absolute explanation of the mechanism of this method, but there are various theories. 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.

Practice

Renaissance artists used rabatment as a foundation to art and architectural works, but the rabatment can be observed in art taken from almost any period. 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. 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. The concept of rabatment can be applied to rectangles of any proportion. 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. 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. 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. 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.

Examples

References

External links "The painting's secret geometry" by François Murez "Rabatment as a Compositional Tool" by Judith Reeve

Illustrations

Worked examples

Example 1 — a first encounter with Rabatment of the rectangle

Start with the simplest possible case. Write down what Rabatment of the rectangle claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Rabatment of the rectangle before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Rabatment of the rectangle ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Rabatment of the rectangle

In research: Rabatment of the rectangle appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Rabatment of the rectangle in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Rabatment of the rectangle is common in secondary-school and first-year university syllabi. It links to neighbouring topics Composition in visual art, Geometry, so understanding it makes those chapters shorter.
In everyday life: Look for Rabatment of the rectangle outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Rabatment of the rectangle in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Rabatment of the rectangle means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Rabatment of the rectangle out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Rabatment of the rectangle in simple terms?

Why does Rabatment of the rectangle matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Rabatment of the rectangle?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Rabatment of the rectangle.