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In geometry, a golden rectangle is a rectangle with side lengths in golden ratio or with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity: if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well. Construction of a golden rectangle. [a]
The golden rectangle is a rectangle whose sides are in the golden ratio, that is (a + b)/a = a/b = φ, where a is the width, a + b is the length of the rectangle, and φ is the golden ratio: φ = (1+√5)/2.
A golden rectangle is a rectangle with side lengths that are in the golden ratio (about 1:1.618). This article also explains how to construct a square, which is needed to construct a golden rectangle.
Use this simple calculator to find the area and side length of a golden rectangle. Calculate the area of a golden rectangle with our step-by-step guide.
A golden rectangle is a rectangle whose length to width ratio equal to the golden ratio, φ, which has a value of or approximately 1.618, assuming the length is the larger value. The following diagram shows what it looks like visually:
Given a rectangle having sides in the ratio 1:phi, the golden ratio phi is defined such that partitioning the original rectangle into a square and new rectangle results in a new rectangle having sides with a ratio 1:phi. Such a rectangle is called a golden rectangle. Euclid used the following construction to construct them.
A golden rectangle with long side a + b and short side a can be divided into two pieces: a similar golden rectangle (shaded red, right) with long side a and short side b and a square (shaded blue, left) with sides of length a. This illustrates the relationship a + b = a = φ.
The golden rectangle R, constructed by the Greeks, has the property that when a square is removed a smaller rectangle of the same shape remains. Thus a smaller square can be removed, and so on, with a spiral pattern resulting.
Golden Rectangle. Definition: A golden rectangle is a rectangle that can be cut up into a square and a rectangle similar to the original one. More precisely, Let ABCD be a rectangle, with width AB < length BC.
A golden rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1.618:1. It is often considered aesthetically pleasing and appears frequently in art and architecture.