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]

Sep 17, 2024 · 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.

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 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:

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.

The Golden rectangle has been known since antiquity as one having a pleasing shape, and is frequently found in art and architecture as a rectangular shape that seems 'right' to the eye. It is mentioned in Euclid's Elements and was known to artists and philosophers such as …

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.

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.

Nov 21, 2023 · The golden rectangle is a rectangle whose sides follow the golden ratio (1:{eq}\phi {/eq}). This means if one side is 1 unit long, then the other side is {eq}\phi {/eq}...

This all-in-one online Golden Rectangle Calculator is used to calculate the missing parameters of the golden rectangle given one known parameter. Enter the value of any parameter (width a , length a+b , difference of length and width b , or area a (a+b) ) in the fields of this calculator and find the other three parameters of the golden rectangle.